Hindawi Publishing CorporationThe Scientific World JournalVolume 2013 Article ID 794549 9 pageshttpdxdoiorg1011552013794549

Research ArticleOn the Relationship between MulticastBroadcast Throughputand Resource Utilizations in Wireless Mesh Networks

Avid Avokh1 Ghasem Mirjalily1 Jamshid Abouei1 and Shahrokh Valaee2

1 Faculty of Electrical and Computer Engineering Yazd University Yazd 8915818411 Iran2Department of Electrical and Computer Engineering University of Toronto Toronto ON Canada M5S 3G4

Correspondence should be addressed to Avid Avokh aavokhstuyazdacir

Received 29 August 2013 Accepted 23 September 2013

Academic Editors C-L Chang K Dejhan J Garcia-Reinoso and C Pan

Copyright copy 2013 Avid Avokh et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper deals with the problem of multicastbroadcast throughput in multi-channel multi-radio wireless mesh networks thatsuffer from the resource constraints We provide a formulation to capture the utilization of the network resources and deriveanalytical relationships for the networkrsquos throughput in terms of the node utilization the channel utilization and the numberof transmissions Our model relies on the on-demand quality of service multicastbroadcast sessions where each admitted sessioncreates a unique tree with a specific bandwidth As an advantage the derived relationships are independent of the type of tree builtfor each session and can be used for different protocols The proposed formulation considers the channel assignment strategy andreflects both the wireless broadcast advantage and the interference constraint We also offer a comprehensive discussion to evaluatethe effects of load-balancing and number of transmissions on the networkrsquos throughput Numerical results confirm the accuracy ofthe presented analysis

1 Introduction

Wireless mesh networks (WMNs) have been recognized asa new class of multihop networks that provide low-costsolutions for broadband wireless applications [1] A WMN iscomposed of three types of nodes gateways mesh routersand mesh clients [1 2] Gateways enable the integration ofvarious networks for example Wi-Fi Zigbee WiMAX andcellular networks Mesh routers have minimal mobility andform the backbone of the networkThey have the functional-ity of both an access point and a relay node As a relay nodemesh routers forward the packets from the source node to thedestination nodes However as an access point they providenetwork access for mesh clients within their coverage areaOne challenge in WMNs is the degradation of the networkrsquoscapacity due to the co-channel interference This problemhas motivated the researchers to improve the networkrsquosthroughput using efficient schemes An effective approachto mitigate the co-channel interference is to equip themesh routers with multiple radios tuned to non-overlapping

channels The ability to utilize multiple radios allows themesh routers to sendreceive packets simultaneously ondistinct channels and therefore increases the bandwidthavailable to the network [2] However due to the limitednumber of radios and non-overlapping channels some linksinterfere with each other and cannot be active at the sametime These resource constraints degrade the performance ofMulti-Channel Multi-Radio WMNs (MCMR-WMNs) Thusa proper resource assignment strategy is required to improvethe performance of such networks

On the other hand recently the popularity of multime-dia services such as IP-TV video conference and distanteducation has significantly increased [3ndash5] In this regardthe multicast routing provides underlying facilities for themultimedia applications in WMNs The basic differencebetween multicast routing in wireless and wired networks isthe broadcast nature of the wireless medium that results ina well-known property named wireless broadcast advantage(WBA) [6 7] Based on the WBA a single transmission in anode simultaneously covers multiple neighboring receivers

2 The Scientific World Journal

Minimizing the number of transmissions improves the uti-lization of the network resources and subsequently increasesthe networkrsquos throughput Besides the number of transmis-sions the load-balancing problem is another pertinent issueto be considered in MCMR-WMNs This problem can bediscussed from two perspectives spatial load-balancing andchannel load-balancing From the viewpoint of a specificchannel when a part of the network experiences congestionthe new traffic flows should not be routed through that partIn addition from the perspective of a specific location thetraffic load must be balanced over all available channels inthe network If the traffic load in the network is balancedthe interference will be decreased and more resources willbe available for accepting the future traffics

To evaluate the performance of a MCMR-WMN thereare several criteria that often interact with each other Thusit is not possible to draw a clear boundary between themIn this regard different approaches try to improve differentaspects of the networks One difficulty in comparing differentschemes is the lack of a standard benchmark Certainlyhaving a prior knowledge about the bounds of criteria andtheir corresponding relationship provides more options forthe system administrator to control the parameters of thenetwork

Taking the above challenges into account the main goalof this paper is to quantify the throughput inMCMR-WMNsWe focus on the scenario of multicast and broadcast sessionswhere each session has a specific bandwidth requirementOn-demand requests arrive dynamically one by one withoutany prior knowledge of future arrivals A session will beaccepted if a routing tree with sufficient bandwidth oneach link can be established In particular we provide aformulation to express the networkrsquos throughput in terms ofthe node utilization the channel utilization and the numberof transmissions We also discuss how appropriate use of theresources affects the networkrsquos throughput

The rest of the paper is organized as follows Section 2surveys the previous related works The details of the net-work model are described in Section 3 Section 4 presents aformulation to capture the resource utilizations In Section 5we derive analytical expressions for the multicastbroadcastthroughput in both small-scale MCMR-WMN and large-scale MCMR-WMN Section 6 presents the numerical resultsand the discussion Finally some concluding remarks areprovided in Section 7

2 Related Work

In past years different aspects of MCMR-WMNs have beenwidely studied for unicast flows In particular some worksendeavor to heuristically improve the networkrsquos performance[2 8] while others focus on the optimization solutions [9ndash11] In this regard several routing metrics (such as ETXETT WCETT WCCETT MIC iAWARE and MIND [1 12])have been proposed However due to the differences betweenunicast and multicast routing the designed unicast schemescannot be efficient for themulticast traffics In one of themostfundamental researches on the multicast routing the work

in [4] compares the performance of the Minimum SteinerTrees (MSTs) and the Shortest Path Trees (SPTs) in Single-Channel Single-RadioWMNs (SCSR-WMNs) Experimentalresults in [4] show that SPTs offer a better performance thanMSTs In addition the implementation difficulty of MSTs isanother factor that makes SPTs more favorable in WMNsHowever none of these protocols consider the problems ofload-balancing and resource utilization

Roy et al [13] study the high-throughput metrics formulticast routing in WMNs They point out the differencebetween unicast and multicast routing and show how toadapt the unicast routing metrics for use in multicast flowsThey also propose a low-overhead adaptive algorithm toincorporate the link-quality-basedmetrics to a representativemulticast routing protocol

As mentioned before the ability to make an appropriateuse of the network resources can efficiently increase thethroughput in WMNs In line with this concept some worksaim to minimize the number of transmissions required todeliver one packet from the source to all the destinations [14ndash16] The authors in [15] propose a multicast routing metricnamed Multi-Channel Minimum Number of Transmissions(MCMNT) that considers the wireless broadcast advantageand the channel diversity to minimize the network band-width consumed by the routing tree MCMNT also tries tominimize the intra-flow interference in the network Zenget al [16] propose two algorithms named Level ChannelAssignment (LCA) and Multi-Channel Multicast (MCM)to minimize the number of forwarding nodes and the totalhop-count distances in MCMR-WMNs These algorithmsreduce the intra-flow interference using the heuristic channelassignment strategies The authors in [16] show that the LCAand the MCM algorithms outperform the single-channelmulticast in terms of the throughput and the delay They alsodemonstrate that using all the partially overlapping channelsinstead of only the non-overlapping channels can furtherdiminish the interference in the network

In [17] Chiu et al challenge the load-balancing issuein MCMR-WMNs The basic idea in [17] is that if thetraffic on the most-heavily loaded channel is minimized thetraffic load in the network will be balanced In this waythey first present an integer linear programming formulationto optimally construct the bandwidth-guaranteed broadcasttreesThen an efficient algorithm is proposed to heuristicallyimprove the call acceptance rate in the network Reference[18] proposes two load-aware metrics named ldquoFlow LoadMulticast Metric (FLMM)rdquo and ldquoReliable Flow Load Mul-ticast Metric (FLMM119877)rdquo for multicast routing in MCMR-WMNsAlthough bothmetrics count the interference and theWBA the latter case further considers the unreliability of theIEEE 80211 MAC protocol FLMM119877 uses the Packet DeliveryRatio (PDR) of the wireless links and reduces retransmis-sion overheads In line with this concept the work in [19]suggests two distributed strategies named ldquoMulticast Auto-Rate Selection (MARS)rdquo and ldquoMARS-Retransmit (MARS-R)rdquo The MARS scheme uses PDR of the wireless links atvarious transmission ratesTheMARS-R algorithm facilitatesthe joint use of rate control and link-layer mechanisms (such

The Scientific World Journal 3

as acknowledgments and retransmissions) to improve thereliability of high-throughput multicast flows

During recent years we have considered the problem oftraffic engineering for multicastbroadcast flows in WMNs[3 7 20] The work in [3] studies the special case ofbroadcasting for the small-scale WMNs In [7] we presentan Interference-Aware Joint Channel and Rate Selection (IA-JCRS) algorithm to choose the best transmission rates andthe best transmission channels for a given fixed routingtree However being bound to a routing tree reduces thefreedom to choose the alternative feasible paths Indeedusing a joint interference-aware routing scheme leads toa better utilization of the network resources Accordinglyin [20] we propose two cross-layer algorithms named theldquoInterference- and Rate-aware Multicast Tree (IRMT)rdquo andthe ldquoInterference- and Rate-aware Broadcast Tree (IRBT)rdquoAs an advantage the proposed algorithms jointly address theproblems of multicastbroadcast routing tree constructiontransmission rate selection transmission channel selectionand call admission control

One drawback of the previous works is that they pay lessattention to the theoretical analysis of multicastbroadcastflows Most of the literature tries to propose some heuristi-cally or optimally solutions to improve different aspects of thenetwork Unlike the previous works this paper quantifies themulticast and the broadcast throughput in both small-scaleMCMR-WMN and large-scale MCMR-WMN In this regardwe also present a simulation-based discussion to simulta-neously study the effects of load-balancing and number oftransmissions on the networkrsquos throughput

3 Network Model and Assumptions

We consider a typical MCMR-WMN consisting of 119899 sta-tionary nodes (In this paper the terms ldquomesh routerrdquo andldquonoderdquo are used interchangeably for convenience) Each node119909 is equipped with 119877

119909half-duplex radios tuned to one of

the 119870 available non-overlapping channels where no channelswitching is allowed For the sake of efficiency the radiosof a node are tuned to different non-overlapping channelsWhen a radio of a node transmits or receives the packets ona channel other radios of the same node are able to com-municate at the same time with neighboring nodes on otherchannels In this paper a single-rate framework is assumedfor all link-layer transmissions In addition we suppose thatthe radios of the nodes are equipped with omnidirectionalantennas characterized by the same transmission range andthe same interference range Node 119909 is directly connectedto node 119910 and forms a wireless link if and only if node 119910

is within the transmission range of node 119909 and they share acommon channel In this regard we model the network as adirected graph G = (VE) where V = V

1 V2 V

119899 is the

set of vertices representing 119899 nodes and E denotes the set ofcommunication links In this work we consider the trafficmodel of on-demand multicastbroadcast sessions whereeach admitted session creates a unique tree with a specificbandwidth requirement In this way we adopt a schedule-based MAC protocol in which the conflict-free transmission

is ensured by assigning the interfering transmitters to eithersend on different non-overlapping channels or send on thesame channel but at different time slots

4 Problem Formulation

The limited number of radios and the shared nature of wire-less medium impose some resource constraints on MCMR-WMNs In this section we derive a formulation to capturethe utilization of the network resources and to analyze thefeasibility of multicastbroadcast session requests

Definition 1 The capacity of the 119894th mesh router is definedas 119862(119894) = 119877

1198941198880 where 119877

119894represents the number of its radios

and 1198880is the capacity of the channels In addition we define

the sent and the received traffic loads of the 119894th mesh routerdenoted by 119897

119904(119894) and 119897

119903(119894) respectively as 119897

119904(119894) = sum

119877119894

119887=1119897119904119887(119894)

and 119897119903(119894) = sum

119877119894

119887=1119897119903119887(119894) 119894 = 1 119899 where 119897

119904119887(119894) and 119897

119903119887(119894) are

the sent and the received traffic loads of the 119887th radio in the119894th mesh router respectivelyThus the total traffic load of the119894th mesh router is obtained as 119897(119894) = 119897

119904(119894) + 119897

119903(119894) 119894 = 1 119899

According to the assumption of the half-duplex radioseach radio can only send or receive on a fixed channel 119896 atany time slot therefore it is required that

119897119904119887

(119894) + 119897119903119887

(119894) le 1198880 forall119894 isin V 119887 = 1 119877

119894 (1)

Let 119897119895119894denote the created load by the 119895th session on the 119894th

mesh routerThus the total load of the 119894thmesh router can berewritten as 119897(119894) = sum

119899119904

119895=1119897119895

119894 119894 = 1 119899 where 119899

119904is the number

of active sessions In general each multicastbroadcast tree119879119895 is composed of a set of MAC multicast transmissions on

different nodes and channels The number of transmissionsof node 119894 at the 119895th tree denoted by NT119895

119894 is given by

NT119895119894= sum

119896isinK119902119895

119894119896 119894 = 1 119899 (2)

where K is the set of 119870 available non-overlapping channelsand 119902

119895

119894119896= 1 if node 119894 is a forwarding node on channel 119896 at

the 119895th tree and 119902119895

119894119896= 0 otherwise In this case we define the

total number of transmissions for the 119895th tree as

NT (119879119895) = sum

119894isinVNT119895119894 (3)

In fact NT(119879119895) shows the number of transmissions required

to deliver one packet from the source node to all the desti-nations at the 119895th multicastbroadcast tree Thus the averagenumber of transmissions per active session is expressed as

NT =

1

119899119904

119899119904

sum

119895=1

NT (119879119895) (4)

Since more transmissions take longer time on schedul-ing frame minimizing the number of transmissions helpsto improve the networkrsquos throughput In a typical multi-castbroadcast tree 119879

119895 there are three kinds of nodes source

4 The Scientific World Journal

A

C

D

G

H

E

B

F

L

I

1

1

1

1

2

2

2

2

3

3

3

M

N

P

K

J

Figure 1 A typical multicast routing tree

node 119904119895 forwarding nodes set (FWD119895) and leaf nodes

set (LF119895) For example consider the multicast tree shownin Figure 1 Here the number associated with each linkrepresents the channel assigned to that link All nodes of treeexcept the source node have one parent The source node(eg node A) as the root of the tree sends data toward itschildren A forwarding node (eg nodes BC E F and I) actsas both parent and child node as a child node it receives datafrom its parent while in the role of a parent node it sends thetraffic toward its children A leaf node (eg nodesD K LMN and P) only plays the role of a child and receives data fromits parent It is clear from Figure 1 that NT119895

119860= NT119895119861= NT119895119862

=

NT119895119864= 1 while NT119895

119868= NT119895119865= 2 (ie NT(119879

119895) = 8)

Since we assume the bandwidth-guaranteed trees withbandwidth requirement tr119895

119904 the created load by the 119895th

session on the 119894th node can be generally formulated by therole of node and the number of its transmissions as

119897119895

119894=

tr119895119904(1 + NT119895

119894) if 119894 isin FWDj

tr119895119904times NT119895119894

if 119894 = 119904119895

tr119895119904

if 119894 isin LF1198950 if 119894 notin 119879

119895

(5)

Here we define the utilization of the 119894th mesh routerdenoted by 119880(119894) as follows

119880 (119894) =

119897 (119894)

119862 (119894)

=

1

119862 (119894)

119899119904

sum

119895=1

119897119895

119894 (6)

where119880(119894) indicates the percentage of the 119894th nodersquos capacityused for routing of 119899

119904multicastbroadcast sessions For this

case the average utilization of the nodes is defined as

119880 =

1

119899

119899

sum

119894=1

119880 (119894) (7)

where 119899 is the total number of nodes in the networkOn the other hand due to the shared nature of thewireless

medium adjacent transmissions cannot occur simultane-ously on the same channel To formulate this issue we use

the channel utilization concept defined in [17] with minormodifications For the described MCMR-WMNmodel con-sider a fixed transmission rate of 119888

0 Each MAC multicast

transmission in the 119895th routing tree uses a time fraction ofthe scheduling frame that is equal to tr119895

1199041198880 By definition

the utilization of channel 119896 observed by node 119910 (119883119896119910) is the

sum of the time fractions assigned to all nodes within theinterference range of node 119910 that are intended to transmit onchannel 119896Thus considering 119899

119904admittedmulticastbroadcast

sessions the utilization of channel 119896 observed by node 119910 isformulated as

119883119896

119910=

119899119904

sum

119895=1

sum

119894isinintf(119910)

tr119895119904

1198880

119902119895

119894119896 (8)

where intf(119910) denotes the set of interfering nodes locatedwithin the interference range of node 119910 For this case thechannel capacity constraint is given by

119883119896

119910le 1 forall119910 isin V forall119896 isin ch list (119910) (9)

where ch list(119910) indicates the set of assigned channelsto the radios of node 119910 Since the radios of each nodeare assigned to different non-overlapping channels and nochannel switching is allowed one can show that condition(9) satisfies the described condition in (1) Therefore thebandwidth-guaranteed multicastbroadcast sessions are fea-sible and schedulable if all interfering transmissions have atotal load less than the normalized channel capacity Differentfrom the best-effort routing algorithms quality of service(QoS) routing algorithms must use call admission controlmechanisms to protect the QoS requirements of the existingflows [17 21] Clearly it is desired to maximize the numberof admitted sessions In this regard we define the networkrsquosthroughput denoted by 120591 as the sum of the traffic load of alladmitted feasible sessions as 120591 = sum

119899119904

119895=1tr119895119904

5 Networkrsquos Throughput versus ResourceUtilizations in MCMR-WMNs

In this section we aim to derive analytical relationships forthe networkrsquos throughput in terms of the node utilizationsthe channel utilizations and the number of transmissions

Theorem 2 If all sessions have the same traffic load forexample tr119895

119904= 1198790 and the capacity of all nodes in the network

is identical for example 119877119894= 119877 and 119862(119894) = 119862 the average

number of transmissions for the multicast flows is expressed as

NT =

119899119862

1198991199041198790

119880 minus 119882 (10)

where 119899119904and 119880 denote the number of admitted sessions and

the average node utilization respectively In addition 119882 =

(1119899119904) sum119899119904

119895=1119882119895 shows the average number of links in the tree of

each session and119882119895 is the number of links in the 119895th multicast

tree

The Scientific World Journal 5

Proof Under the assumption 119862(119894) = 119862 and using (6) and (7)we have

119880 =

1

119899119862

119899119904

sum

119895=1

119899

sum

119894=1

119897119895

119894

(119886)

=

1

119899119862

119899119904

sum

119895=1

( sum

119894isinFWD119895tr119895119904(1 + NT119895

119894) + tr119895119904NT119895119904+ sum

119894isin119871119865119895

tr119895119904)

=

1198790

119899119862

119899119904

sum

119895=1

( sum

119894isin119904119895FWD119895

NT119895119894+

10038161003816100381610038161003816FWD1198951003816100381610038161003816

1003816+

10038161003816100381610038161003816LF1198951003816100381610038161003816

1003816)

(11)

where (119886) comes from (5) and the fact that each multicastrouting tree includes three kinds of nodes a source nodeforwarding nodes and leaf nodes In the above equationsNT119895119904is the number of transmissions of source node and

|FWD119895| and |LF119895| denote the number of forwarding nodesand leaf nodes at the 119895th tree respectively On the other handfrom the graph theory [22]

10038161003816100381610038161003816FWD1198951003816100381610038161003816

1003816+

10038161003816100381610038161003816LF1198951003816100381610038161003816

1003816= 119882119895 (12)

Thus (11) can be simplified as

119880 =

1198790

119899119862

119899119904

sum

119895=1

( sum

119894isin119904119895FWD119895

NT119895119894+ 119882119895)

=

1198790

119899119862

[

[

119899119904

sum

119895=1

sum

119894isin119904119895FWD119895

NT119895119894+

119899119904

sum

119895=1

119882119895]

]

(13)

According to (3) and (4) and considering the fact thatNT119895119894= 0 for 119894 notin 119904

119895 FWD119895 we have

NT =

1

119899119904

119899119904

sum

119895=1

sum

119894isin119904119895FWD119895

NT119895119894 (14)

Thus

119880 =

1198790

119899119862

[119899119904NT + 119899

119904119882] =

1198991199041198790

119899119862

[NT + 119882] (15)

As a result NT = (1198991198621198991199041198790)119880 minus 119882

Corollary 3 For the broadcast case (12) can be rewritten as|FWD119895| + |119871119865

119895| = 119899 minus 1 [22] Thus

119873119879 =

119899119862

1198991199041198790

119880 minus 119899 + 1 (16)

In the rest of the section we first present the problemfor the small-scale MCMR-WMNs and then we extend ourwork to the case of large-scale MCMR-WMNs In additiondue to the similarity of equations for the multicast andthe broadcast sessions we follow the problem only for thebroadcast sessions

Small-Scale MCMR-WMNs In a small-scale MCMR-WMNwe suppose that all nodes are located in the interference range

of each other Thus the channel utilization observed by anynode is identical For a small-scale MCMR-WMN we definethe utilization of channel 119896 denoted by 119883

119896 and the averagechannel utilization 119883SS as follows

119883119896=

119899119904

sum

119895=1

sum

119894isinV

tr119895119904

1198880

119902119895

119894119896 forall119896 isin K (17)

119883SS =

1

119870

119870

sum

119896=1

119883119896 (18)

Lemma 4 Under the same conditions as in Theorem 2the broadcast throughput of a small-scale MCMR-WMN isexpressed in terms of the average node utilization and theaverage channel utilization as follows

120591 =

1198880

119899 minus 1

(119899119877119880 minus 119870X119878119878) (19)

Proof Using (17) and averaging the utilization on differentchannels we have

119883SS =

1

119870

119899119904

sum

119895=1

119870

sum

119896=1

sum

119894isinV

tr119895119904

1198880

119902119895

119894119896

(119886)

=

1198991199041198790

1198701198880

NT (20)

where (119886) comes from (2)ndash(4) and the assumption tr119895119904= 1198790

Considering 120591 = 1198991199041198790 119862 = 119877119888

0 and replacing NT with the

result in (16) for broadcast sessions the throughput 120591 can beexpressed as 120591 = (119888

0119899 minus 1)(119899119877119880 minus 119870119883SS)

Large-Scale MCMR-WMNs Now we extend the result ofLemma 4 to the large-scale MCMR-WMN case In generalthe channel utilization is a location-dependent parameterHowever due to the shared nature of the wireless mediumthe channel utilizations observed by neighboring nodes areclose to each other Thus considering the channel utilizationobserved by all nodes gives a lot of redundancy One idea isto study the channel utilization observed by a special nodeon behalf of its neighbors To address this solution we definethe ldquointerference domain (ID)rdquo and the ldquointerference domainheadrdquo as follows

Definition 5 The ldquointerference domainrdquo is defined as a subsetof the networkrsquos nodes which satisfies three conditions

(i) The interference domains have no common node thatis ID119894⋂ ID119895= Oslash 119894 = 119895

(ii) The interference domains span all nodes in the net-work that is ⋃119872

119898=1ID119898

= V where 119872 denotes thetotal number of interference domains

(iii) Each interference domain for example the 119898thinterference domain includes a node denoted by 120585

119898

so that only the nodes of ID119898

are located withinthe interference range of 120585

119898 We define 120585

119898as the

ldquointerference domain headrdquo of ID119898

It is clear from Definition 5 that a small-scale MCMR-WMN is a special case which consists of only one interference

6 The Scientific World Journal

domain The feasibility of condition (iii) is justified by thefact that mesh routers are usually deployed with carefulplanning To clarify the above definition consider a typicalgrid topology plotted in Figure 2 as a popular topology forthe WMNs Let the grid length be set to 119871

0 In this case

for the interference range 119889intf assume radic21198710

lt 119889intf lt 21198710

which is a reasonable interference range [2] Thus we canmodel the interference domains as a 3 times 3 square grids asshown in Figure 2(b) This modeling satisfies conditions (i)ndash(iii) in Definition 5 In Figure 2(a) each circle represents aninterference domain and the central black nodes play the roleof the corresponding interference domain head

Now let the network be composed of 119872 interferencedomains ID

1 ID

119872 For large-scale MCMR-WMNs we

define the average channel utilization 119883LS as follows

119883LS =

1

119872119870

119870

sum

119896=1

119872

sum

119898=1

119883119896

119898 (21)

where 119883119896

119898denotes the utilization of channel 119896 observed by

the 119898th interference domain head

Theorem 6 Assume all sessions have the same traffic load forexample 119905119903119895

119904= 1198790 The networkrsquos throughput of the large-scale

MCMR-WMN is obtained as

120591 =

1198721198701198880

119873119879

119883119871119878

(22)

Proof According to (8) and considering the condition (iii) inDefinition 5 the utilization of the channel 119896 observed by the119898th interference domain head is given by

119883119896

119898=

119899119904

sum

119895=1

sum

119894isinID119898

tr119895119904

1198880

119902119895

119894119896 forall119896 isin K 119898 = 1 119872 (23)

Using (23) and averaging the utilization on differentchannels and different interference domain heads we have

119883LS =

1

119872119870

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

tr119895119904

1198880

119902119895

119894119896 (24)

119883LS(119886)

=

1198790

1198721198701198880

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (25)

where (119886) comes from assumption tr119895119904= 1198790 Under conditions

(i) and (ii) in Definition 5 and using (2)ndash(4) we obtain

NT =

1

119899119904

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (26)

Thus (25) can be simplified as

119883LS =

1198991199041198790NT

1198721198701198880

(27)

As a result since 120591 = 1198991199041198790 the networkrsquos throughput can

be obtained as 120591 = (1198721198701198880119873119879)119883

119871119878

Corollary 7 Under the same conditions as in Theorem 2considering 119862 = 119877119888

0and replacing 119873119879 with the result in

(16) the broadcast throughput of a large-scale MCMR-WMNis expressed in terms of the average node utilization and theaverage channel utilization as follows

120591 =

1198880

119899 minus 1

(119899119877119880 minus 119872119870119883119871119878

) (28)

It is clear that different parameters of the network interactwith each other Thus it is not possible to draw a specifiedboundary between themDue to the limited number of radiosand non-overlapping channels proper use of the resourcescould improve the performance of the network In thisregard as we will show in the next section the number oftransmissions and the load-balancing significantly affect thenetworkrsquos throughput

6 Numerical Results

In this section we present a comprehensive evaluation onthe relationship between the networkrsquos throughput and theresource utilizations For this purpose we apply the followingprotocols in a single-rate framework SPT-JCRS [7] MCM-JCRS [7] IRMT [20] and IRBT [20] In our Matlab simula-tion setup as shown in Figure 3 we consider a 6 times 6 squaregrid with 119899 = 36 and119872 = 4 where nodes 8 11 26 and 29 arethe interference domain heads The grid length (the distancebetween neighbor nodes in the same row or column) and theinterference range are set to 150m and 280m respectivelyWe also use the random channel assignment in which theradios of each node are randomly assigned to the distinctchannels Obviously in the cases that the number of channelsis less than or equal to the number of radios this method willact as the common channel assignment strategy

In the simulations the broadcast session requests arriveone by one at the network without any knowledge of thefuture requests The source of each session is selected ran-domly In addition the trafficmodel of all sessions is assumedto be Constant Bit Rate (CBR)with tr119895

119904= 04Mbps Assuming

119877 = 3 1198880

= 12Mbps and 25 broadcast session requests westudy the performance of the network for different numberof channels that is 119870 = 1 6 It is clear that in thecase of 119870 = 1 we have a SCSR-WMN Figure 4 comparesthe throughput of the aforementioned protocols in terms ofthe number of channels 119870 In addition Table 1 shows thesimulation results inmore details It should be noted that eachdata point is obtained by averaging the results of 15 individualruns on different randomly experiments In this table NT119880 119883LS and 120591sim present the experimental results obtainedfor the average number of transmissions the average nodeutilization the average channel utilization and the networkrsquosthroughput respectively It is worth noting that the results inTable 1 exactly follow the described theoretical relationshipsin (16) (22) and (28) As an example Table 1 compares 120591simwith the theoretical throughput 120591theory extracted from (28)Obviously 120591sim is similar to 120591theory for different number of

The Scientific World Journal 7

1205851 1205852 1205853

1205854 1205855 1205856

1205857 1205858 1205859

ID1 ID2 ID3

ID7 ID8 ID9

(a)

2radic2L0

radic2L0

radic5L0

2L0

r

(b)

Figure 2 (a) A typical grid MCMR-WMN with its interference domains (b) an interference domain

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

8

11

26

29

150m

150m

Figure 3 The grid topology considered in the simulations

channels This shows the validity of our analysis This com-parison can be also verified for relationships (16) and (22)It is clear that different parameters of the network interactwith each other In this situation given the limited numberof radios and channels proper use of the resources couldimprove the performance of the network Actually using anefficient traffic engineering mechanism leads to better spec-trum utilization and increases the fairness in the networkThusmore resources will be available for accepting the futuresessions and the overall throughput will be increased In thisregard it is observed that the performance of the IRBT andthe IRMT algorithms much better than that of the othertwo algorithms In fact the IRBT and the IRMT algorithms

jointly address the transmission channel selection and theload-balanced routing tree construction [20] These schemesnot only take into account the number of transmissions butalso consider both inter-flow and intra-flow interferences toroute the sessions through alternative feasible pathsThus thetraffic load is balanced in the network However the MCM-JCRS and the SPT-JCRS algorithms cannot efficiently usethe resources of the network due to being limited to non-interference-aware routing trees

In [20] we demonstrated that the IRBT algorithm bal-ances the traffic load in the network more efficiently than theIRMTalgorithmThe results in Table 1 also confirm this issueFrom this table we can see that the IRBT approach improvesthe utilization of the network resources For 119870 = 1 2 3

(ie common channel assignment) although the IRMTalgorithm leads to less number of transmissions than theIRBT algorithm the load-balancing ability of the IRBTmakesboth schemes have the same networkrsquos throughput If thetraffic load in the network is balanced the interference willbe decreased and consequently the call acceptance rate willbe increased In contrast for 119870 gt 3 both IRMT and IRBTalgorithms nearly have the same number of transmissions Inthis situation the load-balancing factor plays more efficientrole in the networkrsquos performance This causes the IRBTalgorithm to show better throughput

On the other hand by increasing the number of channelsfirst the networkrsquos throughput linearly increases Howeverfor 119870 gt 3 it is gradually saturated Due to the randomchannel assignment strategy further increasing of the chan-nels leads to the less number of common channels betweenthe neighbor nodes Thus the possibility of enjoying thewireless broadcast advantagewill be decreasedThis increasesthe number of transmissions as shown in Table 1 In this

8 The Scientific World Journal

Table 1 Performance comparison for different number of channels

Number of channels Algorithm NT 119880 119883LS 120591sim (Mbps) 120591theory (Mbps)

119870 = 1

IRBT 20002 00961 09428 22667 22655IRMT 159444 00912 077 232 2321

MCM-JCRS 181 00787 07239 192 19214SPT-JCRS 2395 00703 07717 15467 15448

119870 = 2

IRBT 197273 01998 09722 47333 47317IRMT 159967 01888 07993 48 47986

MCM-JCRS 178833 01578 07205 38667 38669SPT-JCRS 233780 01411 07628 31333 31325

119870 = 3

IRBT 200016 02970 09719 7 69988IRMT 162761 02769 07911 7 69984

MCM-JCRS 18225 02481 07644 604 60418SPT-JCRS 234697 02093 07561 464 46392

119870 = 4

IRBT 202207 03702 09144 86909 86918IRMT 186563 03086 07244 74545 74531

MCM-JCRS 18966 02483 0589 59636 59631SPT-JCRS 241418 02455 06761 53818 53816

119870 = 5

IRBT 215448 03909 08040 896 89613IRMT 206932 03043 06105 708 70815

MCM-JCRS 217823 02225 04608 508 50791SPT-JCRS 26238 02155 04987 456 456

119870 = 6

IRBT 239454 03929 07182 864 86388IRMT 236876 02862 05197 632 63212

MCM-JCRS 242579 02088 03854 456 45603SPT-JCRS 272301 02133 04204 444 44389

1 2 3 4 5 60

2

4

6

8

10

Number of channels (K)

Thro

ughp

ut (M

bps)

IRBT

IRMT

MCM-JCRS

SPT-JCRS

Figure 4 Networkrsquos throughput as function of the number ofchannels

situation the lack of load-balancing could sufficiently reducethe networkrsquos throughput

7 Conclusion

In this paper the throughput of a MCMR-WMN wasquantified We focused on the scenario of on-demand QoSmulticastbroadcast sessions where each session has a spe-cific bandwidth requirement In particular considering theresource constraints we derived analytical relationships forthe networkrsquos throughput in terms of the node utilization thechannel utilization and the number of transmissions Thisgives simple solutions for the future designs to predict thenetworkrsquos throughput based on the resource utilizations Inline with the proposed relationships we also demonstratedthat the networkrsquos throughput is significantly affected by bothnumber of transmissions and degree of load-balancing Onone hand minimizing the number of transmissions reducesthe use of the network resources On the other hand load-balancing increases the fairness in the network In thissituation more resources will be available for accepting thefuture sessions Thus the overall networkrsquos throughput willbe increased

Acknowledgment

This work is supported by the Iranian TelecommunicationResearch Center (ITRC)

The Scientific World Journal 9

References

[1] PH Pathak andRDutta ldquoA survey of network design problemsand joint design approaches in wireless mesh networksrdquo IEEECommunications Surveys and Tutorials vol 13 no 3 pp 396ndash428 2011

[2] A Raniwala and T-C Chiueh ldquoArchitecture and algorithms foran IEEE 80211-based multi-channel wireless mesh networkrdquo inProceedings of the IEEE International Conference on ComputerCommunications (INFOCOM rsquo05) vol 3 pp 2223ndash2234March2005

[3] A Avokh and G Mirjalily ldquoPerformance analysis of broad-casting in small-scale multi-radio multi-channel wireless meshnetworksrdquo in Proceedings of the 14th International Conference onAdvanced Communication Technology (ICACT rsquo12) pp 537ndash542February 2012

[4] U T Nguyen and J Xu ldquoMulticast routing in wireless meshnetworks minimum cost trees or shortest path treesrdquo IEEECommunications Magazine vol 45 no 11 pp 72ndash77 2007

[5] Y Li and I Chen ldquoDynamic agent-based hierarchical multicastfor wireless mesh networksrdquo Ad Hoc Networks vol 11 no 6 pp1683ndash1698 2013

[6] J E Wieselthier G D Nguyen and A Ephremides ldquoEnergy-efficient broadcast and multicast trees in wireless networksrdquoMobile Networks and Applications vol 7 no 6 pp 481ndash4922002

[7] A Avokh G Mirjalily and J Abouei ldquoJoint channel andrate selection for multicast routing trees in wireless meshnetworksrdquo in Proceedings of the International Symposium onTelecommunications pp 548ndash553 November 2012

[8] K N Ramachandran E M Belding K C Almeroth andM M Buddhikot ldquoInterference-aware channel assignment inmulti-radio wireless mesh networksrdquo in Proceedings of the 25thIEEE International Conference on Computer Communications(INFOCOM rsquo06) pp 1ndash12 April 2006

[9] R-H Jan S-Y Huang and C-F Wang ldquoAn upper bound ofthe throughput for multi-radio wireless mesh networksrdquo IEEECommunications Letters vol 14 no 8 pp 698ndash700 2010

[10] A Capone G Carello I Filippini S Gualandi and F Malu-celli ldquoRouting scheduling and channel assignment in wirelessmesh networks optimization models and algorithmsrdquo Ad HocNetworks vol 8 no 6 pp 545ndash563 2010

[11] E Alotaibi V Ramamurthi M Batayneh and B MukherjeeldquoInterference-aware routing for multi-hop wireless mesh net-worksrdquo Computer Communications vol 33 no 16 pp 1961ndash1971 2010

[12] V C M Borges D Pereira M Curado and E MonteiroldquoRoutingmetric for interference and channel diversity inmulti-radio wireless mesh networksrdquo in Ad-Hoc Mobile and WirelessNetworks vol 5793 of Lecture Notes in Computer Science pp55ndash68 Springer Berlin Germany 2009

[13] S Roy D Koutsonikolas S Das and Y C Hu ldquoHigh-throughput multicast routing metrics in wireless mesh net-worksrdquo Ad Hoc Networks vol 6 no 6 pp 878ndash899 2008

[14] P M Ruiz and A F Gomez-Skarmeta ldquoApproximating optimalmulticast trees in wireless multihop networksrdquo in Proceedings ofthe 10th IEEE Symposium on Computers and Communications(ISCC rsquo05) pp 686ndash691 June 2005

[15] H L Nguyen and U T Nguyen ldquoBandwidth efficient multicastrouting in multi-channel multi-radio wireless mesh networksrdquoin Proceedings of the International Conference on Ultra Modern

Telecommunications and Workshops (ICUMT rsquo09) pp 1ndash8October 2009

[16] G Zeng B Wang Y Ding L Xiao and M Mutka ldquoEfficientmulticast algorithms formultichannel wireless mesh networksrdquoIEEE Transactions on Parallel and Distributed Systems vol 21no 1 pp 86ndash99 2010

[17] H S Chiu K L Yeung and K-S Lui ldquoMaximizing broadcastload in multi-channel Multi-interface wireless mesh networksrdquoin Proceedings of the IEEE Global Telecommunications Confer-ence (GLOBECOM rsquo08) pp 533ndash537 December 2008

[18] F Li Y Fang F Hu and X Liu ldquoLoad-aware multicast routingmetrics in multi-radio multi-channel wireless mesh networksrdquoComputer Networks vol 55 no 9 pp 2150ndash2167 2011

[19] P A K Acharya and E M Belding ldquoMARS link-layer rateselection for multicast transmissions in wireless mesh net-worksrdquo Ad Hoc Networks vol 9 no 1 pp 48ndash60 2011

[20] A Avokh and G Mirjalily ldquoInterference-aware multicast andbroadcast routing in wireless mesh networks using both rateand channel diversityrdquo Computers amp Electrical Engineering2013

[21] T Kim Y Yang J C Hou and S V Krishnamurthy ldquoResourceallocation for QoS support in wireless mesh networksrdquo IEEETransactions on Wireless Communications vol 12 no 5 pp2046ndash2054 2013

[22] W Kocay and D Kreher Graphs Algorithms and Optimiza-tion Discrete Mathematics and Its Applications Chapman ampHallCRC Boca Raton Fla USA 2005

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2 The Scientific World Journal

Minimizing the number of transmissions improves the uti-lization of the network resources and subsequently increasesthe networkrsquos throughput Besides the number of transmis-sions the load-balancing problem is another pertinent issueto be considered in MCMR-WMNs This problem can bediscussed from two perspectives spatial load-balancing andchannel load-balancing From the viewpoint of a specificchannel when a part of the network experiences congestionthe new traffic flows should not be routed through that partIn addition from the perspective of a specific location thetraffic load must be balanced over all available channels inthe network If the traffic load in the network is balancedthe interference will be decreased and more resources willbe available for accepting the future traffics

To evaluate the performance of a MCMR-WMN thereare several criteria that often interact with each other Thusit is not possible to draw a clear boundary between themIn this regard different approaches try to improve differentaspects of the networks One difficulty in comparing differentschemes is the lack of a standard benchmark Certainlyhaving a prior knowledge about the bounds of criteria andtheir corresponding relationship provides more options forthe system administrator to control the parameters of thenetwork

Taking the above challenges into account the main goalof this paper is to quantify the throughput inMCMR-WMNsWe focus on the scenario of multicast and broadcast sessionswhere each session has a specific bandwidth requirementOn-demand requests arrive dynamically one by one withoutany prior knowledge of future arrivals A session will beaccepted if a routing tree with sufficient bandwidth oneach link can be established In particular we provide aformulation to express the networkrsquos throughput in terms ofthe node utilization the channel utilization and the numberof transmissions We also discuss how appropriate use of theresources affects the networkrsquos throughput

The rest of the paper is organized as follows Section 2surveys the previous related works The details of the net-work model are described in Section 3 Section 4 presents aformulation to capture the resource utilizations In Section 5we derive analytical expressions for the multicastbroadcastthroughput in both small-scale MCMR-WMN and large-scale MCMR-WMN Section 6 presents the numerical resultsand the discussion Finally some concluding remarks areprovided in Section 7

2 Related Work

In past years different aspects of MCMR-WMNs have beenwidely studied for unicast flows In particular some worksendeavor to heuristically improve the networkrsquos performance[2 8] while others focus on the optimization solutions [9ndash11] In this regard several routing metrics (such as ETXETT WCETT WCCETT MIC iAWARE and MIND [1 12])have been proposed However due to the differences betweenunicast and multicast routing the designed unicast schemescannot be efficient for themulticast traffics In one of themostfundamental researches on the multicast routing the work

in [4] compares the performance of the Minimum SteinerTrees (MSTs) and the Shortest Path Trees (SPTs) in Single-Channel Single-RadioWMNs (SCSR-WMNs) Experimentalresults in [4] show that SPTs offer a better performance thanMSTs In addition the implementation difficulty of MSTs isanother factor that makes SPTs more favorable in WMNsHowever none of these protocols consider the problems ofload-balancing and resource utilization

Roy et al [13] study the high-throughput metrics formulticast routing in WMNs They point out the differencebetween unicast and multicast routing and show how toadapt the unicast routing metrics for use in multicast flowsThey also propose a low-overhead adaptive algorithm toincorporate the link-quality-basedmetrics to a representativemulticast routing protocol

As mentioned before the ability to make an appropriateuse of the network resources can efficiently increase thethroughput in WMNs In line with this concept some worksaim to minimize the number of transmissions required todeliver one packet from the source to all the destinations [14ndash16] The authors in [15] propose a multicast routing metricnamed Multi-Channel Minimum Number of Transmissions(MCMNT) that considers the wireless broadcast advantageand the channel diversity to minimize the network band-width consumed by the routing tree MCMNT also tries tominimize the intra-flow interference in the network Zenget al [16] propose two algorithms named Level ChannelAssignment (LCA) and Multi-Channel Multicast (MCM)to minimize the number of forwarding nodes and the totalhop-count distances in MCMR-WMNs These algorithmsreduce the intra-flow interference using the heuristic channelassignment strategies The authors in [16] show that the LCAand the MCM algorithms outperform the single-channelmulticast in terms of the throughput and the delay They alsodemonstrate that using all the partially overlapping channelsinstead of only the non-overlapping channels can furtherdiminish the interference in the network

In [17] Chiu et al challenge the load-balancing issuein MCMR-WMNs The basic idea in [17] is that if thetraffic on the most-heavily loaded channel is minimized thetraffic load in the network will be balanced In this waythey first present an integer linear programming formulationto optimally construct the bandwidth-guaranteed broadcasttreesThen an efficient algorithm is proposed to heuristicallyimprove the call acceptance rate in the network Reference[18] proposes two load-aware metrics named ldquoFlow LoadMulticast Metric (FLMM)rdquo and ldquoReliable Flow Load Mul-ticast Metric (FLMM119877)rdquo for multicast routing in MCMR-WMNsAlthough bothmetrics count the interference and theWBA the latter case further considers the unreliability of theIEEE 80211 MAC protocol FLMM119877 uses the Packet DeliveryRatio (PDR) of the wireless links and reduces retransmis-sion overheads In line with this concept the work in [19]suggests two distributed strategies named ldquoMulticast Auto-Rate Selection (MARS)rdquo and ldquoMARS-Retransmit (MARS-R)rdquo The MARS scheme uses PDR of the wireless links atvarious transmission ratesTheMARS-R algorithm facilitatesthe joint use of rate control and link-layer mechanisms (such

The Scientific World Journal 3

as acknowledgments and retransmissions) to improve thereliability of high-throughput multicast flows

During recent years we have considered the problem oftraffic engineering for multicastbroadcast flows in WMNs[3 7 20] The work in [3] studies the special case ofbroadcasting for the small-scale WMNs In [7] we presentan Interference-Aware Joint Channel and Rate Selection (IA-JCRS) algorithm to choose the best transmission rates andthe best transmission channels for a given fixed routingtree However being bound to a routing tree reduces thefreedom to choose the alternative feasible paths Indeedusing a joint interference-aware routing scheme leads toa better utilization of the network resources Accordinglyin [20] we propose two cross-layer algorithms named theldquoInterference- and Rate-aware Multicast Tree (IRMT)rdquo andthe ldquoInterference- and Rate-aware Broadcast Tree (IRBT)rdquoAs an advantage the proposed algorithms jointly address theproblems of multicastbroadcast routing tree constructiontransmission rate selection transmission channel selectionand call admission control

One drawback of the previous works is that they pay lessattention to the theoretical analysis of multicastbroadcastflows Most of the literature tries to propose some heuristi-cally or optimally solutions to improve different aspects of thenetwork Unlike the previous works this paper quantifies themulticast and the broadcast throughput in both small-scaleMCMR-WMN and large-scale MCMR-WMN In this regardwe also present a simulation-based discussion to simulta-neously study the effects of load-balancing and number oftransmissions on the networkrsquos throughput

3 Network Model and Assumptions

We consider a typical MCMR-WMN consisting of 119899 sta-tionary nodes (In this paper the terms ldquomesh routerrdquo andldquonoderdquo are used interchangeably for convenience) Each node119909 is equipped with 119877

119909half-duplex radios tuned to one of

the 119870 available non-overlapping channels where no channelswitching is allowed For the sake of efficiency the radiosof a node are tuned to different non-overlapping channelsWhen a radio of a node transmits or receives the packets ona channel other radios of the same node are able to com-municate at the same time with neighboring nodes on otherchannels In this paper a single-rate framework is assumedfor all link-layer transmissions In addition we suppose thatthe radios of the nodes are equipped with omnidirectionalantennas characterized by the same transmission range andthe same interference range Node 119909 is directly connectedto node 119910 and forms a wireless link if and only if node 119910

is within the transmission range of node 119909 and they share acommon channel In this regard we model the network as adirected graph G = (VE) where V = V

1 V2 V

119899 is the

set of vertices representing 119899 nodes and E denotes the set ofcommunication links In this work we consider the trafficmodel of on-demand multicastbroadcast sessions whereeach admitted session creates a unique tree with a specificbandwidth requirement In this way we adopt a schedule-based MAC protocol in which the conflict-free transmission

is ensured by assigning the interfering transmitters to eithersend on different non-overlapping channels or send on thesame channel but at different time slots

4 Problem Formulation

The limited number of radios and the shared nature of wire-less medium impose some resource constraints on MCMR-WMNs In this section we derive a formulation to capturethe utilization of the network resources and to analyze thefeasibility of multicastbroadcast session requests

Definition 1 The capacity of the 119894th mesh router is definedas 119862(119894) = 119877

1198941198880 where 119877

119894represents the number of its radios

and 1198880is the capacity of the channels In addition we define

the sent and the received traffic loads of the 119894th mesh routerdenoted by 119897

119904(119894) and 119897

119903(119894) respectively as 119897

119904(119894) = sum

119877119894

119887=1119897119904119887(119894)

and 119897119903(119894) = sum

119877119894

119887=1119897119903119887(119894) 119894 = 1 119899 where 119897

119904119887(119894) and 119897

119903119887(119894) are

the sent and the received traffic loads of the 119887th radio in the119894th mesh router respectivelyThus the total traffic load of the119894th mesh router is obtained as 119897(119894) = 119897

119904(119894) + 119897

119903(119894) 119894 = 1 119899

According to the assumption of the half-duplex radioseach radio can only send or receive on a fixed channel 119896 atany time slot therefore it is required that

119897119904119887

(119894) + 119897119903119887

(119894) le 1198880 forall119894 isin V 119887 = 1 119877

119894 (1)

Let 119897119895119894denote the created load by the 119895th session on the 119894th

mesh routerThus the total load of the 119894thmesh router can berewritten as 119897(119894) = sum

119899119904

119895=1119897119895

119894 119894 = 1 119899 where 119899

119904is the number

of active sessions In general each multicastbroadcast tree119879119895 is composed of a set of MAC multicast transmissions on

different nodes and channels The number of transmissionsof node 119894 at the 119895th tree denoted by NT119895

119894 is given by

NT119895119894= sum

119896isinK119902119895

119894119896 119894 = 1 119899 (2)

where K is the set of 119870 available non-overlapping channelsand 119902

119895

119894119896= 1 if node 119894 is a forwarding node on channel 119896 at

the 119895th tree and 119902119895

119894119896= 0 otherwise In this case we define the

total number of transmissions for the 119895th tree as

NT (119879119895) = sum

119894isinVNT119895119894 (3)

In fact NT(119879119895) shows the number of transmissions required

to deliver one packet from the source node to all the desti-nations at the 119895th multicastbroadcast tree Thus the averagenumber of transmissions per active session is expressed as

NT =

1

119899119904

119899119904

sum

119895=1

NT (119879119895) (4)

Since more transmissions take longer time on schedul-ing frame minimizing the number of transmissions helpsto improve the networkrsquos throughput In a typical multi-castbroadcast tree 119879

119895 there are three kinds of nodes source

4 The Scientific World Journal

A

C

D

G

H

E

B

F

L

I

1

1

1

1

2

2

2

2

3

3

3

M

N

P

K

J

Figure 1 A typical multicast routing tree

node 119904119895 forwarding nodes set (FWD119895) and leaf nodes

set (LF119895) For example consider the multicast tree shownin Figure 1 Here the number associated with each linkrepresents the channel assigned to that link All nodes of treeexcept the source node have one parent The source node(eg node A) as the root of the tree sends data toward itschildren A forwarding node (eg nodes BC E F and I) actsas both parent and child node as a child node it receives datafrom its parent while in the role of a parent node it sends thetraffic toward its children A leaf node (eg nodesD K LMN and P) only plays the role of a child and receives data fromits parent It is clear from Figure 1 that NT119895

119860= NT119895119861= NT119895119862

=

NT119895119864= 1 while NT119895

119868= NT119895119865= 2 (ie NT(119879

119895) = 8)

Since we assume the bandwidth-guaranteed trees withbandwidth requirement tr119895

119904 the created load by the 119895th

session on the 119894th node can be generally formulated by therole of node and the number of its transmissions as

119897119895

119894=

tr119895119904(1 + NT119895

119894) if 119894 isin FWDj

tr119895119904times NT119895119894

if 119894 = 119904119895

tr119895119904

if 119894 isin LF1198950 if 119894 notin 119879

119895

(5)

Here we define the utilization of the 119894th mesh routerdenoted by 119880(119894) as follows

119880 (119894) =

119897 (119894)

119862 (119894)

=

1

119862 (119894)

119899119904

sum

119895=1

119897119895

119894 (6)

where119880(119894) indicates the percentage of the 119894th nodersquos capacityused for routing of 119899

119904multicastbroadcast sessions For this

case the average utilization of the nodes is defined as

119880 =

1

119899

119899

sum

119894=1

119880 (119894) (7)

where 119899 is the total number of nodes in the networkOn the other hand due to the shared nature of thewireless

medium adjacent transmissions cannot occur simultane-ously on the same channel To formulate this issue we use

the channel utilization concept defined in [17] with minormodifications For the described MCMR-WMNmodel con-sider a fixed transmission rate of 119888

0 Each MAC multicast

transmission in the 119895th routing tree uses a time fraction ofthe scheduling frame that is equal to tr119895

1199041198880 By definition

the utilization of channel 119896 observed by node 119910 (119883119896119910) is the

sum of the time fractions assigned to all nodes within theinterference range of node 119910 that are intended to transmit onchannel 119896Thus considering 119899

119904admittedmulticastbroadcast

sessions the utilization of channel 119896 observed by node 119910 isformulated as

119883119896

119910=

119899119904

sum

119895=1

sum

119894isinintf(119910)

tr119895119904

1198880

119902119895

119894119896 (8)

where intf(119910) denotes the set of interfering nodes locatedwithin the interference range of node 119910 For this case thechannel capacity constraint is given by

119883119896

119910le 1 forall119910 isin V forall119896 isin ch list (119910) (9)

where ch list(119910) indicates the set of assigned channelsto the radios of node 119910 Since the radios of each nodeare assigned to different non-overlapping channels and nochannel switching is allowed one can show that condition(9) satisfies the described condition in (1) Therefore thebandwidth-guaranteed multicastbroadcast sessions are fea-sible and schedulable if all interfering transmissions have atotal load less than the normalized channel capacity Differentfrom the best-effort routing algorithms quality of service(QoS) routing algorithms must use call admission controlmechanisms to protect the QoS requirements of the existingflows [17 21] Clearly it is desired to maximize the numberof admitted sessions In this regard we define the networkrsquosthroughput denoted by 120591 as the sum of the traffic load of alladmitted feasible sessions as 120591 = sum

119899119904

119895=1tr119895119904

5 Networkrsquos Throughput versus ResourceUtilizations in MCMR-WMNs

In this section we aim to derive analytical relationships forthe networkrsquos throughput in terms of the node utilizationsthe channel utilizations and the number of transmissions

Theorem 2 If all sessions have the same traffic load forexample tr119895

119904= 1198790 and the capacity of all nodes in the network

is identical for example 119877119894= 119877 and 119862(119894) = 119862 the average

number of transmissions for the multicast flows is expressed as

NT =

119899119862

1198991199041198790

119880 minus 119882 (10)

where 119899119904and 119880 denote the number of admitted sessions and

the average node utilization respectively In addition 119882 =

(1119899119904) sum119899119904

119895=1119882119895 shows the average number of links in the tree of

each session and119882119895 is the number of links in the 119895th multicast

tree

The Scientific World Journal 5

Proof Under the assumption 119862(119894) = 119862 and using (6) and (7)we have

119880 =

1

119899119862

119899119904

sum

119895=1

119899

sum

119894=1

119897119895

119894

(119886)

=

1

119899119862

119899119904

sum

119895=1

( sum

119894isinFWD119895tr119895119904(1 + NT119895

119894) + tr119895119904NT119895119904+ sum

119894isin119871119865119895

tr119895119904)

=

1198790

119899119862

119899119904

sum

119895=1

( sum

119894isin119904119895FWD119895

NT119895119894+

10038161003816100381610038161003816FWD1198951003816100381610038161003816

1003816+

10038161003816100381610038161003816LF1198951003816100381610038161003816

1003816)

(11)

where (119886) comes from (5) and the fact that each multicastrouting tree includes three kinds of nodes a source nodeforwarding nodes and leaf nodes In the above equationsNT119895119904is the number of transmissions of source node and

|FWD119895| and |LF119895| denote the number of forwarding nodesand leaf nodes at the 119895th tree respectively On the other handfrom the graph theory [22]

10038161003816100381610038161003816FWD1198951003816100381610038161003816

1003816+

10038161003816100381610038161003816LF1198951003816100381610038161003816

1003816= 119882119895 (12)

Thus (11) can be simplified as

119880 =

1198790

119899119862

119899119904

sum

119895=1

( sum

119894isin119904119895FWD119895

NT119895119894+ 119882119895)

=

1198790

119899119862

[

[

119899119904

sum

119895=1

sum

119894isin119904119895FWD119895

NT119895119894+

119899119904

sum

119895=1

119882119895]

]

(13)

According to (3) and (4) and considering the fact thatNT119895119894= 0 for 119894 notin 119904

119895 FWD119895 we have

NT =

1

119899119904

119899119904

sum

119895=1

sum

119894isin119904119895FWD119895

NT119895119894 (14)

Thus

119880 =

1198790

119899119862

[119899119904NT + 119899

119904119882] =

1198991199041198790

119899119862

[NT + 119882] (15)

As a result NT = (1198991198621198991199041198790)119880 minus 119882

Corollary 3 For the broadcast case (12) can be rewritten as|FWD119895| + |119871119865

119895| = 119899 minus 1 [22] Thus

119873119879 =

119899119862

1198991199041198790

119880 minus 119899 + 1 (16)

In the rest of the section we first present the problemfor the small-scale MCMR-WMNs and then we extend ourwork to the case of large-scale MCMR-WMNs In additiondue to the similarity of equations for the multicast andthe broadcast sessions we follow the problem only for thebroadcast sessions

Small-Scale MCMR-WMNs In a small-scale MCMR-WMNwe suppose that all nodes are located in the interference range

of each other Thus the channel utilization observed by anynode is identical For a small-scale MCMR-WMN we definethe utilization of channel 119896 denoted by 119883

119896 and the averagechannel utilization 119883SS as follows

119883119896=

119899119904

sum

119895=1

sum

119894isinV

tr119895119904

1198880

119902119895

119894119896 forall119896 isin K (17)

119883SS =

1

119870

119870

sum

119896=1

119883119896 (18)

Lemma 4 Under the same conditions as in Theorem 2the broadcast throughput of a small-scale MCMR-WMN isexpressed in terms of the average node utilization and theaverage channel utilization as follows

120591 =

1198880

119899 minus 1

(119899119877119880 minus 119870X119878119878) (19)

Proof Using (17) and averaging the utilization on differentchannels we have

119883SS =

1

119870

119899119904

sum

119895=1

119870

sum

119896=1

sum

119894isinV

tr119895119904

1198880

119902119895

119894119896

(119886)

=

1198991199041198790

1198701198880

NT (20)

where (119886) comes from (2)ndash(4) and the assumption tr119895119904= 1198790

Considering 120591 = 1198991199041198790 119862 = 119877119888

0 and replacing NT with the

result in (16) for broadcast sessions the throughput 120591 can beexpressed as 120591 = (119888

0119899 minus 1)(119899119877119880 minus 119870119883SS)

Large-Scale MCMR-WMNs Now we extend the result ofLemma 4 to the large-scale MCMR-WMN case In generalthe channel utilization is a location-dependent parameterHowever due to the shared nature of the wireless mediumthe channel utilizations observed by neighboring nodes areclose to each other Thus considering the channel utilizationobserved by all nodes gives a lot of redundancy One idea isto study the channel utilization observed by a special nodeon behalf of its neighbors To address this solution we definethe ldquointerference domain (ID)rdquo and the ldquointerference domainheadrdquo as follows

Definition 5 The ldquointerference domainrdquo is defined as a subsetof the networkrsquos nodes which satisfies three conditions

(i) The interference domains have no common node thatis ID119894⋂ ID119895= Oslash 119894 = 119895

(ii) The interference domains span all nodes in the net-work that is ⋃119872

119898=1ID119898

= V where 119872 denotes thetotal number of interference domains

(iii) Each interference domain for example the 119898thinterference domain includes a node denoted by 120585

119898

so that only the nodes of ID119898

are located withinthe interference range of 120585

119898 We define 120585

119898as the

ldquointerference domain headrdquo of ID119898

It is clear from Definition 5 that a small-scale MCMR-WMN is a special case which consists of only one interference

6 The Scientific World Journal

domain The feasibility of condition (iii) is justified by thefact that mesh routers are usually deployed with carefulplanning To clarify the above definition consider a typicalgrid topology plotted in Figure 2 as a popular topology forthe WMNs Let the grid length be set to 119871

0 In this case

for the interference range 119889intf assume radic21198710

lt 119889intf lt 21198710

which is a reasonable interference range [2] Thus we canmodel the interference domains as a 3 times 3 square grids asshown in Figure 2(b) This modeling satisfies conditions (i)ndash(iii) in Definition 5 In Figure 2(a) each circle represents aninterference domain and the central black nodes play the roleof the corresponding interference domain head

Now let the network be composed of 119872 interferencedomains ID

1 ID

119872 For large-scale MCMR-WMNs we

define the average channel utilization 119883LS as follows

119883LS =

1

119872119870

119870

sum

119896=1

119872

sum

119898=1

119883119896

119898 (21)

where 119883119896

119898denotes the utilization of channel 119896 observed by

the 119898th interference domain head

Theorem 6 Assume all sessions have the same traffic load forexample 119905119903119895

119904= 1198790 The networkrsquos throughput of the large-scale

MCMR-WMN is obtained as

120591 =

1198721198701198880

119873119879

119883119871119878

(22)

Proof According to (8) and considering the condition (iii) inDefinition 5 the utilization of the channel 119896 observed by the119898th interference domain head is given by

119883119896

119898=

119899119904

sum

119895=1

sum

119894isinID119898

tr119895119904

1198880

119902119895

119894119896 forall119896 isin K 119898 = 1 119872 (23)

Using (23) and averaging the utilization on differentchannels and different interference domain heads we have

119883LS =

1

119872119870

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

tr119895119904

1198880

119902119895

119894119896 (24)

119883LS(119886)

=

1198790

1198721198701198880

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (25)

where (119886) comes from assumption tr119895119904= 1198790 Under conditions

(i) and (ii) in Definition 5 and using (2)ndash(4) we obtain

NT =

1

119899119904

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (26)

Thus (25) can be simplified as

119883LS =

1198991199041198790NT

1198721198701198880

(27)

As a result since 120591 = 1198991199041198790 the networkrsquos throughput can

be obtained as 120591 = (1198721198701198880119873119879)119883

119871119878

Corollary 7 Under the same conditions as in Theorem 2considering 119862 = 119877119888

0and replacing 119873119879 with the result in

(16) the broadcast throughput of a large-scale MCMR-WMNis expressed in terms of the average node utilization and theaverage channel utilization as follows

120591 =

1198880

119899 minus 1

(119899119877119880 minus 119872119870119883119871119878

) (28)

It is clear that different parameters of the network interactwith each other Thus it is not possible to draw a specifiedboundary between themDue to the limited number of radiosand non-overlapping channels proper use of the resourcescould improve the performance of the network In thisregard as we will show in the next section the number oftransmissions and the load-balancing significantly affect thenetworkrsquos throughput

6 Numerical Results

In this section we present a comprehensive evaluation onthe relationship between the networkrsquos throughput and theresource utilizations For this purpose we apply the followingprotocols in a single-rate framework SPT-JCRS [7] MCM-JCRS [7] IRMT [20] and IRBT [20] In our Matlab simula-tion setup as shown in Figure 3 we consider a 6 times 6 squaregrid with 119899 = 36 and119872 = 4 where nodes 8 11 26 and 29 arethe interference domain heads The grid length (the distancebetween neighbor nodes in the same row or column) and theinterference range are set to 150m and 280m respectivelyWe also use the random channel assignment in which theradios of each node are randomly assigned to the distinctchannels Obviously in the cases that the number of channelsis less than or equal to the number of radios this method willact as the common channel assignment strategy

In the simulations the broadcast session requests arriveone by one at the network without any knowledge of thefuture requests The source of each session is selected ran-domly In addition the trafficmodel of all sessions is assumedto be Constant Bit Rate (CBR)with tr119895

119904= 04Mbps Assuming

119877 = 3 1198880

= 12Mbps and 25 broadcast session requests westudy the performance of the network for different numberof channels that is 119870 = 1 6 It is clear that in thecase of 119870 = 1 we have a SCSR-WMN Figure 4 comparesthe throughput of the aforementioned protocols in terms ofthe number of channels 119870 In addition Table 1 shows thesimulation results inmore details It should be noted that eachdata point is obtained by averaging the results of 15 individualruns on different randomly experiments In this table NT119880 119883LS and 120591sim present the experimental results obtainedfor the average number of transmissions the average nodeutilization the average channel utilization and the networkrsquosthroughput respectively It is worth noting that the results inTable 1 exactly follow the described theoretical relationshipsin (16) (22) and (28) As an example Table 1 compares 120591simwith the theoretical throughput 120591theory extracted from (28)Obviously 120591sim is similar to 120591theory for different number of

The Scientific World Journal 7

1205851 1205852 1205853

1205854 1205855 1205856

1205857 1205858 1205859

ID1 ID2 ID3

ID7 ID8 ID9

(a)

2radic2L0

radic2L0

radic5L0

2L0

r

(b)

Figure 2 (a) A typical grid MCMR-WMN with its interference domains (b) an interference domain

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

8

11

26

29

150m

150m

Figure 3 The grid topology considered in the simulations

channels This shows the validity of our analysis This com-parison can be also verified for relationships (16) and (22)It is clear that different parameters of the network interactwith each other In this situation given the limited numberof radios and channels proper use of the resources couldimprove the performance of the network Actually using anefficient traffic engineering mechanism leads to better spec-trum utilization and increases the fairness in the networkThusmore resources will be available for accepting the futuresessions and the overall throughput will be increased In thisregard it is observed that the performance of the IRBT andthe IRMT algorithms much better than that of the othertwo algorithms In fact the IRBT and the IRMT algorithms

jointly address the transmission channel selection and theload-balanced routing tree construction [20] These schemesnot only take into account the number of transmissions butalso consider both inter-flow and intra-flow interferences toroute the sessions through alternative feasible pathsThus thetraffic load is balanced in the network However the MCM-JCRS and the SPT-JCRS algorithms cannot efficiently usethe resources of the network due to being limited to non-interference-aware routing trees

In [20] we demonstrated that the IRBT algorithm bal-ances the traffic load in the network more efficiently than theIRMTalgorithmThe results in Table 1 also confirm this issueFrom this table we can see that the IRBT approach improvesthe utilization of the network resources For 119870 = 1 2 3

(ie common channel assignment) although the IRMTalgorithm leads to less number of transmissions than theIRBT algorithm the load-balancing ability of the IRBTmakesboth schemes have the same networkrsquos throughput If thetraffic load in the network is balanced the interference willbe decreased and consequently the call acceptance rate willbe increased In contrast for 119870 gt 3 both IRMT and IRBTalgorithms nearly have the same number of transmissions Inthis situation the load-balancing factor plays more efficientrole in the networkrsquos performance This causes the IRBTalgorithm to show better throughput

On the other hand by increasing the number of channelsfirst the networkrsquos throughput linearly increases Howeverfor 119870 gt 3 it is gradually saturated Due to the randomchannel assignment strategy further increasing of the chan-nels leads to the less number of common channels betweenthe neighbor nodes Thus the possibility of enjoying thewireless broadcast advantagewill be decreasedThis increasesthe number of transmissions as shown in Table 1 In this

8 The Scientific World Journal

Table 1 Performance comparison for different number of channels

Number of channels Algorithm NT 119880 119883LS 120591sim (Mbps) 120591theory (Mbps)

119870 = 1

IRBT 20002 00961 09428 22667 22655IRMT 159444 00912 077 232 2321

MCM-JCRS 181 00787 07239 192 19214SPT-JCRS 2395 00703 07717 15467 15448

119870 = 2

IRBT 197273 01998 09722 47333 47317IRMT 159967 01888 07993 48 47986

MCM-JCRS 178833 01578 07205 38667 38669SPT-JCRS 233780 01411 07628 31333 31325

119870 = 3

IRBT 200016 02970 09719 7 69988IRMT 162761 02769 07911 7 69984

MCM-JCRS 18225 02481 07644 604 60418SPT-JCRS 234697 02093 07561 464 46392

119870 = 4

IRBT 202207 03702 09144 86909 86918IRMT 186563 03086 07244 74545 74531

MCM-JCRS 18966 02483 0589 59636 59631SPT-JCRS 241418 02455 06761 53818 53816

119870 = 5

IRBT 215448 03909 08040 896 89613IRMT 206932 03043 06105 708 70815

MCM-JCRS 217823 02225 04608 508 50791SPT-JCRS 26238 02155 04987 456 456

119870 = 6

IRBT 239454 03929 07182 864 86388IRMT 236876 02862 05197 632 63212

MCM-JCRS 242579 02088 03854 456 45603SPT-JCRS 272301 02133 04204 444 44389

1 2 3 4 5 60

2

4

6

8

10

Number of channels (K)

Thro

ughp

ut (M

bps)

IRBT

IRMT

MCM-JCRS

SPT-JCRS

Figure 4 Networkrsquos throughput as function of the number ofchannels

situation the lack of load-balancing could sufficiently reducethe networkrsquos throughput

7 Conclusion

In this paper the throughput of a MCMR-WMN wasquantified We focused on the scenario of on-demand QoSmulticastbroadcast sessions where each session has a spe-cific bandwidth requirement In particular considering theresource constraints we derived analytical relationships forthe networkrsquos throughput in terms of the node utilization thechannel utilization and the number of transmissions Thisgives simple solutions for the future designs to predict thenetworkrsquos throughput based on the resource utilizations Inline with the proposed relationships we also demonstratedthat the networkrsquos throughput is significantly affected by bothnumber of transmissions and degree of load-balancing Onone hand minimizing the number of transmissions reducesthe use of the network resources On the other hand load-balancing increases the fairness in the network In thissituation more resources will be available for accepting thefuture sessions Thus the overall networkrsquos throughput willbe increased

Acknowledgment

This work is supported by the Iranian TelecommunicationResearch Center (ITRC)

The Scientific World Journal 9

References

[1] PH Pathak andRDutta ldquoA survey of network design problemsand joint design approaches in wireless mesh networksrdquo IEEECommunications Surveys and Tutorials vol 13 no 3 pp 396ndash428 2011

[2] A Raniwala and T-C Chiueh ldquoArchitecture and algorithms foran IEEE 80211-based multi-channel wireless mesh networkrdquo inProceedings of the IEEE International Conference on ComputerCommunications (INFOCOM rsquo05) vol 3 pp 2223ndash2234March2005

[3] A Avokh and G Mirjalily ldquoPerformance analysis of broad-casting in small-scale multi-radio multi-channel wireless meshnetworksrdquo in Proceedings of the 14th International Conference onAdvanced Communication Technology (ICACT rsquo12) pp 537ndash542February 2012

[4] U T Nguyen and J Xu ldquoMulticast routing in wireless meshnetworks minimum cost trees or shortest path treesrdquo IEEECommunications Magazine vol 45 no 11 pp 72ndash77 2007

[5] Y Li and I Chen ldquoDynamic agent-based hierarchical multicastfor wireless mesh networksrdquo Ad Hoc Networks vol 11 no 6 pp1683ndash1698 2013

[6] J E Wieselthier G D Nguyen and A Ephremides ldquoEnergy-efficient broadcast and multicast trees in wireless networksrdquoMobile Networks and Applications vol 7 no 6 pp 481ndash4922002

[7] A Avokh G Mirjalily and J Abouei ldquoJoint channel andrate selection for multicast routing trees in wireless meshnetworksrdquo in Proceedings of the International Symposium onTelecommunications pp 548ndash553 November 2012

[8] K N Ramachandran E M Belding K C Almeroth andM M Buddhikot ldquoInterference-aware channel assignment inmulti-radio wireless mesh networksrdquo in Proceedings of the 25thIEEE International Conference on Computer Communications(INFOCOM rsquo06) pp 1ndash12 April 2006

[9] R-H Jan S-Y Huang and C-F Wang ldquoAn upper bound ofthe throughput for multi-radio wireless mesh networksrdquo IEEECommunications Letters vol 14 no 8 pp 698ndash700 2010

[10] A Capone G Carello I Filippini S Gualandi and F Malu-celli ldquoRouting scheduling and channel assignment in wirelessmesh networks optimization models and algorithmsrdquo Ad HocNetworks vol 8 no 6 pp 545ndash563 2010

[11] E Alotaibi V Ramamurthi M Batayneh and B MukherjeeldquoInterference-aware routing for multi-hop wireless mesh net-worksrdquo Computer Communications vol 33 no 16 pp 1961ndash1971 2010

[12] V C M Borges D Pereira M Curado and E MonteiroldquoRoutingmetric for interference and channel diversity inmulti-radio wireless mesh networksrdquo in Ad-Hoc Mobile and WirelessNetworks vol 5793 of Lecture Notes in Computer Science pp55ndash68 Springer Berlin Germany 2009

[13] S Roy D Koutsonikolas S Das and Y C Hu ldquoHigh-throughput multicast routing metrics in wireless mesh net-worksrdquo Ad Hoc Networks vol 6 no 6 pp 878ndash899 2008

[14] P M Ruiz and A F Gomez-Skarmeta ldquoApproximating optimalmulticast trees in wireless multihop networksrdquo in Proceedings ofthe 10th IEEE Symposium on Computers and Communications(ISCC rsquo05) pp 686ndash691 June 2005

[15] H L Nguyen and U T Nguyen ldquoBandwidth efficient multicastrouting in multi-channel multi-radio wireless mesh networksrdquoin Proceedings of the International Conference on Ultra Modern

Telecommunications and Workshops (ICUMT rsquo09) pp 1ndash8October 2009

[16] G Zeng B Wang Y Ding L Xiao and M Mutka ldquoEfficientmulticast algorithms formultichannel wireless mesh networksrdquoIEEE Transactions on Parallel and Distributed Systems vol 21no 1 pp 86ndash99 2010

[17] H S Chiu K L Yeung and K-S Lui ldquoMaximizing broadcastload in multi-channel Multi-interface wireless mesh networksrdquoin Proceedings of the IEEE Global Telecommunications Confer-ence (GLOBECOM rsquo08) pp 533ndash537 December 2008

[18] F Li Y Fang F Hu and X Liu ldquoLoad-aware multicast routingmetrics in multi-radio multi-channel wireless mesh networksrdquoComputer Networks vol 55 no 9 pp 2150ndash2167 2011

[19] P A K Acharya and E M Belding ldquoMARS link-layer rateselection for multicast transmissions in wireless mesh net-worksrdquo Ad Hoc Networks vol 9 no 1 pp 48ndash60 2011

[20] A Avokh and G Mirjalily ldquoInterference-aware multicast andbroadcast routing in wireless mesh networks using both rateand channel diversityrdquo Computers amp Electrical Engineering2013

[21] T Kim Y Yang J C Hou and S V Krishnamurthy ldquoResourceallocation for QoS support in wireless mesh networksrdquo IEEETransactions on Wireless Communications vol 12 no 5 pp2046ndash2054 2013

[22] W Kocay and D Kreher Graphs Algorithms and Optimiza-tion Discrete Mathematics and Its Applications Chapman ampHallCRC Boca Raton Fla USA 2005

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The Scientific World Journal 3

as acknowledgments and retransmissions) to improve thereliability of high-throughput multicast flows

During recent years we have considered the problem oftraffic engineering for multicastbroadcast flows in WMNs[3 7 20] The work in [3] studies the special case ofbroadcasting for the small-scale WMNs In [7] we presentan Interference-Aware Joint Channel and Rate Selection (IA-JCRS) algorithm to choose the best transmission rates andthe best transmission channels for a given fixed routingtree However being bound to a routing tree reduces thefreedom to choose the alternative feasible paths Indeedusing a joint interference-aware routing scheme leads toa better utilization of the network resources Accordinglyin [20] we propose two cross-layer algorithms named theldquoInterference- and Rate-aware Multicast Tree (IRMT)rdquo andthe ldquoInterference- and Rate-aware Broadcast Tree (IRBT)rdquoAs an advantage the proposed algorithms jointly address theproblems of multicastbroadcast routing tree constructiontransmission rate selection transmission channel selectionand call admission control

One drawback of the previous works is that they pay lessattention to the theoretical analysis of multicastbroadcastflows Most of the literature tries to propose some heuristi-cally or optimally solutions to improve different aspects of thenetwork Unlike the previous works this paper quantifies themulticast and the broadcast throughput in both small-scaleMCMR-WMN and large-scale MCMR-WMN In this regardwe also present a simulation-based discussion to simulta-neously study the effects of load-balancing and number oftransmissions on the networkrsquos throughput

3 Network Model and Assumptions

We consider a typical MCMR-WMN consisting of 119899 sta-tionary nodes (In this paper the terms ldquomesh routerrdquo andldquonoderdquo are used interchangeably for convenience) Each node119909 is equipped with 119877

119909half-duplex radios tuned to one of

the 119870 available non-overlapping channels where no channelswitching is allowed For the sake of efficiency the radiosof a node are tuned to different non-overlapping channelsWhen a radio of a node transmits or receives the packets ona channel other radios of the same node are able to com-municate at the same time with neighboring nodes on otherchannels In this paper a single-rate framework is assumedfor all link-layer transmissions In addition we suppose thatthe radios of the nodes are equipped with omnidirectionalantennas characterized by the same transmission range andthe same interference range Node 119909 is directly connectedto node 119910 and forms a wireless link if and only if node 119910

is within the transmission range of node 119909 and they share acommon channel In this regard we model the network as adirected graph G = (VE) where V = V

1 V2 V

119899 is the

set of vertices representing 119899 nodes and E denotes the set ofcommunication links In this work we consider the trafficmodel of on-demand multicastbroadcast sessions whereeach admitted session creates a unique tree with a specificbandwidth requirement In this way we adopt a schedule-based MAC protocol in which the conflict-free transmission

is ensured by assigning the interfering transmitters to eithersend on different non-overlapping channels or send on thesame channel but at different time slots

4 Problem Formulation

The limited number of radios and the shared nature of wire-less medium impose some resource constraints on MCMR-WMNs In this section we derive a formulation to capturethe utilization of the network resources and to analyze thefeasibility of multicastbroadcast session requests

Definition 1 The capacity of the 119894th mesh router is definedas 119862(119894) = 119877

1198941198880 where 119877

119894represents the number of its radios

and 1198880is the capacity of the channels In addition we define

the sent and the received traffic loads of the 119894th mesh routerdenoted by 119897

119904(119894) and 119897

119903(119894) respectively as 119897

119904(119894) = sum

119877119894

119887=1119897119904119887(119894)

and 119897119903(119894) = sum

119877119894

119887=1119897119903119887(119894) 119894 = 1 119899 where 119897

119904119887(119894) and 119897

119903119887(119894) are

the sent and the received traffic loads of the 119887th radio in the119894th mesh router respectivelyThus the total traffic load of the119894th mesh router is obtained as 119897(119894) = 119897

119904(119894) + 119897

119903(119894) 119894 = 1 119899

According to the assumption of the half-duplex radioseach radio can only send or receive on a fixed channel 119896 atany time slot therefore it is required that

119897119904119887

(119894) + 119897119903119887

(119894) le 1198880 forall119894 isin V 119887 = 1 119877

119894 (1)

Let 119897119895119894denote the created load by the 119895th session on the 119894th

mesh routerThus the total load of the 119894thmesh router can berewritten as 119897(119894) = sum

119899119904

119895=1119897119895

119894 119894 = 1 119899 where 119899

119904is the number

of active sessions In general each multicastbroadcast tree119879119895 is composed of a set of MAC multicast transmissions on

different nodes and channels The number of transmissionsof node 119894 at the 119895th tree denoted by NT119895

119894 is given by

NT119895119894= sum

119896isinK119902119895

119894119896 119894 = 1 119899 (2)

where K is the set of 119870 available non-overlapping channelsand 119902

119895

119894119896= 1 if node 119894 is a forwarding node on channel 119896 at

the 119895th tree and 119902119895

119894119896= 0 otherwise In this case we define the

total number of transmissions for the 119895th tree as

NT (119879119895) = sum

119894isinVNT119895119894 (3)

In fact NT(119879119895) shows the number of transmissions required

to deliver one packet from the source node to all the desti-nations at the 119895th multicastbroadcast tree Thus the averagenumber of transmissions per active session is expressed as

NT =

1

119899119904

119899119904

sum

119895=1

NT (119879119895) (4)

Since more transmissions take longer time on schedul-ing frame minimizing the number of transmissions helpsto improve the networkrsquos throughput In a typical multi-castbroadcast tree 119879

119895 there are three kinds of nodes source

4 The Scientific World Journal

A

C

D

G

H

E

B

F

L

I

1

1

1

1

2

2

2

2

3

3

3

M

N

P

K

J

Figure 1 A typical multicast routing tree

node 119904119895 forwarding nodes set (FWD119895) and leaf nodes

set (LF119895) For example consider the multicast tree shownin Figure 1 Here the number associated with each linkrepresents the channel assigned to that link All nodes of treeexcept the source node have one parent The source node(eg node A) as the root of the tree sends data toward itschildren A forwarding node (eg nodes BC E F and I) actsas both parent and child node as a child node it receives datafrom its parent while in the role of a parent node it sends thetraffic toward its children A leaf node (eg nodesD K LMN and P) only plays the role of a child and receives data fromits parent It is clear from Figure 1 that NT119895

119860= NT119895119861= NT119895119862

=

NT119895119864= 1 while NT119895

119868= NT119895119865= 2 (ie NT(119879

119895) = 8)

Since we assume the bandwidth-guaranteed trees withbandwidth requirement tr119895

119904 the created load by the 119895th

session on the 119894th node can be generally formulated by therole of node and the number of its transmissions as

119897119895

119894=

tr119895119904(1 + NT119895

119894) if 119894 isin FWDj

tr119895119904times NT119895119894

if 119894 = 119904119895

tr119895119904

if 119894 isin LF1198950 if 119894 notin 119879

119895

(5)

Here we define the utilization of the 119894th mesh routerdenoted by 119880(119894) as follows

119880 (119894) =

119897 (119894)

119862 (119894)

=

1

119862 (119894)

119899119904

sum

119895=1

119897119895

119894 (6)

where119880(119894) indicates the percentage of the 119894th nodersquos capacityused for routing of 119899

119904multicastbroadcast sessions For this

case the average utilization of the nodes is defined as

119880 =

1

119899

119899

sum

119894=1

119880 (119894) (7)

where 119899 is the total number of nodes in the networkOn the other hand due to the shared nature of thewireless

medium adjacent transmissions cannot occur simultane-ously on the same channel To formulate this issue we use

the channel utilization concept defined in [17] with minormodifications For the described MCMR-WMNmodel con-sider a fixed transmission rate of 119888

0 Each MAC multicast

transmission in the 119895th routing tree uses a time fraction ofthe scheduling frame that is equal to tr119895

1199041198880 By definition

the utilization of channel 119896 observed by node 119910 (119883119896119910) is the

sum of the time fractions assigned to all nodes within theinterference range of node 119910 that are intended to transmit onchannel 119896Thus considering 119899

119904admittedmulticastbroadcast

sessions the utilization of channel 119896 observed by node 119910 isformulated as

119883119896

119910=

119899119904

sum

119895=1

sum

119894isinintf(119910)

tr119895119904

1198880

119902119895

119894119896 (8)

where intf(119910) denotes the set of interfering nodes locatedwithin the interference range of node 119910 For this case thechannel capacity constraint is given by

119883119896

119910le 1 forall119910 isin V forall119896 isin ch list (119910) (9)

where ch list(119910) indicates the set of assigned channelsto the radios of node 119910 Since the radios of each nodeare assigned to different non-overlapping channels and nochannel switching is allowed one can show that condition(9) satisfies the described condition in (1) Therefore thebandwidth-guaranteed multicastbroadcast sessions are fea-sible and schedulable if all interfering transmissions have atotal load less than the normalized channel capacity Differentfrom the best-effort routing algorithms quality of service(QoS) routing algorithms must use call admission controlmechanisms to protect the QoS requirements of the existingflows [17 21] Clearly it is desired to maximize the numberof admitted sessions In this regard we define the networkrsquosthroughput denoted by 120591 as the sum of the traffic load of alladmitted feasible sessions as 120591 = sum

119899119904

119895=1tr119895119904

5 Networkrsquos Throughput versus ResourceUtilizations in MCMR-WMNs

In this section we aim to derive analytical relationships forthe networkrsquos throughput in terms of the node utilizationsthe channel utilizations and the number of transmissions

Theorem 2 If all sessions have the same traffic load forexample tr119895

119904= 1198790 and the capacity of all nodes in the network

is identical for example 119877119894= 119877 and 119862(119894) = 119862 the average

number of transmissions for the multicast flows is expressed as

NT =

119899119862

1198991199041198790

119880 minus 119882 (10)

where 119899119904and 119880 denote the number of admitted sessions and

the average node utilization respectively In addition 119882 =

(1119899119904) sum119899119904

119895=1119882119895 shows the average number of links in the tree of

each session and119882119895 is the number of links in the 119895th multicast

tree

The Scientific World Journal 5

Proof Under the assumption 119862(119894) = 119862 and using (6) and (7)we have

119880 =

1

119899119862

119899119904

sum

119895=1

119899

sum

119894=1

119897119895

119894

(119886)

=

1

119899119862

119899119904

sum

119895=1

( sum

119894isinFWD119895tr119895119904(1 + NT119895

119894) + tr119895119904NT119895119904+ sum

119894isin119871119865119895

tr119895119904)

=

1198790

119899119862

119899119904

sum

119895=1

( sum

119894isin119904119895FWD119895

NT119895119894+

10038161003816100381610038161003816FWD1198951003816100381610038161003816

1003816+

10038161003816100381610038161003816LF1198951003816100381610038161003816

1003816)

(11)

where (119886) comes from (5) and the fact that each multicastrouting tree includes three kinds of nodes a source nodeforwarding nodes and leaf nodes In the above equationsNT119895119904is the number of transmissions of source node and

|FWD119895| and |LF119895| denote the number of forwarding nodesand leaf nodes at the 119895th tree respectively On the other handfrom the graph theory [22]

10038161003816100381610038161003816FWD1198951003816100381610038161003816

1003816+

10038161003816100381610038161003816LF1198951003816100381610038161003816

1003816= 119882119895 (12)

Thus (11) can be simplified as

119880 =

1198790

119899119862

119899119904

sum

119895=1

( sum

119894isin119904119895FWD119895

NT119895119894+ 119882119895)

=

1198790

119899119862

[

[

119899119904

sum

119895=1

sum

119894isin119904119895FWD119895

NT119895119894+

119899119904

sum

119895=1

119882119895]

]

(13)

According to (3) and (4) and considering the fact thatNT119895119894= 0 for 119894 notin 119904

119895 FWD119895 we have

NT =

1

119899119904

119899119904

sum

119895=1

sum

119894isin119904119895FWD119895

NT119895119894 (14)

Thus

119880 =

1198790

119899119862

[119899119904NT + 119899

119904119882] =

1198991199041198790

119899119862

[NT + 119882] (15)

As a result NT = (1198991198621198991199041198790)119880 minus 119882

Corollary 3 For the broadcast case (12) can be rewritten as|FWD119895| + |119871119865

119895| = 119899 minus 1 [22] Thus

119873119879 =

119899119862

1198991199041198790

119880 minus 119899 + 1 (16)

In the rest of the section we first present the problemfor the small-scale MCMR-WMNs and then we extend ourwork to the case of large-scale MCMR-WMNs In additiondue to the similarity of equations for the multicast andthe broadcast sessions we follow the problem only for thebroadcast sessions

Small-Scale MCMR-WMNs In a small-scale MCMR-WMNwe suppose that all nodes are located in the interference range

of each other Thus the channel utilization observed by anynode is identical For a small-scale MCMR-WMN we definethe utilization of channel 119896 denoted by 119883

119896 and the averagechannel utilization 119883SS as follows

119883119896=

119899119904

sum

119895=1

sum

119894isinV

tr119895119904

1198880

119902119895

119894119896 forall119896 isin K (17)

119883SS =

1

119870

119870

sum

119896=1

119883119896 (18)

Lemma 4 Under the same conditions as in Theorem 2the broadcast throughput of a small-scale MCMR-WMN isexpressed in terms of the average node utilization and theaverage channel utilization as follows

120591 =

1198880

119899 minus 1

(119899119877119880 minus 119870X119878119878) (19)

Proof Using (17) and averaging the utilization on differentchannels we have

119883SS =

1

119870

119899119904

sum

119895=1

119870

sum

119896=1

sum

119894isinV

tr119895119904

1198880

119902119895

119894119896

(119886)

=

1198991199041198790

1198701198880

NT (20)

where (119886) comes from (2)ndash(4) and the assumption tr119895119904= 1198790

Considering 120591 = 1198991199041198790 119862 = 119877119888

0 and replacing NT with the

result in (16) for broadcast sessions the throughput 120591 can beexpressed as 120591 = (119888

0119899 minus 1)(119899119877119880 minus 119870119883SS)

Large-Scale MCMR-WMNs Now we extend the result ofLemma 4 to the large-scale MCMR-WMN case In generalthe channel utilization is a location-dependent parameterHowever due to the shared nature of the wireless mediumthe channel utilizations observed by neighboring nodes areclose to each other Thus considering the channel utilizationobserved by all nodes gives a lot of redundancy One idea isto study the channel utilization observed by a special nodeon behalf of its neighbors To address this solution we definethe ldquointerference domain (ID)rdquo and the ldquointerference domainheadrdquo as follows

Definition 5 The ldquointerference domainrdquo is defined as a subsetof the networkrsquos nodes which satisfies three conditions

(i) The interference domains have no common node thatis ID119894⋂ ID119895= Oslash 119894 = 119895

(ii) The interference domains span all nodes in the net-work that is ⋃119872

119898=1ID119898

= V where 119872 denotes thetotal number of interference domains

(iii) Each interference domain for example the 119898thinterference domain includes a node denoted by 120585

119898

so that only the nodes of ID119898

are located withinthe interference range of 120585

119898 We define 120585

119898as the

ldquointerference domain headrdquo of ID119898

It is clear from Definition 5 that a small-scale MCMR-WMN is a special case which consists of only one interference

6 The Scientific World Journal

domain The feasibility of condition (iii) is justified by thefact that mesh routers are usually deployed with carefulplanning To clarify the above definition consider a typicalgrid topology plotted in Figure 2 as a popular topology forthe WMNs Let the grid length be set to 119871

0 In this case

for the interference range 119889intf assume radic21198710

lt 119889intf lt 21198710

which is a reasonable interference range [2] Thus we canmodel the interference domains as a 3 times 3 square grids asshown in Figure 2(b) This modeling satisfies conditions (i)ndash(iii) in Definition 5 In Figure 2(a) each circle represents aninterference domain and the central black nodes play the roleof the corresponding interference domain head

Now let the network be composed of 119872 interferencedomains ID

1 ID

119872 For large-scale MCMR-WMNs we

define the average channel utilization 119883LS as follows

119883LS =

1

119872119870

119870

sum

119896=1

119872

sum

119898=1

119883119896

119898 (21)

where 119883119896

119898denotes the utilization of channel 119896 observed by

the 119898th interference domain head

Theorem 6 Assume all sessions have the same traffic load forexample 119905119903119895

119904= 1198790 The networkrsquos throughput of the large-scale

MCMR-WMN is obtained as

120591 =

1198721198701198880

119873119879

119883119871119878

(22)

Proof According to (8) and considering the condition (iii) inDefinition 5 the utilization of the channel 119896 observed by the119898th interference domain head is given by

119883119896

119898=

119899119904

sum

119895=1

sum

119894isinID119898

tr119895119904

1198880

119902119895

119894119896 forall119896 isin K 119898 = 1 119872 (23)

Using (23) and averaging the utilization on differentchannels and different interference domain heads we have

119883LS =

1

119872119870

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

tr119895119904

1198880

119902119895

119894119896 (24)

119883LS(119886)

=

1198790

1198721198701198880

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (25)

where (119886) comes from assumption tr119895119904= 1198790 Under conditions

(i) and (ii) in Definition 5 and using (2)ndash(4) we obtain

NT =

1

119899119904

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (26)

Thus (25) can be simplified as

119883LS =

1198991199041198790NT

1198721198701198880

(27)

As a result since 120591 = 1198991199041198790 the networkrsquos throughput can

be obtained as 120591 = (1198721198701198880119873119879)119883

119871119878

Corollary 7 Under the same conditions as in Theorem 2considering 119862 = 119877119888

0and replacing 119873119879 with the result in

(16) the broadcast throughput of a large-scale MCMR-WMNis expressed in terms of the average node utilization and theaverage channel utilization as follows

120591 =

1198880

119899 minus 1

(119899119877119880 minus 119872119870119883119871119878

) (28)

It is clear that different parameters of the network interactwith each other Thus it is not possible to draw a specifiedboundary between themDue to the limited number of radiosand non-overlapping channels proper use of the resourcescould improve the performance of the network In thisregard as we will show in the next section the number oftransmissions and the load-balancing significantly affect thenetworkrsquos throughput

6 Numerical Results

In this section we present a comprehensive evaluation onthe relationship between the networkrsquos throughput and theresource utilizations For this purpose we apply the followingprotocols in a single-rate framework SPT-JCRS [7] MCM-JCRS [7] IRMT [20] and IRBT [20] In our Matlab simula-tion setup as shown in Figure 3 we consider a 6 times 6 squaregrid with 119899 = 36 and119872 = 4 where nodes 8 11 26 and 29 arethe interference domain heads The grid length (the distancebetween neighbor nodes in the same row or column) and theinterference range are set to 150m and 280m respectivelyWe also use the random channel assignment in which theradios of each node are randomly assigned to the distinctchannels Obviously in the cases that the number of channelsis less than or equal to the number of radios this method willact as the common channel assignment strategy

In the simulations the broadcast session requests arriveone by one at the network without any knowledge of thefuture requests The source of each session is selected ran-domly In addition the trafficmodel of all sessions is assumedto be Constant Bit Rate (CBR)with tr119895

119904= 04Mbps Assuming

119877 = 3 1198880

= 12Mbps and 25 broadcast session requests westudy the performance of the network for different numberof channels that is 119870 = 1 6 It is clear that in thecase of 119870 = 1 we have a SCSR-WMN Figure 4 comparesthe throughput of the aforementioned protocols in terms ofthe number of channels 119870 In addition Table 1 shows thesimulation results inmore details It should be noted that eachdata point is obtained by averaging the results of 15 individualruns on different randomly experiments In this table NT119880 119883LS and 120591sim present the experimental results obtainedfor the average number of transmissions the average nodeutilization the average channel utilization and the networkrsquosthroughput respectively It is worth noting that the results inTable 1 exactly follow the described theoretical relationshipsin (16) (22) and (28) As an example Table 1 compares 120591simwith the theoretical throughput 120591theory extracted from (28)Obviously 120591sim is similar to 120591theory for different number of

The Scientific World Journal 7

1205851 1205852 1205853

1205854 1205855 1205856

1205857 1205858 1205859

ID1 ID2 ID3

ID7 ID8 ID9

(a)

2radic2L0

radic2L0

radic5L0

2L0

r

(b)

Figure 2 (a) A typical grid MCMR-WMN with its interference domains (b) an interference domain

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

8

11

26

29

150m

150m

Figure 3 The grid topology considered in the simulations

channels This shows the validity of our analysis This com-parison can be also verified for relationships (16) and (22)It is clear that different parameters of the network interactwith each other In this situation given the limited numberof radios and channels proper use of the resources couldimprove the performance of the network Actually using anefficient traffic engineering mechanism leads to better spec-trum utilization and increases the fairness in the networkThusmore resources will be available for accepting the futuresessions and the overall throughput will be increased In thisregard it is observed that the performance of the IRBT andthe IRMT algorithms much better than that of the othertwo algorithms In fact the IRBT and the IRMT algorithms

jointly address the transmission channel selection and theload-balanced routing tree construction [20] These schemesnot only take into account the number of transmissions butalso consider both inter-flow and intra-flow interferences toroute the sessions through alternative feasible pathsThus thetraffic load is balanced in the network However the MCM-JCRS and the SPT-JCRS algorithms cannot efficiently usethe resources of the network due to being limited to non-interference-aware routing trees

In [20] we demonstrated that the IRBT algorithm bal-ances the traffic load in the network more efficiently than theIRMTalgorithmThe results in Table 1 also confirm this issueFrom this table we can see that the IRBT approach improvesthe utilization of the network resources For 119870 = 1 2 3

(ie common channel assignment) although the IRMTalgorithm leads to less number of transmissions than theIRBT algorithm the load-balancing ability of the IRBTmakesboth schemes have the same networkrsquos throughput If thetraffic load in the network is balanced the interference willbe decreased and consequently the call acceptance rate willbe increased In contrast for 119870 gt 3 both IRMT and IRBTalgorithms nearly have the same number of transmissions Inthis situation the load-balancing factor plays more efficientrole in the networkrsquos performance This causes the IRBTalgorithm to show better throughput

On the other hand by increasing the number of channelsfirst the networkrsquos throughput linearly increases Howeverfor 119870 gt 3 it is gradually saturated Due to the randomchannel assignment strategy further increasing of the chan-nels leads to the less number of common channels betweenthe neighbor nodes Thus the possibility of enjoying thewireless broadcast advantagewill be decreasedThis increasesthe number of transmissions as shown in Table 1 In this

8 The Scientific World Journal

Table 1 Performance comparison for different number of channels

Number of channels Algorithm NT 119880 119883LS 120591sim (Mbps) 120591theory (Mbps)

119870 = 1

IRBT 20002 00961 09428 22667 22655IRMT 159444 00912 077 232 2321

MCM-JCRS 181 00787 07239 192 19214SPT-JCRS 2395 00703 07717 15467 15448

119870 = 2

IRBT 197273 01998 09722 47333 47317IRMT 159967 01888 07993 48 47986

MCM-JCRS 178833 01578 07205 38667 38669SPT-JCRS 233780 01411 07628 31333 31325

119870 = 3

IRBT 200016 02970 09719 7 69988IRMT 162761 02769 07911 7 69984

MCM-JCRS 18225 02481 07644 604 60418SPT-JCRS 234697 02093 07561 464 46392

119870 = 4

IRBT 202207 03702 09144 86909 86918IRMT 186563 03086 07244 74545 74531

MCM-JCRS 18966 02483 0589 59636 59631SPT-JCRS 241418 02455 06761 53818 53816

119870 = 5

IRBT 215448 03909 08040 896 89613IRMT 206932 03043 06105 708 70815

MCM-JCRS 217823 02225 04608 508 50791SPT-JCRS 26238 02155 04987 456 456

119870 = 6

IRBT 239454 03929 07182 864 86388IRMT 236876 02862 05197 632 63212

MCM-JCRS 242579 02088 03854 456 45603SPT-JCRS 272301 02133 04204 444 44389

1 2 3 4 5 60

2

4

6

8

10

Number of channels (K)

Thro

ughp

ut (M

bps)

IRBT

IRMT

MCM-JCRS

SPT-JCRS

Figure 4 Networkrsquos throughput as function of the number ofchannels

situation the lack of load-balancing could sufficiently reducethe networkrsquos throughput

7 Conclusion

In this paper the throughput of a MCMR-WMN wasquantified We focused on the scenario of on-demand QoSmulticastbroadcast sessions where each session has a spe-cific bandwidth requirement In particular considering theresource constraints we derived analytical relationships forthe networkrsquos throughput in terms of the node utilization thechannel utilization and the number of transmissions Thisgives simple solutions for the future designs to predict thenetworkrsquos throughput based on the resource utilizations Inline with the proposed relationships we also demonstratedthat the networkrsquos throughput is significantly affected by bothnumber of transmissions and degree of load-balancing Onone hand minimizing the number of transmissions reducesthe use of the network resources On the other hand load-balancing increases the fairness in the network In thissituation more resources will be available for accepting thefuture sessions Thus the overall networkrsquos throughput willbe increased

Acknowledgment

This work is supported by the Iranian TelecommunicationResearch Center (ITRC)

The Scientific World Journal 9

References

[1] PH Pathak andRDutta ldquoA survey of network design problemsand joint design approaches in wireless mesh networksrdquo IEEECommunications Surveys and Tutorials vol 13 no 3 pp 396ndash428 2011

[2] A Raniwala and T-C Chiueh ldquoArchitecture and algorithms foran IEEE 80211-based multi-channel wireless mesh networkrdquo inProceedings of the IEEE International Conference on ComputerCommunications (INFOCOM rsquo05) vol 3 pp 2223ndash2234March2005

[3] A Avokh and G Mirjalily ldquoPerformance analysis of broad-casting in small-scale multi-radio multi-channel wireless meshnetworksrdquo in Proceedings of the 14th International Conference onAdvanced Communication Technology (ICACT rsquo12) pp 537ndash542February 2012

[4] U T Nguyen and J Xu ldquoMulticast routing in wireless meshnetworks minimum cost trees or shortest path treesrdquo IEEECommunications Magazine vol 45 no 11 pp 72ndash77 2007

[5] Y Li and I Chen ldquoDynamic agent-based hierarchical multicastfor wireless mesh networksrdquo Ad Hoc Networks vol 11 no 6 pp1683ndash1698 2013

[6] J E Wieselthier G D Nguyen and A Ephremides ldquoEnergy-efficient broadcast and multicast trees in wireless networksrdquoMobile Networks and Applications vol 7 no 6 pp 481ndash4922002

[7] A Avokh G Mirjalily and J Abouei ldquoJoint channel andrate selection for multicast routing trees in wireless meshnetworksrdquo in Proceedings of the International Symposium onTelecommunications pp 548ndash553 November 2012

[8] K N Ramachandran E M Belding K C Almeroth andM M Buddhikot ldquoInterference-aware channel assignment inmulti-radio wireless mesh networksrdquo in Proceedings of the 25thIEEE International Conference on Computer Communications(INFOCOM rsquo06) pp 1ndash12 April 2006

[9] R-H Jan S-Y Huang and C-F Wang ldquoAn upper bound ofthe throughput for multi-radio wireless mesh networksrdquo IEEECommunications Letters vol 14 no 8 pp 698ndash700 2010

[10] A Capone G Carello I Filippini S Gualandi and F Malu-celli ldquoRouting scheduling and channel assignment in wirelessmesh networks optimization models and algorithmsrdquo Ad HocNetworks vol 8 no 6 pp 545ndash563 2010

[11] E Alotaibi V Ramamurthi M Batayneh and B MukherjeeldquoInterference-aware routing for multi-hop wireless mesh net-worksrdquo Computer Communications vol 33 no 16 pp 1961ndash1971 2010

[12] V C M Borges D Pereira M Curado and E MonteiroldquoRoutingmetric for interference and channel diversity inmulti-radio wireless mesh networksrdquo in Ad-Hoc Mobile and WirelessNetworks vol 5793 of Lecture Notes in Computer Science pp55ndash68 Springer Berlin Germany 2009

[13] S Roy D Koutsonikolas S Das and Y C Hu ldquoHigh-throughput multicast routing metrics in wireless mesh net-worksrdquo Ad Hoc Networks vol 6 no 6 pp 878ndash899 2008

[14] P M Ruiz and A F Gomez-Skarmeta ldquoApproximating optimalmulticast trees in wireless multihop networksrdquo in Proceedings ofthe 10th IEEE Symposium on Computers and Communications(ISCC rsquo05) pp 686ndash691 June 2005

[15] H L Nguyen and U T Nguyen ldquoBandwidth efficient multicastrouting in multi-channel multi-radio wireless mesh networksrdquoin Proceedings of the International Conference on Ultra Modern

Telecommunications and Workshops (ICUMT rsquo09) pp 1ndash8October 2009

[16] G Zeng B Wang Y Ding L Xiao and M Mutka ldquoEfficientmulticast algorithms formultichannel wireless mesh networksrdquoIEEE Transactions on Parallel and Distributed Systems vol 21no 1 pp 86ndash99 2010

[17] H S Chiu K L Yeung and K-S Lui ldquoMaximizing broadcastload in multi-channel Multi-interface wireless mesh networksrdquoin Proceedings of the IEEE Global Telecommunications Confer-ence (GLOBECOM rsquo08) pp 533ndash537 December 2008

[18] F Li Y Fang F Hu and X Liu ldquoLoad-aware multicast routingmetrics in multi-radio multi-channel wireless mesh networksrdquoComputer Networks vol 55 no 9 pp 2150ndash2167 2011

[19] P A K Acharya and E M Belding ldquoMARS link-layer rateselection for multicast transmissions in wireless mesh net-worksrdquo Ad Hoc Networks vol 9 no 1 pp 48ndash60 2011

[20] A Avokh and G Mirjalily ldquoInterference-aware multicast andbroadcast routing in wireless mesh networks using both rateand channel diversityrdquo Computers amp Electrical Engineering2013

[21] T Kim Y Yang J C Hou and S V Krishnamurthy ldquoResourceallocation for QoS support in wireless mesh networksrdquo IEEETransactions on Wireless Communications vol 12 no 5 pp2046ndash2054 2013

[22] W Kocay and D Kreher Graphs Algorithms and Optimiza-tion Discrete Mathematics and Its Applications Chapman ampHallCRC Boca Raton Fla USA 2005

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DistributedSensor Networks

International Journal of

4 The Scientific World Journal

A

C

D

G

H

E

B

F

L

I

1

1

1

1

2

2

2

2

3

3

3

M

N

P

K

J

Figure 1 A typical multicast routing tree

node 119904119895 forwarding nodes set (FWD119895) and leaf nodes

set (LF119895) For example consider the multicast tree shownin Figure 1 Here the number associated with each linkrepresents the channel assigned to that link All nodes of treeexcept the source node have one parent The source node(eg node A) as the root of the tree sends data toward itschildren A forwarding node (eg nodes BC E F and I) actsas both parent and child node as a child node it receives datafrom its parent while in the role of a parent node it sends thetraffic toward its children A leaf node (eg nodesD K LMN and P) only plays the role of a child and receives data fromits parent It is clear from Figure 1 that NT119895

119860= NT119895119861= NT119895119862

=

NT119895119864= 1 while NT119895

119868= NT119895119865= 2 (ie NT(119879

119895) = 8)

Since we assume the bandwidth-guaranteed trees withbandwidth requirement tr119895

119904 the created load by the 119895th

session on the 119894th node can be generally formulated by therole of node and the number of its transmissions as

119897119895

119894=

tr119895119904(1 + NT119895

119894) if 119894 isin FWDj

tr119895119904times NT119895119894

if 119894 = 119904119895

tr119895119904

if 119894 isin LF1198950 if 119894 notin 119879

119895

(5)

Here we define the utilization of the 119894th mesh routerdenoted by 119880(119894) as follows

119880 (119894) =

119897 (119894)

119862 (119894)

=

1

119862 (119894)

119899119904

sum

119895=1

119897119895

119894 (6)

where119880(119894) indicates the percentage of the 119894th nodersquos capacityused for routing of 119899

119904multicastbroadcast sessions For this

case the average utilization of the nodes is defined as

119880 =

1

119899

119899

sum

119894=1

119880 (119894) (7)

where 119899 is the total number of nodes in the networkOn the other hand due to the shared nature of thewireless

medium adjacent transmissions cannot occur simultane-ously on the same channel To formulate this issue we use

the channel utilization concept defined in [17] with minormodifications For the described MCMR-WMNmodel con-sider a fixed transmission rate of 119888

0 Each MAC multicast

transmission in the 119895th routing tree uses a time fraction ofthe scheduling frame that is equal to tr119895

1199041198880 By definition

the utilization of channel 119896 observed by node 119910 (119883119896119910) is the

sum of the time fractions assigned to all nodes within theinterference range of node 119910 that are intended to transmit onchannel 119896Thus considering 119899

119904admittedmulticastbroadcast

sessions the utilization of channel 119896 observed by node 119910 isformulated as

119883119896

119910=

119899119904

sum

119895=1

sum

119894isinintf(119910)

tr119895119904

1198880

119902119895

119894119896 (8)

where intf(119910) denotes the set of interfering nodes locatedwithin the interference range of node 119910 For this case thechannel capacity constraint is given by

119883119896

119910le 1 forall119910 isin V forall119896 isin ch list (119910) (9)

where ch list(119910) indicates the set of assigned channelsto the radios of node 119910 Since the radios of each nodeare assigned to different non-overlapping channels and nochannel switching is allowed one can show that condition(9) satisfies the described condition in (1) Therefore thebandwidth-guaranteed multicastbroadcast sessions are fea-sible and schedulable if all interfering transmissions have atotal load less than the normalized channel capacity Differentfrom the best-effort routing algorithms quality of service(QoS) routing algorithms must use call admission controlmechanisms to protect the QoS requirements of the existingflows [17 21] Clearly it is desired to maximize the numberof admitted sessions In this regard we define the networkrsquosthroughput denoted by 120591 as the sum of the traffic load of alladmitted feasible sessions as 120591 = sum

119899119904

119895=1tr119895119904

5 Networkrsquos Throughput versus ResourceUtilizations in MCMR-WMNs

In this section we aim to derive analytical relationships forthe networkrsquos throughput in terms of the node utilizationsthe channel utilizations and the number of transmissions

Theorem 2 If all sessions have the same traffic load forexample tr119895

119904= 1198790 and the capacity of all nodes in the network

is identical for example 119877119894= 119877 and 119862(119894) = 119862 the average

number of transmissions for the multicast flows is expressed as

NT =

119899119862

1198991199041198790

119880 minus 119882 (10)

where 119899119904and 119880 denote the number of admitted sessions and

the average node utilization respectively In addition 119882 =

(1119899119904) sum119899119904

119895=1119882119895 shows the average number of links in the tree of

each session and119882119895 is the number of links in the 119895th multicast

tree

The Scientific World Journal 5

Proof Under the assumption 119862(119894) = 119862 and using (6) and (7)we have

119880 =

1

119899119862

119899119904

sum

119895=1

119899

sum

119894=1

119897119895

119894

(119886)

=

1

119899119862

119899119904

sum

119895=1

( sum

119894isinFWD119895tr119895119904(1 + NT119895

119894) + tr119895119904NT119895119904+ sum

119894isin119871119865119895

tr119895119904)

=

1198790

119899119862

119899119904

sum

119895=1

( sum

119894isin119904119895FWD119895

NT119895119894+

10038161003816100381610038161003816FWD1198951003816100381610038161003816

1003816+

10038161003816100381610038161003816LF1198951003816100381610038161003816

1003816)

(11)

where (119886) comes from (5) and the fact that each multicastrouting tree includes three kinds of nodes a source nodeforwarding nodes and leaf nodes In the above equationsNT119895119904is the number of transmissions of source node and

|FWD119895| and |LF119895| denote the number of forwarding nodesand leaf nodes at the 119895th tree respectively On the other handfrom the graph theory [22]

10038161003816100381610038161003816FWD1198951003816100381610038161003816

1003816+

10038161003816100381610038161003816LF1198951003816100381610038161003816

1003816= 119882119895 (12)

Thus (11) can be simplified as

119880 =

1198790

119899119862

119899119904

sum

119895=1

( sum

119894isin119904119895FWD119895

NT119895119894+ 119882119895)

=

1198790

119899119862

[

[

119899119904

sum

119895=1

sum

119894isin119904119895FWD119895

NT119895119894+

119899119904

sum

119895=1

119882119895]

]

(13)

According to (3) and (4) and considering the fact thatNT119895119894= 0 for 119894 notin 119904

119895 FWD119895 we have

NT =

1

119899119904

119899119904

sum

119895=1

sum

119894isin119904119895FWD119895

NT119895119894 (14)

Thus

119880 =

1198790

119899119862

[119899119904NT + 119899

119904119882] =

1198991199041198790

119899119862

[NT + 119882] (15)

As a result NT = (1198991198621198991199041198790)119880 minus 119882

Corollary 3 For the broadcast case (12) can be rewritten as|FWD119895| + |119871119865

119895| = 119899 minus 1 [22] Thus

119873119879 =

119899119862

1198991199041198790

119880 minus 119899 + 1 (16)

In the rest of the section we first present the problemfor the small-scale MCMR-WMNs and then we extend ourwork to the case of large-scale MCMR-WMNs In additiondue to the similarity of equations for the multicast andthe broadcast sessions we follow the problem only for thebroadcast sessions

Small-Scale MCMR-WMNs In a small-scale MCMR-WMNwe suppose that all nodes are located in the interference range

of each other Thus the channel utilization observed by anynode is identical For a small-scale MCMR-WMN we definethe utilization of channel 119896 denoted by 119883

119896 and the averagechannel utilization 119883SS as follows

119883119896=

119899119904

sum

119895=1

sum

119894isinV

tr119895119904

1198880

119902119895

119894119896 forall119896 isin K (17)

119883SS =

1

119870

119870

sum

119896=1

119883119896 (18)

Lemma 4 Under the same conditions as in Theorem 2the broadcast throughput of a small-scale MCMR-WMN isexpressed in terms of the average node utilization and theaverage channel utilization as follows

120591 =

1198880

119899 minus 1

(119899119877119880 minus 119870X119878119878) (19)

Proof Using (17) and averaging the utilization on differentchannels we have

119883SS =

1

119870

119899119904

sum

119895=1

119870

sum

119896=1

sum

119894isinV

tr119895119904

1198880

119902119895

119894119896

(119886)

=

1198991199041198790

1198701198880

NT (20)

where (119886) comes from (2)ndash(4) and the assumption tr119895119904= 1198790

Considering 120591 = 1198991199041198790 119862 = 119877119888

0 and replacing NT with the

result in (16) for broadcast sessions the throughput 120591 can beexpressed as 120591 = (119888

0119899 minus 1)(119899119877119880 minus 119870119883SS)

Large-Scale MCMR-WMNs Now we extend the result ofLemma 4 to the large-scale MCMR-WMN case In generalthe channel utilization is a location-dependent parameterHowever due to the shared nature of the wireless mediumthe channel utilizations observed by neighboring nodes areclose to each other Thus considering the channel utilizationobserved by all nodes gives a lot of redundancy One idea isto study the channel utilization observed by a special nodeon behalf of its neighbors To address this solution we definethe ldquointerference domain (ID)rdquo and the ldquointerference domainheadrdquo as follows

Definition 5 The ldquointerference domainrdquo is defined as a subsetof the networkrsquos nodes which satisfies three conditions

(i) The interference domains have no common node thatis ID119894⋂ ID119895= Oslash 119894 = 119895

(ii) The interference domains span all nodes in the net-work that is ⋃119872

119898=1ID119898

= V where 119872 denotes thetotal number of interference domains

(iii) Each interference domain for example the 119898thinterference domain includes a node denoted by 120585

119898

so that only the nodes of ID119898

are located withinthe interference range of 120585

119898 We define 120585

119898as the

ldquointerference domain headrdquo of ID119898

It is clear from Definition 5 that a small-scale MCMR-WMN is a special case which consists of only one interference

6 The Scientific World Journal

domain The feasibility of condition (iii) is justified by thefact that mesh routers are usually deployed with carefulplanning To clarify the above definition consider a typicalgrid topology plotted in Figure 2 as a popular topology forthe WMNs Let the grid length be set to 119871

0 In this case

for the interference range 119889intf assume radic21198710

lt 119889intf lt 21198710

which is a reasonable interference range [2] Thus we canmodel the interference domains as a 3 times 3 square grids asshown in Figure 2(b) This modeling satisfies conditions (i)ndash(iii) in Definition 5 In Figure 2(a) each circle represents aninterference domain and the central black nodes play the roleof the corresponding interference domain head

Now let the network be composed of 119872 interferencedomains ID

1 ID

119872 For large-scale MCMR-WMNs we

define the average channel utilization 119883LS as follows

119883LS =

1

119872119870

119870

sum

119896=1

119872

sum

119898=1

119883119896

119898 (21)

where 119883119896

119898denotes the utilization of channel 119896 observed by

the 119898th interference domain head

Theorem 6 Assume all sessions have the same traffic load forexample 119905119903119895

119904= 1198790 The networkrsquos throughput of the large-scale

MCMR-WMN is obtained as

120591 =

1198721198701198880

119873119879

119883119871119878

(22)

Proof According to (8) and considering the condition (iii) inDefinition 5 the utilization of the channel 119896 observed by the119898th interference domain head is given by

119883119896

119898=

119899119904

sum

119895=1

sum

119894isinID119898

tr119895119904

1198880

119902119895

119894119896 forall119896 isin K 119898 = 1 119872 (23)

Using (23) and averaging the utilization on differentchannels and different interference domain heads we have

119883LS =

1

119872119870

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

tr119895119904

1198880

119902119895

119894119896 (24)

119883LS(119886)

=

1198790

1198721198701198880

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (25)

where (119886) comes from assumption tr119895119904= 1198790 Under conditions

(i) and (ii) in Definition 5 and using (2)ndash(4) we obtain

NT =

1

119899119904

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (26)

Thus (25) can be simplified as

119883LS =

1198991199041198790NT

1198721198701198880

(27)

As a result since 120591 = 1198991199041198790 the networkrsquos throughput can

be obtained as 120591 = (1198721198701198880119873119879)119883

119871119878

Corollary 7 Under the same conditions as in Theorem 2considering 119862 = 119877119888

0and replacing 119873119879 with the result in

(16) the broadcast throughput of a large-scale MCMR-WMNis expressed in terms of the average node utilization and theaverage channel utilization as follows

120591 =

1198880

119899 minus 1

(119899119877119880 minus 119872119870119883119871119878

) (28)

It is clear that different parameters of the network interactwith each other Thus it is not possible to draw a specifiedboundary between themDue to the limited number of radiosand non-overlapping channels proper use of the resourcescould improve the performance of the network In thisregard as we will show in the next section the number oftransmissions and the load-balancing significantly affect thenetworkrsquos throughput

6 Numerical Results

In this section we present a comprehensive evaluation onthe relationship between the networkrsquos throughput and theresource utilizations For this purpose we apply the followingprotocols in a single-rate framework SPT-JCRS [7] MCM-JCRS [7] IRMT [20] and IRBT [20] In our Matlab simula-tion setup as shown in Figure 3 we consider a 6 times 6 squaregrid with 119899 = 36 and119872 = 4 where nodes 8 11 26 and 29 arethe interference domain heads The grid length (the distancebetween neighbor nodes in the same row or column) and theinterference range are set to 150m and 280m respectivelyWe also use the random channel assignment in which theradios of each node are randomly assigned to the distinctchannels Obviously in the cases that the number of channelsis less than or equal to the number of radios this method willact as the common channel assignment strategy

In the simulations the broadcast session requests arriveone by one at the network without any knowledge of thefuture requests The source of each session is selected ran-domly In addition the trafficmodel of all sessions is assumedto be Constant Bit Rate (CBR)with tr119895

119904= 04Mbps Assuming

119877 = 3 1198880

= 12Mbps and 25 broadcast session requests westudy the performance of the network for different numberof channels that is 119870 = 1 6 It is clear that in thecase of 119870 = 1 we have a SCSR-WMN Figure 4 comparesthe throughput of the aforementioned protocols in terms ofthe number of channels 119870 In addition Table 1 shows thesimulation results inmore details It should be noted that eachdata point is obtained by averaging the results of 15 individualruns on different randomly experiments In this table NT119880 119883LS and 120591sim present the experimental results obtainedfor the average number of transmissions the average nodeutilization the average channel utilization and the networkrsquosthroughput respectively It is worth noting that the results inTable 1 exactly follow the described theoretical relationshipsin (16) (22) and (28) As an example Table 1 compares 120591simwith the theoretical throughput 120591theory extracted from (28)Obviously 120591sim is similar to 120591theory for different number of

The Scientific World Journal 7

1205851 1205852 1205853

1205854 1205855 1205856

1205857 1205858 1205859

ID1 ID2 ID3

ID7 ID8 ID9

(a)

2radic2L0

radic2L0

radic5L0

2L0

r

(b)

Figure 2 (a) A typical grid MCMR-WMN with its interference domains (b) an interference domain

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

8

11

26

29

150m

150m

Figure 3 The grid topology considered in the simulations

channels This shows the validity of our analysis This com-parison can be also verified for relationships (16) and (22)It is clear that different parameters of the network interactwith each other In this situation given the limited numberof radios and channels proper use of the resources couldimprove the performance of the network Actually using anefficient traffic engineering mechanism leads to better spec-trum utilization and increases the fairness in the networkThusmore resources will be available for accepting the futuresessions and the overall throughput will be increased In thisregard it is observed that the performance of the IRBT andthe IRMT algorithms much better than that of the othertwo algorithms In fact the IRBT and the IRMT algorithms

jointly address the transmission channel selection and theload-balanced routing tree construction [20] These schemesnot only take into account the number of transmissions butalso consider both inter-flow and intra-flow interferences toroute the sessions through alternative feasible pathsThus thetraffic load is balanced in the network However the MCM-JCRS and the SPT-JCRS algorithms cannot efficiently usethe resources of the network due to being limited to non-interference-aware routing trees

In [20] we demonstrated that the IRBT algorithm bal-ances the traffic load in the network more efficiently than theIRMTalgorithmThe results in Table 1 also confirm this issueFrom this table we can see that the IRBT approach improvesthe utilization of the network resources For 119870 = 1 2 3

(ie common channel assignment) although the IRMTalgorithm leads to less number of transmissions than theIRBT algorithm the load-balancing ability of the IRBTmakesboth schemes have the same networkrsquos throughput If thetraffic load in the network is balanced the interference willbe decreased and consequently the call acceptance rate willbe increased In contrast for 119870 gt 3 both IRMT and IRBTalgorithms nearly have the same number of transmissions Inthis situation the load-balancing factor plays more efficientrole in the networkrsquos performance This causes the IRBTalgorithm to show better throughput

On the other hand by increasing the number of channelsfirst the networkrsquos throughput linearly increases Howeverfor 119870 gt 3 it is gradually saturated Due to the randomchannel assignment strategy further increasing of the chan-nels leads to the less number of common channels betweenthe neighbor nodes Thus the possibility of enjoying thewireless broadcast advantagewill be decreasedThis increasesthe number of transmissions as shown in Table 1 In this

8 The Scientific World Journal

Table 1 Performance comparison for different number of channels

Number of channels Algorithm NT 119880 119883LS 120591sim (Mbps) 120591theory (Mbps)

119870 = 1

IRBT 20002 00961 09428 22667 22655IRMT 159444 00912 077 232 2321

MCM-JCRS 181 00787 07239 192 19214SPT-JCRS 2395 00703 07717 15467 15448

119870 = 2

IRBT 197273 01998 09722 47333 47317IRMT 159967 01888 07993 48 47986

MCM-JCRS 178833 01578 07205 38667 38669SPT-JCRS 233780 01411 07628 31333 31325

119870 = 3

IRBT 200016 02970 09719 7 69988IRMT 162761 02769 07911 7 69984

MCM-JCRS 18225 02481 07644 604 60418SPT-JCRS 234697 02093 07561 464 46392

119870 = 4

IRBT 202207 03702 09144 86909 86918IRMT 186563 03086 07244 74545 74531

MCM-JCRS 18966 02483 0589 59636 59631SPT-JCRS 241418 02455 06761 53818 53816

119870 = 5

IRBT 215448 03909 08040 896 89613IRMT 206932 03043 06105 708 70815

MCM-JCRS 217823 02225 04608 508 50791SPT-JCRS 26238 02155 04987 456 456

119870 = 6

IRBT 239454 03929 07182 864 86388IRMT 236876 02862 05197 632 63212

MCM-JCRS 242579 02088 03854 456 45603SPT-JCRS 272301 02133 04204 444 44389

1 2 3 4 5 60

2

4

6

8

10

Number of channels (K)

Thro

ughp

ut (M

bps)

IRBT

IRMT

MCM-JCRS

SPT-JCRS

Figure 4 Networkrsquos throughput as function of the number ofchannels

situation the lack of load-balancing could sufficiently reducethe networkrsquos throughput

7 Conclusion

In this paper the throughput of a MCMR-WMN wasquantified We focused on the scenario of on-demand QoSmulticastbroadcast sessions where each session has a spe-cific bandwidth requirement In particular considering theresource constraints we derived analytical relationships forthe networkrsquos throughput in terms of the node utilization thechannel utilization and the number of transmissions Thisgives simple solutions for the future designs to predict thenetworkrsquos throughput based on the resource utilizations Inline with the proposed relationships we also demonstratedthat the networkrsquos throughput is significantly affected by bothnumber of transmissions and degree of load-balancing Onone hand minimizing the number of transmissions reducesthe use of the network resources On the other hand load-balancing increases the fairness in the network In thissituation more resources will be available for accepting thefuture sessions Thus the overall networkrsquos throughput willbe increased

Acknowledgment

This work is supported by the Iranian TelecommunicationResearch Center (ITRC)

The Scientific World Journal 9

References

[1] PH Pathak andRDutta ldquoA survey of network design problemsand joint design approaches in wireless mesh networksrdquo IEEECommunications Surveys and Tutorials vol 13 no 3 pp 396ndash428 2011

[2] A Raniwala and T-C Chiueh ldquoArchitecture and algorithms foran IEEE 80211-based multi-channel wireless mesh networkrdquo inProceedings of the IEEE International Conference on ComputerCommunications (INFOCOM rsquo05) vol 3 pp 2223ndash2234March2005

[3] A Avokh and G Mirjalily ldquoPerformance analysis of broad-casting in small-scale multi-radio multi-channel wireless meshnetworksrdquo in Proceedings of the 14th International Conference onAdvanced Communication Technology (ICACT rsquo12) pp 537ndash542February 2012

[4] U T Nguyen and J Xu ldquoMulticast routing in wireless meshnetworks minimum cost trees or shortest path treesrdquo IEEECommunications Magazine vol 45 no 11 pp 72ndash77 2007

[5] Y Li and I Chen ldquoDynamic agent-based hierarchical multicastfor wireless mesh networksrdquo Ad Hoc Networks vol 11 no 6 pp1683ndash1698 2013

[6] J E Wieselthier G D Nguyen and A Ephremides ldquoEnergy-efficient broadcast and multicast trees in wireless networksrdquoMobile Networks and Applications vol 7 no 6 pp 481ndash4922002

[7] A Avokh G Mirjalily and J Abouei ldquoJoint channel andrate selection for multicast routing trees in wireless meshnetworksrdquo in Proceedings of the International Symposium onTelecommunications pp 548ndash553 November 2012

[8] K N Ramachandran E M Belding K C Almeroth andM M Buddhikot ldquoInterference-aware channel assignment inmulti-radio wireless mesh networksrdquo in Proceedings of the 25thIEEE International Conference on Computer Communications(INFOCOM rsquo06) pp 1ndash12 April 2006

[9] R-H Jan S-Y Huang and C-F Wang ldquoAn upper bound ofthe throughput for multi-radio wireless mesh networksrdquo IEEECommunications Letters vol 14 no 8 pp 698ndash700 2010

[10] A Capone G Carello I Filippini S Gualandi and F Malu-celli ldquoRouting scheduling and channel assignment in wirelessmesh networks optimization models and algorithmsrdquo Ad HocNetworks vol 8 no 6 pp 545ndash563 2010

[11] E Alotaibi V Ramamurthi M Batayneh and B MukherjeeldquoInterference-aware routing for multi-hop wireless mesh net-worksrdquo Computer Communications vol 33 no 16 pp 1961ndash1971 2010

[12] V C M Borges D Pereira M Curado and E MonteiroldquoRoutingmetric for interference and channel diversity inmulti-radio wireless mesh networksrdquo in Ad-Hoc Mobile and WirelessNetworks vol 5793 of Lecture Notes in Computer Science pp55ndash68 Springer Berlin Germany 2009

[13] S Roy D Koutsonikolas S Das and Y C Hu ldquoHigh-throughput multicast routing metrics in wireless mesh net-worksrdquo Ad Hoc Networks vol 6 no 6 pp 878ndash899 2008

[14] P M Ruiz and A F Gomez-Skarmeta ldquoApproximating optimalmulticast trees in wireless multihop networksrdquo in Proceedings ofthe 10th IEEE Symposium on Computers and Communications(ISCC rsquo05) pp 686ndash691 June 2005

[15] H L Nguyen and U T Nguyen ldquoBandwidth efficient multicastrouting in multi-channel multi-radio wireless mesh networksrdquoin Proceedings of the International Conference on Ultra Modern

Telecommunications and Workshops (ICUMT rsquo09) pp 1ndash8October 2009

[16] G Zeng B Wang Y Ding L Xiao and M Mutka ldquoEfficientmulticast algorithms formultichannel wireless mesh networksrdquoIEEE Transactions on Parallel and Distributed Systems vol 21no 1 pp 86ndash99 2010

[17] H S Chiu K L Yeung and K-S Lui ldquoMaximizing broadcastload in multi-channel Multi-interface wireless mesh networksrdquoin Proceedings of the IEEE Global Telecommunications Confer-ence (GLOBECOM rsquo08) pp 533ndash537 December 2008

[18] F Li Y Fang F Hu and X Liu ldquoLoad-aware multicast routingmetrics in multi-radio multi-channel wireless mesh networksrdquoComputer Networks vol 55 no 9 pp 2150ndash2167 2011

[19] P A K Acharya and E M Belding ldquoMARS link-layer rateselection for multicast transmissions in wireless mesh net-worksrdquo Ad Hoc Networks vol 9 no 1 pp 48ndash60 2011

[20] A Avokh and G Mirjalily ldquoInterference-aware multicast andbroadcast routing in wireless mesh networks using both rateand channel diversityrdquo Computers amp Electrical Engineering2013

[21] T Kim Y Yang J C Hou and S V Krishnamurthy ldquoResourceallocation for QoS support in wireless mesh networksrdquo IEEETransactions on Wireless Communications vol 12 no 5 pp2046ndash2054 2013

[22] W Kocay and D Kreher Graphs Algorithms and Optimiza-tion Discrete Mathematics and Its Applications Chapman ampHallCRC Boca Raton Fla USA 2005

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

The Scientific World Journal 5

Proof Under the assumption 119862(119894) = 119862 and using (6) and (7)we have

119880 =

1

119899119862

119899119904

sum

119895=1

119899

sum

119894=1

119897119895

119894

(119886)

=

1

119899119862

119899119904

sum

119895=1

( sum

119894isinFWD119895tr119895119904(1 + NT119895

119894) + tr119895119904NT119895119904+ sum

119894isin119871119865119895

tr119895119904)

=

1198790

119899119862

119899119904

sum

119895=1

( sum

119894isin119904119895FWD119895

NT119895119894+

10038161003816100381610038161003816FWD1198951003816100381610038161003816

1003816+

10038161003816100381610038161003816LF1198951003816100381610038161003816

1003816)

(11)

where (119886) comes from (5) and the fact that each multicastrouting tree includes three kinds of nodes a source nodeforwarding nodes and leaf nodes In the above equationsNT119895119904is the number of transmissions of source node and

|FWD119895| and |LF119895| denote the number of forwarding nodesand leaf nodes at the 119895th tree respectively On the other handfrom the graph theory [22]

10038161003816100381610038161003816FWD1198951003816100381610038161003816

1003816+

10038161003816100381610038161003816LF1198951003816100381610038161003816

1003816= 119882119895 (12)

Thus (11) can be simplified as

119880 =

1198790

119899119862

119899119904

sum

119895=1

( sum

119894isin119904119895FWD119895

NT119895119894+ 119882119895)

=

1198790

119899119862

[

[

119899119904

sum

119895=1

sum

119894isin119904119895FWD119895

NT119895119894+

119899119904

sum

119895=1

119882119895]

]

(13)

According to (3) and (4) and considering the fact thatNT119895119894= 0 for 119894 notin 119904

119895 FWD119895 we have

NT =

1

119899119904

119899119904

sum

119895=1

sum

119894isin119904119895FWD119895

NT119895119894 (14)

Thus

119880 =

1198790

119899119862

[119899119904NT + 119899

119904119882] =

1198991199041198790

119899119862

[NT + 119882] (15)

As a result NT = (1198991198621198991199041198790)119880 minus 119882

Corollary 3 For the broadcast case (12) can be rewritten as|FWD119895| + |119871119865

119895| = 119899 minus 1 [22] Thus

119873119879 =

119899119862

1198991199041198790

119880 minus 119899 + 1 (16)

In the rest of the section we first present the problemfor the small-scale MCMR-WMNs and then we extend ourwork to the case of large-scale MCMR-WMNs In additiondue to the similarity of equations for the multicast andthe broadcast sessions we follow the problem only for thebroadcast sessions

Small-Scale MCMR-WMNs In a small-scale MCMR-WMNwe suppose that all nodes are located in the interference range

of each other Thus the channel utilization observed by anynode is identical For a small-scale MCMR-WMN we definethe utilization of channel 119896 denoted by 119883

119896 and the averagechannel utilization 119883SS as follows

119883119896=

119899119904

sum

119895=1

sum

119894isinV

tr119895119904

1198880

119902119895

119894119896 forall119896 isin K (17)

119883SS =

1

119870

119870

sum

119896=1

119883119896 (18)

Lemma 4 Under the same conditions as in Theorem 2the broadcast throughput of a small-scale MCMR-WMN isexpressed in terms of the average node utilization and theaverage channel utilization as follows

120591 =

1198880

119899 minus 1

(119899119877119880 minus 119870X119878119878) (19)

Proof Using (17) and averaging the utilization on differentchannels we have

119883SS =

1

119870

119899119904

sum

119895=1

119870

sum

119896=1

sum

119894isinV

tr119895119904

1198880

119902119895

119894119896

(119886)

=

1198991199041198790

1198701198880

NT (20)

where (119886) comes from (2)ndash(4) and the assumption tr119895119904= 1198790

Considering 120591 = 1198991199041198790 119862 = 119877119888

0 and replacing NT with the

result in (16) for broadcast sessions the throughput 120591 can beexpressed as 120591 = (119888

0119899 minus 1)(119899119877119880 minus 119870119883SS)

Large-Scale MCMR-WMNs Now we extend the result ofLemma 4 to the large-scale MCMR-WMN case In generalthe channel utilization is a location-dependent parameterHowever due to the shared nature of the wireless mediumthe channel utilizations observed by neighboring nodes areclose to each other Thus considering the channel utilizationobserved by all nodes gives a lot of redundancy One idea isto study the channel utilization observed by a special nodeon behalf of its neighbors To address this solution we definethe ldquointerference domain (ID)rdquo and the ldquointerference domainheadrdquo as follows

Definition 5 The ldquointerference domainrdquo is defined as a subsetof the networkrsquos nodes which satisfies three conditions

(i) The interference domains have no common node thatis ID119894⋂ ID119895= Oslash 119894 = 119895

(ii) The interference domains span all nodes in the net-work that is ⋃119872

119898=1ID119898

= V where 119872 denotes thetotal number of interference domains

(iii) Each interference domain for example the 119898thinterference domain includes a node denoted by 120585

119898

so that only the nodes of ID119898

are located withinthe interference range of 120585

119898 We define 120585

119898as the

ldquointerference domain headrdquo of ID119898

It is clear from Definition 5 that a small-scale MCMR-WMN is a special case which consists of only one interference

6 The Scientific World Journal

domain The feasibility of condition (iii) is justified by thefact that mesh routers are usually deployed with carefulplanning To clarify the above definition consider a typicalgrid topology plotted in Figure 2 as a popular topology forthe WMNs Let the grid length be set to 119871

0 In this case

for the interference range 119889intf assume radic21198710

lt 119889intf lt 21198710

which is a reasonable interference range [2] Thus we canmodel the interference domains as a 3 times 3 square grids asshown in Figure 2(b) This modeling satisfies conditions (i)ndash(iii) in Definition 5 In Figure 2(a) each circle represents aninterference domain and the central black nodes play the roleof the corresponding interference domain head

Now let the network be composed of 119872 interferencedomains ID

1 ID

119872 For large-scale MCMR-WMNs we

define the average channel utilization 119883LS as follows

119883LS =

1

119872119870

119870

sum

119896=1

119872

sum

119898=1

119883119896

119898 (21)

where 119883119896

119898denotes the utilization of channel 119896 observed by

the 119898th interference domain head

Theorem 6 Assume all sessions have the same traffic load forexample 119905119903119895

119904= 1198790 The networkrsquos throughput of the large-scale

MCMR-WMN is obtained as

120591 =

1198721198701198880

119873119879

119883119871119878

(22)

Proof According to (8) and considering the condition (iii) inDefinition 5 the utilization of the channel 119896 observed by the119898th interference domain head is given by

119883119896

119898=

119899119904

sum

119895=1

sum

119894isinID119898

tr119895119904

1198880

119902119895

119894119896 forall119896 isin K 119898 = 1 119872 (23)

Using (23) and averaging the utilization on differentchannels and different interference domain heads we have

119883LS =

1

119872119870

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

tr119895119904

1198880

119902119895

119894119896 (24)

119883LS(119886)

=

1198790

1198721198701198880

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (25)

where (119886) comes from assumption tr119895119904= 1198790 Under conditions

(i) and (ii) in Definition 5 and using (2)ndash(4) we obtain

NT =

1

119899119904

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (26)

Thus (25) can be simplified as

119883LS =

1198991199041198790NT

1198721198701198880

(27)

As a result since 120591 = 1198991199041198790 the networkrsquos throughput can

be obtained as 120591 = (1198721198701198880119873119879)119883

119871119878

Corollary 7 Under the same conditions as in Theorem 2considering 119862 = 119877119888

0and replacing 119873119879 with the result in

(16) the broadcast throughput of a large-scale MCMR-WMNis expressed in terms of the average node utilization and theaverage channel utilization as follows

120591 =

1198880

119899 minus 1

(119899119877119880 minus 119872119870119883119871119878

) (28)

It is clear that different parameters of the network interactwith each other Thus it is not possible to draw a specifiedboundary between themDue to the limited number of radiosand non-overlapping channels proper use of the resourcescould improve the performance of the network In thisregard as we will show in the next section the number oftransmissions and the load-balancing significantly affect thenetworkrsquos throughput

6 Numerical Results

In this section we present a comprehensive evaluation onthe relationship between the networkrsquos throughput and theresource utilizations For this purpose we apply the followingprotocols in a single-rate framework SPT-JCRS [7] MCM-JCRS [7] IRMT [20] and IRBT [20] In our Matlab simula-tion setup as shown in Figure 3 we consider a 6 times 6 squaregrid with 119899 = 36 and119872 = 4 where nodes 8 11 26 and 29 arethe interference domain heads The grid length (the distancebetween neighbor nodes in the same row or column) and theinterference range are set to 150m and 280m respectivelyWe also use the random channel assignment in which theradios of each node are randomly assigned to the distinctchannels Obviously in the cases that the number of channelsis less than or equal to the number of radios this method willact as the common channel assignment strategy

In the simulations the broadcast session requests arriveone by one at the network without any knowledge of thefuture requests The source of each session is selected ran-domly In addition the trafficmodel of all sessions is assumedto be Constant Bit Rate (CBR)with tr119895

119904= 04Mbps Assuming

119877 = 3 1198880

= 12Mbps and 25 broadcast session requests westudy the performance of the network for different numberof channels that is 119870 = 1 6 It is clear that in thecase of 119870 = 1 we have a SCSR-WMN Figure 4 comparesthe throughput of the aforementioned protocols in terms ofthe number of channels 119870 In addition Table 1 shows thesimulation results inmore details It should be noted that eachdata point is obtained by averaging the results of 15 individualruns on different randomly experiments In this table NT119880 119883LS and 120591sim present the experimental results obtainedfor the average number of transmissions the average nodeutilization the average channel utilization and the networkrsquosthroughput respectively It is worth noting that the results inTable 1 exactly follow the described theoretical relationshipsin (16) (22) and (28) As an example Table 1 compares 120591simwith the theoretical throughput 120591theory extracted from (28)Obviously 120591sim is similar to 120591theory for different number of

The Scientific World Journal 7

1205851 1205852 1205853

1205854 1205855 1205856

1205857 1205858 1205859

ID1 ID2 ID3

ID7 ID8 ID9

(a)

2radic2L0

radic2L0

radic5L0

2L0

r

(b)

Figure 2 (a) A typical grid MCMR-WMN with its interference domains (b) an interference domain

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

8

11

26

29

150m

150m

Figure 3 The grid topology considered in the simulations

channels This shows the validity of our analysis This com-parison can be also verified for relationships (16) and (22)It is clear that different parameters of the network interactwith each other In this situation given the limited numberof radios and channels proper use of the resources couldimprove the performance of the network Actually using anefficient traffic engineering mechanism leads to better spec-trum utilization and increases the fairness in the networkThusmore resources will be available for accepting the futuresessions and the overall throughput will be increased In thisregard it is observed that the performance of the IRBT andthe IRMT algorithms much better than that of the othertwo algorithms In fact the IRBT and the IRMT algorithms

jointly address the transmission channel selection and theload-balanced routing tree construction [20] These schemesnot only take into account the number of transmissions butalso consider both inter-flow and intra-flow interferences toroute the sessions through alternative feasible pathsThus thetraffic load is balanced in the network However the MCM-JCRS and the SPT-JCRS algorithms cannot efficiently usethe resources of the network due to being limited to non-interference-aware routing trees

In [20] we demonstrated that the IRBT algorithm bal-ances the traffic load in the network more efficiently than theIRMTalgorithmThe results in Table 1 also confirm this issueFrom this table we can see that the IRBT approach improvesthe utilization of the network resources For 119870 = 1 2 3

(ie common channel assignment) although the IRMTalgorithm leads to less number of transmissions than theIRBT algorithm the load-balancing ability of the IRBTmakesboth schemes have the same networkrsquos throughput If thetraffic load in the network is balanced the interference willbe decreased and consequently the call acceptance rate willbe increased In contrast for 119870 gt 3 both IRMT and IRBTalgorithms nearly have the same number of transmissions Inthis situation the load-balancing factor plays more efficientrole in the networkrsquos performance This causes the IRBTalgorithm to show better throughput

On the other hand by increasing the number of channelsfirst the networkrsquos throughput linearly increases Howeverfor 119870 gt 3 it is gradually saturated Due to the randomchannel assignment strategy further increasing of the chan-nels leads to the less number of common channels betweenthe neighbor nodes Thus the possibility of enjoying thewireless broadcast advantagewill be decreasedThis increasesthe number of transmissions as shown in Table 1 In this

8 The Scientific World Journal

Table 1 Performance comparison for different number of channels

Number of channels Algorithm NT 119880 119883LS 120591sim (Mbps) 120591theory (Mbps)

119870 = 1

IRBT 20002 00961 09428 22667 22655IRMT 159444 00912 077 232 2321

MCM-JCRS 181 00787 07239 192 19214SPT-JCRS 2395 00703 07717 15467 15448

119870 = 2

IRBT 197273 01998 09722 47333 47317IRMT 159967 01888 07993 48 47986

MCM-JCRS 178833 01578 07205 38667 38669SPT-JCRS 233780 01411 07628 31333 31325

119870 = 3

IRBT 200016 02970 09719 7 69988IRMT 162761 02769 07911 7 69984

MCM-JCRS 18225 02481 07644 604 60418SPT-JCRS 234697 02093 07561 464 46392

119870 = 4

IRBT 202207 03702 09144 86909 86918IRMT 186563 03086 07244 74545 74531

MCM-JCRS 18966 02483 0589 59636 59631SPT-JCRS 241418 02455 06761 53818 53816

119870 = 5

IRBT 215448 03909 08040 896 89613IRMT 206932 03043 06105 708 70815

MCM-JCRS 217823 02225 04608 508 50791SPT-JCRS 26238 02155 04987 456 456

119870 = 6

IRBT 239454 03929 07182 864 86388IRMT 236876 02862 05197 632 63212

MCM-JCRS 242579 02088 03854 456 45603SPT-JCRS 272301 02133 04204 444 44389

1 2 3 4 5 60

2

4

6

8

10

Number of channels (K)

Thro

ughp

ut (M

bps)

IRBT

IRMT

MCM-JCRS

SPT-JCRS

Figure 4 Networkrsquos throughput as function of the number ofchannels

situation the lack of load-balancing could sufficiently reducethe networkrsquos throughput

7 Conclusion

In this paper the throughput of a MCMR-WMN wasquantified We focused on the scenario of on-demand QoSmulticastbroadcast sessions where each session has a spe-cific bandwidth requirement In particular considering theresource constraints we derived analytical relationships forthe networkrsquos throughput in terms of the node utilization thechannel utilization and the number of transmissions Thisgives simple solutions for the future designs to predict thenetworkrsquos throughput based on the resource utilizations Inline with the proposed relationships we also demonstratedthat the networkrsquos throughput is significantly affected by bothnumber of transmissions and degree of load-balancing Onone hand minimizing the number of transmissions reducesthe use of the network resources On the other hand load-balancing increases the fairness in the network In thissituation more resources will be available for accepting thefuture sessions Thus the overall networkrsquos throughput willbe increased

Acknowledgment

This work is supported by the Iranian TelecommunicationResearch Center (ITRC)

The Scientific World Journal 9

References

[1] PH Pathak andRDutta ldquoA survey of network design problemsand joint design approaches in wireless mesh networksrdquo IEEECommunications Surveys and Tutorials vol 13 no 3 pp 396ndash428 2011

[2] A Raniwala and T-C Chiueh ldquoArchitecture and algorithms foran IEEE 80211-based multi-channel wireless mesh networkrdquo inProceedings of the IEEE International Conference on ComputerCommunications (INFOCOM rsquo05) vol 3 pp 2223ndash2234March2005

[3] A Avokh and G Mirjalily ldquoPerformance analysis of broad-casting in small-scale multi-radio multi-channel wireless meshnetworksrdquo in Proceedings of the 14th International Conference onAdvanced Communication Technology (ICACT rsquo12) pp 537ndash542February 2012

[4] U T Nguyen and J Xu ldquoMulticast routing in wireless meshnetworks minimum cost trees or shortest path treesrdquo IEEECommunications Magazine vol 45 no 11 pp 72ndash77 2007

[5] Y Li and I Chen ldquoDynamic agent-based hierarchical multicastfor wireless mesh networksrdquo Ad Hoc Networks vol 11 no 6 pp1683ndash1698 2013

[6] J E Wieselthier G D Nguyen and A Ephremides ldquoEnergy-efficient broadcast and multicast trees in wireless networksrdquoMobile Networks and Applications vol 7 no 6 pp 481ndash4922002

[7] A Avokh G Mirjalily and J Abouei ldquoJoint channel andrate selection for multicast routing trees in wireless meshnetworksrdquo in Proceedings of the International Symposium onTelecommunications pp 548ndash553 November 2012

[8] K N Ramachandran E M Belding K C Almeroth andM M Buddhikot ldquoInterference-aware channel assignment inmulti-radio wireless mesh networksrdquo in Proceedings of the 25thIEEE International Conference on Computer Communications(INFOCOM rsquo06) pp 1ndash12 April 2006

[9] R-H Jan S-Y Huang and C-F Wang ldquoAn upper bound ofthe throughput for multi-radio wireless mesh networksrdquo IEEECommunications Letters vol 14 no 8 pp 698ndash700 2010

[10] A Capone G Carello I Filippini S Gualandi and F Malu-celli ldquoRouting scheduling and channel assignment in wirelessmesh networks optimization models and algorithmsrdquo Ad HocNetworks vol 8 no 6 pp 545ndash563 2010

[11] E Alotaibi V Ramamurthi M Batayneh and B MukherjeeldquoInterference-aware routing for multi-hop wireless mesh net-worksrdquo Computer Communications vol 33 no 16 pp 1961ndash1971 2010

[12] V C M Borges D Pereira M Curado and E MonteiroldquoRoutingmetric for interference and channel diversity inmulti-radio wireless mesh networksrdquo in Ad-Hoc Mobile and WirelessNetworks vol 5793 of Lecture Notes in Computer Science pp55ndash68 Springer Berlin Germany 2009

[13] S Roy D Koutsonikolas S Das and Y C Hu ldquoHigh-throughput multicast routing metrics in wireless mesh net-worksrdquo Ad Hoc Networks vol 6 no 6 pp 878ndash899 2008

[14] P M Ruiz and A F Gomez-Skarmeta ldquoApproximating optimalmulticast trees in wireless multihop networksrdquo in Proceedings ofthe 10th IEEE Symposium on Computers and Communications(ISCC rsquo05) pp 686ndash691 June 2005

[15] H L Nguyen and U T Nguyen ldquoBandwidth efficient multicastrouting in multi-channel multi-radio wireless mesh networksrdquoin Proceedings of the International Conference on Ultra Modern

Telecommunications and Workshops (ICUMT rsquo09) pp 1ndash8October 2009

[16] G Zeng B Wang Y Ding L Xiao and M Mutka ldquoEfficientmulticast algorithms formultichannel wireless mesh networksrdquoIEEE Transactions on Parallel and Distributed Systems vol 21no 1 pp 86ndash99 2010

[17] H S Chiu K L Yeung and K-S Lui ldquoMaximizing broadcastload in multi-channel Multi-interface wireless mesh networksrdquoin Proceedings of the IEEE Global Telecommunications Confer-ence (GLOBECOM rsquo08) pp 533ndash537 December 2008

[18] F Li Y Fang F Hu and X Liu ldquoLoad-aware multicast routingmetrics in multi-radio multi-channel wireless mesh networksrdquoComputer Networks vol 55 no 9 pp 2150ndash2167 2011

[19] P A K Acharya and E M Belding ldquoMARS link-layer rateselection for multicast transmissions in wireless mesh net-worksrdquo Ad Hoc Networks vol 9 no 1 pp 48ndash60 2011

[20] A Avokh and G Mirjalily ldquoInterference-aware multicast andbroadcast routing in wireless mesh networks using both rateand channel diversityrdquo Computers amp Electrical Engineering2013

[21] T Kim Y Yang J C Hou and S V Krishnamurthy ldquoResourceallocation for QoS support in wireless mesh networksrdquo IEEETransactions on Wireless Communications vol 12 no 5 pp2046ndash2054 2013

[22] W Kocay and D Kreher Graphs Algorithms and Optimiza-tion Discrete Mathematics and Its Applications Chapman ampHallCRC Boca Raton Fla USA 2005

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 The Scientific World Journal

domain The feasibility of condition (iii) is justified by thefact that mesh routers are usually deployed with carefulplanning To clarify the above definition consider a typicalgrid topology plotted in Figure 2 as a popular topology forthe WMNs Let the grid length be set to 119871

0 In this case

for the interference range 119889intf assume radic21198710

lt 119889intf lt 21198710

which is a reasonable interference range [2] Thus we canmodel the interference domains as a 3 times 3 square grids asshown in Figure 2(b) This modeling satisfies conditions (i)ndash(iii) in Definition 5 In Figure 2(a) each circle represents aninterference domain and the central black nodes play the roleof the corresponding interference domain head

Now let the network be composed of 119872 interferencedomains ID

1 ID

119872 For large-scale MCMR-WMNs we

define the average channel utilization 119883LS as follows

119883LS =

1

119872119870

119870

sum

119896=1

119872

sum

119898=1

119883119896

119898 (21)

where 119883119896

119898denotes the utilization of channel 119896 observed by

the 119898th interference domain head

Theorem 6 Assume all sessions have the same traffic load forexample 119905119903119895

119904= 1198790 The networkrsquos throughput of the large-scale

MCMR-WMN is obtained as

120591 =

1198721198701198880

119873119879

119883119871119878

(22)

Proof According to (8) and considering the condition (iii) inDefinition 5 the utilization of the channel 119896 observed by the119898th interference domain head is given by

119883119896

119898=

119899119904

sum

119895=1

sum

119894isinID119898

tr119895119904

1198880

119902119895

119894119896 forall119896 isin K 119898 = 1 119872 (23)

Using (23) and averaging the utilization on differentchannels and different interference domain heads we have

119883LS =

1

119872119870

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

tr119895119904

1198880

119902119895

119894119896 (24)

119883LS(119886)

=

1198790

1198721198701198880

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (25)

where (119886) comes from assumption tr119895119904= 1198790 Under conditions

(i) and (ii) in Definition 5 and using (2)ndash(4) we obtain

NT =

1

119899119904

119899119904

sum

119895=1

119872

sum

119898=1

sum

119894isinID119898

119870

sum

119896=1

119902119895

119894119896 (26)

Thus (25) can be simplified as

119883LS =

1198991199041198790NT

1198721198701198880

(27)

As a result since 120591 = 1198991199041198790 the networkrsquos throughput can

be obtained as 120591 = (1198721198701198880119873119879)119883

119871119878

Corollary 7 Under the same conditions as in Theorem 2considering 119862 = 119877119888

0and replacing 119873119879 with the result in

(16) the broadcast throughput of a large-scale MCMR-WMNis expressed in terms of the average node utilization and theaverage channel utilization as follows

120591 =

1198880

119899 minus 1

(119899119877119880 minus 119872119870119883119871119878

) (28)

It is clear that different parameters of the network interactwith each other Thus it is not possible to draw a specifiedboundary between themDue to the limited number of radiosand non-overlapping channels proper use of the resourcescould improve the performance of the network In thisregard as we will show in the next section the number oftransmissions and the load-balancing significantly affect thenetworkrsquos throughput

6 Numerical Results

In this section we present a comprehensive evaluation onthe relationship between the networkrsquos throughput and theresource utilizations For this purpose we apply the followingprotocols in a single-rate framework SPT-JCRS [7] MCM-JCRS [7] IRMT [20] and IRBT [20] In our Matlab simula-tion setup as shown in Figure 3 we consider a 6 times 6 squaregrid with 119899 = 36 and119872 = 4 where nodes 8 11 26 and 29 arethe interference domain heads The grid length (the distancebetween neighbor nodes in the same row or column) and theinterference range are set to 150m and 280m respectivelyWe also use the random channel assignment in which theradios of each node are randomly assigned to the distinctchannels Obviously in the cases that the number of channelsis less than or equal to the number of radios this method willact as the common channel assignment strategy

In the simulations the broadcast session requests arriveone by one at the network without any knowledge of thefuture requests The source of each session is selected ran-domly In addition the trafficmodel of all sessions is assumedto be Constant Bit Rate (CBR)with tr119895

119904= 04Mbps Assuming

119877 = 3 1198880

= 12Mbps and 25 broadcast session requests westudy the performance of the network for different numberof channels that is 119870 = 1 6 It is clear that in thecase of 119870 = 1 we have a SCSR-WMN Figure 4 comparesthe throughput of the aforementioned protocols in terms ofthe number of channels 119870 In addition Table 1 shows thesimulation results inmore details It should be noted that eachdata point is obtained by averaging the results of 15 individualruns on different randomly experiments In this table NT119880 119883LS and 120591sim present the experimental results obtainedfor the average number of transmissions the average nodeutilization the average channel utilization and the networkrsquosthroughput respectively It is worth noting that the results inTable 1 exactly follow the described theoretical relationshipsin (16) (22) and (28) As an example Table 1 compares 120591simwith the theoretical throughput 120591theory extracted from (28)Obviously 120591sim is similar to 120591theory for different number of

The Scientific World Journal 7

1205851 1205852 1205853

1205854 1205855 1205856

1205857 1205858 1205859

ID1 ID2 ID3

ID7 ID8 ID9

(a)

2radic2L0

radic2L0

radic5L0

2L0

r

(b)

Figure 2 (a) A typical grid MCMR-WMN with its interference domains (b) an interference domain

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

8

11

26

29

150m

150m

Figure 3 The grid topology considered in the simulations

channels This shows the validity of our analysis This com-parison can be also verified for relationships (16) and (22)It is clear that different parameters of the network interactwith each other In this situation given the limited numberof radios and channels proper use of the resources couldimprove the performance of the network Actually using anefficient traffic engineering mechanism leads to better spec-trum utilization and increases the fairness in the networkThusmore resources will be available for accepting the futuresessions and the overall throughput will be increased In thisregard it is observed that the performance of the IRBT andthe IRMT algorithms much better than that of the othertwo algorithms In fact the IRBT and the IRMT algorithms

jointly address the transmission channel selection and theload-balanced routing tree construction [20] These schemesnot only take into account the number of transmissions butalso consider both inter-flow and intra-flow interferences toroute the sessions through alternative feasible pathsThus thetraffic load is balanced in the network However the MCM-JCRS and the SPT-JCRS algorithms cannot efficiently usethe resources of the network due to being limited to non-interference-aware routing trees

In [20] we demonstrated that the IRBT algorithm bal-ances the traffic load in the network more efficiently than theIRMTalgorithmThe results in Table 1 also confirm this issueFrom this table we can see that the IRBT approach improvesthe utilization of the network resources For 119870 = 1 2 3

(ie common channel assignment) although the IRMTalgorithm leads to less number of transmissions than theIRBT algorithm the load-balancing ability of the IRBTmakesboth schemes have the same networkrsquos throughput If thetraffic load in the network is balanced the interference willbe decreased and consequently the call acceptance rate willbe increased In contrast for 119870 gt 3 both IRMT and IRBTalgorithms nearly have the same number of transmissions Inthis situation the load-balancing factor plays more efficientrole in the networkrsquos performance This causes the IRBTalgorithm to show better throughput

On the other hand by increasing the number of channelsfirst the networkrsquos throughput linearly increases Howeverfor 119870 gt 3 it is gradually saturated Due to the randomchannel assignment strategy further increasing of the chan-nels leads to the less number of common channels betweenthe neighbor nodes Thus the possibility of enjoying thewireless broadcast advantagewill be decreasedThis increasesthe number of transmissions as shown in Table 1 In this

8 The Scientific World Journal

Table 1 Performance comparison for different number of channels

Number of channels Algorithm NT 119880 119883LS 120591sim (Mbps) 120591theory (Mbps)

119870 = 1

IRBT 20002 00961 09428 22667 22655IRMT 159444 00912 077 232 2321

MCM-JCRS 181 00787 07239 192 19214SPT-JCRS 2395 00703 07717 15467 15448

119870 = 2

IRBT 197273 01998 09722 47333 47317IRMT 159967 01888 07993 48 47986

MCM-JCRS 178833 01578 07205 38667 38669SPT-JCRS 233780 01411 07628 31333 31325

119870 = 3

IRBT 200016 02970 09719 7 69988IRMT 162761 02769 07911 7 69984

MCM-JCRS 18225 02481 07644 604 60418SPT-JCRS 234697 02093 07561 464 46392

119870 = 4

IRBT 202207 03702 09144 86909 86918IRMT 186563 03086 07244 74545 74531

MCM-JCRS 18966 02483 0589 59636 59631SPT-JCRS 241418 02455 06761 53818 53816

119870 = 5

IRBT 215448 03909 08040 896 89613IRMT 206932 03043 06105 708 70815

MCM-JCRS 217823 02225 04608 508 50791SPT-JCRS 26238 02155 04987 456 456

119870 = 6

IRBT 239454 03929 07182 864 86388IRMT 236876 02862 05197 632 63212

MCM-JCRS 242579 02088 03854 456 45603SPT-JCRS 272301 02133 04204 444 44389

1 2 3 4 5 60

2

4

6

8

10

Number of channels (K)

Thro

ughp

ut (M

bps)

IRBT

IRMT

MCM-JCRS

SPT-JCRS

Figure 4 Networkrsquos throughput as function of the number ofchannels

situation the lack of load-balancing could sufficiently reducethe networkrsquos throughput

7 Conclusion

In this paper the throughput of a MCMR-WMN wasquantified We focused on the scenario of on-demand QoSmulticastbroadcast sessions where each session has a spe-cific bandwidth requirement In particular considering theresource constraints we derived analytical relationships forthe networkrsquos throughput in terms of the node utilization thechannel utilization and the number of transmissions Thisgives simple solutions for the future designs to predict thenetworkrsquos throughput based on the resource utilizations Inline with the proposed relationships we also demonstratedthat the networkrsquos throughput is significantly affected by bothnumber of transmissions and degree of load-balancing Onone hand minimizing the number of transmissions reducesthe use of the network resources On the other hand load-balancing increases the fairness in the network In thissituation more resources will be available for accepting thefuture sessions Thus the overall networkrsquos throughput willbe increased

Acknowledgment

This work is supported by the Iranian TelecommunicationResearch Center (ITRC)

The Scientific World Journal 9

References

[1] PH Pathak andRDutta ldquoA survey of network design problemsand joint design approaches in wireless mesh networksrdquo IEEECommunications Surveys and Tutorials vol 13 no 3 pp 396ndash428 2011

[2] A Raniwala and T-C Chiueh ldquoArchitecture and algorithms foran IEEE 80211-based multi-channel wireless mesh networkrdquo inProceedings of the IEEE International Conference on ComputerCommunications (INFOCOM rsquo05) vol 3 pp 2223ndash2234March2005

[3] A Avokh and G Mirjalily ldquoPerformance analysis of broad-casting in small-scale multi-radio multi-channel wireless meshnetworksrdquo in Proceedings of the 14th International Conference onAdvanced Communication Technology (ICACT rsquo12) pp 537ndash542February 2012

[4] U T Nguyen and J Xu ldquoMulticast routing in wireless meshnetworks minimum cost trees or shortest path treesrdquo IEEECommunications Magazine vol 45 no 11 pp 72ndash77 2007

[5] Y Li and I Chen ldquoDynamic agent-based hierarchical multicastfor wireless mesh networksrdquo Ad Hoc Networks vol 11 no 6 pp1683ndash1698 2013

[6] J E Wieselthier G D Nguyen and A Ephremides ldquoEnergy-efficient broadcast and multicast trees in wireless networksrdquoMobile Networks and Applications vol 7 no 6 pp 481ndash4922002

[7] A Avokh G Mirjalily and J Abouei ldquoJoint channel andrate selection for multicast routing trees in wireless meshnetworksrdquo in Proceedings of the International Symposium onTelecommunications pp 548ndash553 November 2012

[8] K N Ramachandran E M Belding K C Almeroth andM M Buddhikot ldquoInterference-aware channel assignment inmulti-radio wireless mesh networksrdquo in Proceedings of the 25thIEEE International Conference on Computer Communications(INFOCOM rsquo06) pp 1ndash12 April 2006

[9] R-H Jan S-Y Huang and C-F Wang ldquoAn upper bound ofthe throughput for multi-radio wireless mesh networksrdquo IEEECommunications Letters vol 14 no 8 pp 698ndash700 2010

[10] A Capone G Carello I Filippini S Gualandi and F Malu-celli ldquoRouting scheduling and channel assignment in wirelessmesh networks optimization models and algorithmsrdquo Ad HocNetworks vol 8 no 6 pp 545ndash563 2010

[11] E Alotaibi V Ramamurthi M Batayneh and B MukherjeeldquoInterference-aware routing for multi-hop wireless mesh net-worksrdquo Computer Communications vol 33 no 16 pp 1961ndash1971 2010

[12] V C M Borges D Pereira M Curado and E MonteiroldquoRoutingmetric for interference and channel diversity inmulti-radio wireless mesh networksrdquo in Ad-Hoc Mobile and WirelessNetworks vol 5793 of Lecture Notes in Computer Science pp55ndash68 Springer Berlin Germany 2009

[13] S Roy D Koutsonikolas S Das and Y C Hu ldquoHigh-throughput multicast routing metrics in wireless mesh net-worksrdquo Ad Hoc Networks vol 6 no 6 pp 878ndash899 2008

[14] P M Ruiz and A F Gomez-Skarmeta ldquoApproximating optimalmulticast trees in wireless multihop networksrdquo in Proceedings ofthe 10th IEEE Symposium on Computers and Communications(ISCC rsquo05) pp 686ndash691 June 2005

[15] H L Nguyen and U T Nguyen ldquoBandwidth efficient multicastrouting in multi-channel multi-radio wireless mesh networksrdquoin Proceedings of the International Conference on Ultra Modern

Telecommunications and Workshops (ICUMT rsquo09) pp 1ndash8October 2009

[16] G Zeng B Wang Y Ding L Xiao and M Mutka ldquoEfficientmulticast algorithms formultichannel wireless mesh networksrdquoIEEE Transactions on Parallel and Distributed Systems vol 21no 1 pp 86ndash99 2010

[17] H S Chiu K L Yeung and K-S Lui ldquoMaximizing broadcastload in multi-channel Multi-interface wireless mesh networksrdquoin Proceedings of the IEEE Global Telecommunications Confer-ence (GLOBECOM rsquo08) pp 533ndash537 December 2008

[18] F Li Y Fang F Hu and X Liu ldquoLoad-aware multicast routingmetrics in multi-radio multi-channel wireless mesh networksrdquoComputer Networks vol 55 no 9 pp 2150ndash2167 2011

[19] P A K Acharya and E M Belding ldquoMARS link-layer rateselection for multicast transmissions in wireless mesh net-worksrdquo Ad Hoc Networks vol 9 no 1 pp 48ndash60 2011

[20] A Avokh and G Mirjalily ldquoInterference-aware multicast andbroadcast routing in wireless mesh networks using both rateand channel diversityrdquo Computers amp Electrical Engineering2013

[21] T Kim Y Yang J C Hou and S V Krishnamurthy ldquoResourceallocation for QoS support in wireless mesh networksrdquo IEEETransactions on Wireless Communications vol 12 no 5 pp2046ndash2054 2013

[22] W Kocay and D Kreher Graphs Algorithms and Optimiza-tion Discrete Mathematics and Its Applications Chapman ampHallCRC Boca Raton Fla USA 2005

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

The Scientific World Journal 7

1205851 1205852 1205853

1205854 1205855 1205856

1205857 1205858 1205859

ID1 ID2 ID3

ID7 ID8 ID9

(a)

2radic2L0

radic2L0

radic5L0

2L0

r

(b)

Figure 2 (a) A typical grid MCMR-WMN with its interference domains (b) an interference domain

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

8

11

26

29

150m

150m

Figure 3 The grid topology considered in the simulations

channels This shows the validity of our analysis This com-parison can be also verified for relationships (16) and (22)It is clear that different parameters of the network interactwith each other In this situation given the limited numberof radios and channels proper use of the resources couldimprove the performance of the network Actually using anefficient traffic engineering mechanism leads to better spec-trum utilization and increases the fairness in the networkThusmore resources will be available for accepting the futuresessions and the overall throughput will be increased In thisregard it is observed that the performance of the IRBT andthe IRMT algorithms much better than that of the othertwo algorithms In fact the IRBT and the IRMT algorithms

jointly address the transmission channel selection and theload-balanced routing tree construction [20] These schemesnot only take into account the number of transmissions butalso consider both inter-flow and intra-flow interferences toroute the sessions through alternative feasible pathsThus thetraffic load is balanced in the network However the MCM-JCRS and the SPT-JCRS algorithms cannot efficiently usethe resources of the network due to being limited to non-interference-aware routing trees

In [20] we demonstrated that the IRBT algorithm bal-ances the traffic load in the network more efficiently than theIRMTalgorithmThe results in Table 1 also confirm this issueFrom this table we can see that the IRBT approach improvesthe utilization of the network resources For 119870 = 1 2 3

(ie common channel assignment) although the IRMTalgorithm leads to less number of transmissions than theIRBT algorithm the load-balancing ability of the IRBTmakesboth schemes have the same networkrsquos throughput If thetraffic load in the network is balanced the interference willbe decreased and consequently the call acceptance rate willbe increased In contrast for 119870 gt 3 both IRMT and IRBTalgorithms nearly have the same number of transmissions Inthis situation the load-balancing factor plays more efficientrole in the networkrsquos performance This causes the IRBTalgorithm to show better throughput

On the other hand by increasing the number of channelsfirst the networkrsquos throughput linearly increases Howeverfor 119870 gt 3 it is gradually saturated Due to the randomchannel assignment strategy further increasing of the chan-nels leads to the less number of common channels betweenthe neighbor nodes Thus the possibility of enjoying thewireless broadcast advantagewill be decreasedThis increasesthe number of transmissions as shown in Table 1 In this

8 The Scientific World Journal

Table 1 Performance comparison for different number of channels

Number of channels Algorithm NT 119880 119883LS 120591sim (Mbps) 120591theory (Mbps)

119870 = 1

IRBT 20002 00961 09428 22667 22655IRMT 159444 00912 077 232 2321

MCM-JCRS 181 00787 07239 192 19214SPT-JCRS 2395 00703 07717 15467 15448

119870 = 2

IRBT 197273 01998 09722 47333 47317IRMT 159967 01888 07993 48 47986

MCM-JCRS 178833 01578 07205 38667 38669SPT-JCRS 233780 01411 07628 31333 31325

119870 = 3

IRBT 200016 02970 09719 7 69988IRMT 162761 02769 07911 7 69984

MCM-JCRS 18225 02481 07644 604 60418SPT-JCRS 234697 02093 07561 464 46392

119870 = 4

IRBT 202207 03702 09144 86909 86918IRMT 186563 03086 07244 74545 74531

MCM-JCRS 18966 02483 0589 59636 59631SPT-JCRS 241418 02455 06761 53818 53816

119870 = 5

IRBT 215448 03909 08040 896 89613IRMT 206932 03043 06105 708 70815

MCM-JCRS 217823 02225 04608 508 50791SPT-JCRS 26238 02155 04987 456 456

119870 = 6

IRBT 239454 03929 07182 864 86388IRMT 236876 02862 05197 632 63212

MCM-JCRS 242579 02088 03854 456 45603SPT-JCRS 272301 02133 04204 444 44389

1 2 3 4 5 60

2

4

6

8

10

Number of channels (K)

Thro

ughp

ut (M

bps)

IRBT

IRMT

MCM-JCRS

SPT-JCRS

Figure 4 Networkrsquos throughput as function of the number ofchannels

situation the lack of load-balancing could sufficiently reducethe networkrsquos throughput

7 Conclusion

In this paper the throughput of a MCMR-WMN wasquantified We focused on the scenario of on-demand QoSmulticastbroadcast sessions where each session has a spe-cific bandwidth requirement In particular considering theresource constraints we derived analytical relationships forthe networkrsquos throughput in terms of the node utilization thechannel utilization and the number of transmissions Thisgives simple solutions for the future designs to predict thenetworkrsquos throughput based on the resource utilizations Inline with the proposed relationships we also demonstratedthat the networkrsquos throughput is significantly affected by bothnumber of transmissions and degree of load-balancing Onone hand minimizing the number of transmissions reducesthe use of the network resources On the other hand load-balancing increases the fairness in the network In thissituation more resources will be available for accepting thefuture sessions Thus the overall networkrsquos throughput willbe increased

Acknowledgment

This work is supported by the Iranian TelecommunicationResearch Center (ITRC)

The Scientific World Journal 9

References

[1] PH Pathak andRDutta ldquoA survey of network design problemsand joint design approaches in wireless mesh networksrdquo IEEECommunications Surveys and Tutorials vol 13 no 3 pp 396ndash428 2011

[2] A Raniwala and T-C Chiueh ldquoArchitecture and algorithms foran IEEE 80211-based multi-channel wireless mesh networkrdquo inProceedings of the IEEE International Conference on ComputerCommunications (INFOCOM rsquo05) vol 3 pp 2223ndash2234March2005

[3] A Avokh and G Mirjalily ldquoPerformance analysis of broad-casting in small-scale multi-radio multi-channel wireless meshnetworksrdquo in Proceedings of the 14th International Conference onAdvanced Communication Technology (ICACT rsquo12) pp 537ndash542February 2012

[4] U T Nguyen and J Xu ldquoMulticast routing in wireless meshnetworks minimum cost trees or shortest path treesrdquo IEEECommunications Magazine vol 45 no 11 pp 72ndash77 2007

[5] Y Li and I Chen ldquoDynamic agent-based hierarchical multicastfor wireless mesh networksrdquo Ad Hoc Networks vol 11 no 6 pp1683ndash1698 2013

[6] J E Wieselthier G D Nguyen and A Ephremides ldquoEnergy-efficient broadcast and multicast trees in wireless networksrdquoMobile Networks and Applications vol 7 no 6 pp 481ndash4922002

[7] A Avokh G Mirjalily and J Abouei ldquoJoint channel andrate selection for multicast routing trees in wireless meshnetworksrdquo in Proceedings of the International Symposium onTelecommunications pp 548ndash553 November 2012

[8] K N Ramachandran E M Belding K C Almeroth andM M Buddhikot ldquoInterference-aware channel assignment inmulti-radio wireless mesh networksrdquo in Proceedings of the 25thIEEE International Conference on Computer Communications(INFOCOM rsquo06) pp 1ndash12 April 2006

[9] R-H Jan S-Y Huang and C-F Wang ldquoAn upper bound ofthe throughput for multi-radio wireless mesh networksrdquo IEEECommunications Letters vol 14 no 8 pp 698ndash700 2010

[10] A Capone G Carello I Filippini S Gualandi and F Malu-celli ldquoRouting scheduling and channel assignment in wirelessmesh networks optimization models and algorithmsrdquo Ad HocNetworks vol 8 no 6 pp 545ndash563 2010

[11] E Alotaibi V Ramamurthi M Batayneh and B MukherjeeldquoInterference-aware routing for multi-hop wireless mesh net-worksrdquo Computer Communications vol 33 no 16 pp 1961ndash1971 2010

[12] V C M Borges D Pereira M Curado and E MonteiroldquoRoutingmetric for interference and channel diversity inmulti-radio wireless mesh networksrdquo in Ad-Hoc Mobile and WirelessNetworks vol 5793 of Lecture Notes in Computer Science pp55ndash68 Springer Berlin Germany 2009

[13] S Roy D Koutsonikolas S Das and Y C Hu ldquoHigh-throughput multicast routing metrics in wireless mesh net-worksrdquo Ad Hoc Networks vol 6 no 6 pp 878ndash899 2008

[14] P M Ruiz and A F Gomez-Skarmeta ldquoApproximating optimalmulticast trees in wireless multihop networksrdquo in Proceedings ofthe 10th IEEE Symposium on Computers and Communications(ISCC rsquo05) pp 686ndash691 June 2005

[15] H L Nguyen and U T Nguyen ldquoBandwidth efficient multicastrouting in multi-channel multi-radio wireless mesh networksrdquoin Proceedings of the International Conference on Ultra Modern

Telecommunications and Workshops (ICUMT rsquo09) pp 1ndash8October 2009

[16] G Zeng B Wang Y Ding L Xiao and M Mutka ldquoEfficientmulticast algorithms formultichannel wireless mesh networksrdquoIEEE Transactions on Parallel and Distributed Systems vol 21no 1 pp 86ndash99 2010

[17] H S Chiu K L Yeung and K-S Lui ldquoMaximizing broadcastload in multi-channel Multi-interface wireless mesh networksrdquoin Proceedings of the IEEE Global Telecommunications Confer-ence (GLOBECOM rsquo08) pp 533ndash537 December 2008

[18] F Li Y Fang F Hu and X Liu ldquoLoad-aware multicast routingmetrics in multi-radio multi-channel wireless mesh networksrdquoComputer Networks vol 55 no 9 pp 2150ndash2167 2011

[19] P A K Acharya and E M Belding ldquoMARS link-layer rateselection for multicast transmissions in wireless mesh net-worksrdquo Ad Hoc Networks vol 9 no 1 pp 48ndash60 2011

[20] A Avokh and G Mirjalily ldquoInterference-aware multicast andbroadcast routing in wireless mesh networks using both rateand channel diversityrdquo Computers amp Electrical Engineering2013

[21] T Kim Y Yang J C Hou and S V Krishnamurthy ldquoResourceallocation for QoS support in wireless mesh networksrdquo IEEETransactions on Wireless Communications vol 12 no 5 pp2046ndash2054 2013

[22] W Kocay and D Kreher Graphs Algorithms and Optimiza-tion Discrete Mathematics and Its Applications Chapman ampHallCRC Boca Raton Fla USA 2005

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 The Scientific World Journal

Table 1 Performance comparison for different number of channels

Number of channels Algorithm NT 119880 119883LS 120591sim (Mbps) 120591theory (Mbps)

119870 = 1

IRBT 20002 00961 09428 22667 22655IRMT 159444 00912 077 232 2321

MCM-JCRS 181 00787 07239 192 19214SPT-JCRS 2395 00703 07717 15467 15448

119870 = 2

IRBT 197273 01998 09722 47333 47317IRMT 159967 01888 07993 48 47986

MCM-JCRS 178833 01578 07205 38667 38669SPT-JCRS 233780 01411 07628 31333 31325

119870 = 3

IRBT 200016 02970 09719 7 69988IRMT 162761 02769 07911 7 69984

MCM-JCRS 18225 02481 07644 604 60418SPT-JCRS 234697 02093 07561 464 46392

119870 = 4

IRBT 202207 03702 09144 86909 86918IRMT 186563 03086 07244 74545 74531

MCM-JCRS 18966 02483 0589 59636 59631SPT-JCRS 241418 02455 06761 53818 53816

119870 = 5

IRBT 215448 03909 08040 896 89613IRMT 206932 03043 06105 708 70815

MCM-JCRS 217823 02225 04608 508 50791SPT-JCRS 26238 02155 04987 456 456

119870 = 6

IRBT 239454 03929 07182 864 86388IRMT 236876 02862 05197 632 63212

MCM-JCRS 242579 02088 03854 456 45603SPT-JCRS 272301 02133 04204 444 44389

1 2 3 4 5 60

2

4

6

8

10

Number of channels (K)

Thro

ughp

ut (M

bps)

IRBT

IRMT

MCM-JCRS

SPT-JCRS

Figure 4 Networkrsquos throughput as function of the number ofchannels

situation the lack of load-balancing could sufficiently reducethe networkrsquos throughput

7 Conclusion

In this paper the throughput of a MCMR-WMN wasquantified We focused on the scenario of on-demand QoSmulticastbroadcast sessions where each session has a spe-cific bandwidth requirement In particular considering theresource constraints we derived analytical relationships forthe networkrsquos throughput in terms of the node utilization thechannel utilization and the number of transmissions Thisgives simple solutions for the future designs to predict thenetworkrsquos throughput based on the resource utilizations Inline with the proposed relationships we also demonstratedthat the networkrsquos throughput is significantly affected by bothnumber of transmissions and degree of load-balancing Onone hand minimizing the number of transmissions reducesthe use of the network resources On the other hand load-balancing increases the fairness in the network In thissituation more resources will be available for accepting thefuture sessions Thus the overall networkrsquos throughput willbe increased

Acknowledgment

This work is supported by the Iranian TelecommunicationResearch Center (ITRC)

The Scientific World Journal 9

References

[1] PH Pathak andRDutta ldquoA survey of network design problemsand joint design approaches in wireless mesh networksrdquo IEEECommunications Surveys and Tutorials vol 13 no 3 pp 396ndash428 2011

[2] A Raniwala and T-C Chiueh ldquoArchitecture and algorithms foran IEEE 80211-based multi-channel wireless mesh networkrdquo inProceedings of the IEEE International Conference on ComputerCommunications (INFOCOM rsquo05) vol 3 pp 2223ndash2234March2005

[3] A Avokh and G Mirjalily ldquoPerformance analysis of broad-casting in small-scale multi-radio multi-channel wireless meshnetworksrdquo in Proceedings of the 14th International Conference onAdvanced Communication Technology (ICACT rsquo12) pp 537ndash542February 2012

[4] U T Nguyen and J Xu ldquoMulticast routing in wireless meshnetworks minimum cost trees or shortest path treesrdquo IEEECommunications Magazine vol 45 no 11 pp 72ndash77 2007

[5] Y Li and I Chen ldquoDynamic agent-based hierarchical multicastfor wireless mesh networksrdquo Ad Hoc Networks vol 11 no 6 pp1683ndash1698 2013

[6] J E Wieselthier G D Nguyen and A Ephremides ldquoEnergy-efficient broadcast and multicast trees in wireless networksrdquoMobile Networks and Applications vol 7 no 6 pp 481ndash4922002

[7] A Avokh G Mirjalily and J Abouei ldquoJoint channel andrate selection for multicast routing trees in wireless meshnetworksrdquo in Proceedings of the International Symposium onTelecommunications pp 548ndash553 November 2012

[8] K N Ramachandran E M Belding K C Almeroth andM M Buddhikot ldquoInterference-aware channel assignment inmulti-radio wireless mesh networksrdquo in Proceedings of the 25thIEEE International Conference on Computer Communications(INFOCOM rsquo06) pp 1ndash12 April 2006

[9] R-H Jan S-Y Huang and C-F Wang ldquoAn upper bound ofthe throughput for multi-radio wireless mesh networksrdquo IEEECommunications Letters vol 14 no 8 pp 698ndash700 2010

[10] A Capone G Carello I Filippini S Gualandi and F Malu-celli ldquoRouting scheduling and channel assignment in wirelessmesh networks optimization models and algorithmsrdquo Ad HocNetworks vol 8 no 6 pp 545ndash563 2010

[11] E Alotaibi V Ramamurthi M Batayneh and B MukherjeeldquoInterference-aware routing for multi-hop wireless mesh net-worksrdquo Computer Communications vol 33 no 16 pp 1961ndash1971 2010

[12] V C M Borges D Pereira M Curado and E MonteiroldquoRoutingmetric for interference and channel diversity inmulti-radio wireless mesh networksrdquo in Ad-Hoc Mobile and WirelessNetworks vol 5793 of Lecture Notes in Computer Science pp55ndash68 Springer Berlin Germany 2009

[13] S Roy D Koutsonikolas S Das and Y C Hu ldquoHigh-throughput multicast routing metrics in wireless mesh net-worksrdquo Ad Hoc Networks vol 6 no 6 pp 878ndash899 2008

[14] P M Ruiz and A F Gomez-Skarmeta ldquoApproximating optimalmulticast trees in wireless multihop networksrdquo in Proceedings ofthe 10th IEEE Symposium on Computers and Communications(ISCC rsquo05) pp 686ndash691 June 2005

[15] H L Nguyen and U T Nguyen ldquoBandwidth efficient multicastrouting in multi-channel multi-radio wireless mesh networksrdquoin Proceedings of the International Conference on Ultra Modern

Telecommunications and Workshops (ICUMT rsquo09) pp 1ndash8October 2009

[16] G Zeng B Wang Y Ding L Xiao and M Mutka ldquoEfficientmulticast algorithms formultichannel wireless mesh networksrdquoIEEE Transactions on Parallel and Distributed Systems vol 21no 1 pp 86ndash99 2010

[17] H S Chiu K L Yeung and K-S Lui ldquoMaximizing broadcastload in multi-channel Multi-interface wireless mesh networksrdquoin Proceedings of the IEEE Global Telecommunications Confer-ence (GLOBECOM rsquo08) pp 533ndash537 December 2008

[18] F Li Y Fang F Hu and X Liu ldquoLoad-aware multicast routingmetrics in multi-radio multi-channel wireless mesh networksrdquoComputer Networks vol 55 no 9 pp 2150ndash2167 2011

[19] P A K Acharya and E M Belding ldquoMARS link-layer rateselection for multicast transmissions in wireless mesh net-worksrdquo Ad Hoc Networks vol 9 no 1 pp 48ndash60 2011

[20] A Avokh and G Mirjalily ldquoInterference-aware multicast andbroadcast routing in wireless mesh networks using both rateand channel diversityrdquo Computers amp Electrical Engineering2013

[21] T Kim Y Yang J C Hou and S V Krishnamurthy ldquoResourceallocation for QoS support in wireless mesh networksrdquo IEEETransactions on Wireless Communications vol 12 no 5 pp2046ndash2054 2013

[22] W Kocay and D Kreher Graphs Algorithms and Optimiza-tion Discrete Mathematics and Its Applications Chapman ampHallCRC Boca Raton Fla USA 2005

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

The Scientific World Journal 9

References

[1] PH Pathak andRDutta ldquoA survey of network design problemsand joint design approaches in wireless mesh networksrdquo IEEECommunications Surveys and Tutorials vol 13 no 3 pp 396ndash428 2011

[2] A Raniwala and T-C Chiueh ldquoArchitecture and algorithms foran IEEE 80211-based multi-channel wireless mesh networkrdquo inProceedings of the IEEE International Conference on ComputerCommunications (INFOCOM rsquo05) vol 3 pp 2223ndash2234March2005

[3] A Avokh and G Mirjalily ldquoPerformance analysis of broad-casting in small-scale multi-radio multi-channel wireless meshnetworksrdquo in Proceedings of the 14th International Conference onAdvanced Communication Technology (ICACT rsquo12) pp 537ndash542February 2012

[4] U T Nguyen and J Xu ldquoMulticast routing in wireless meshnetworks minimum cost trees or shortest path treesrdquo IEEECommunications Magazine vol 45 no 11 pp 72ndash77 2007

[5] Y Li and I Chen ldquoDynamic agent-based hierarchical multicastfor wireless mesh networksrdquo Ad Hoc Networks vol 11 no 6 pp1683ndash1698 2013

[6] J E Wieselthier G D Nguyen and A Ephremides ldquoEnergy-efficient broadcast and multicast trees in wireless networksrdquoMobile Networks and Applications vol 7 no 6 pp 481ndash4922002

[7] A Avokh G Mirjalily and J Abouei ldquoJoint channel andrate selection for multicast routing trees in wireless meshnetworksrdquo in Proceedings of the International Symposium onTelecommunications pp 548ndash553 November 2012

[8] K N Ramachandran E M Belding K C Almeroth andM M Buddhikot ldquoInterference-aware channel assignment inmulti-radio wireless mesh networksrdquo in Proceedings of the 25thIEEE International Conference on Computer Communications(INFOCOM rsquo06) pp 1ndash12 April 2006

[9] R-H Jan S-Y Huang and C-F Wang ldquoAn upper bound ofthe throughput for multi-radio wireless mesh networksrdquo IEEECommunications Letters vol 14 no 8 pp 698ndash700 2010

[10] A Capone G Carello I Filippini S Gualandi and F Malu-celli ldquoRouting scheduling and channel assignment in wirelessmesh networks optimization models and algorithmsrdquo Ad HocNetworks vol 8 no 6 pp 545ndash563 2010

[11] E Alotaibi V Ramamurthi M Batayneh and B MukherjeeldquoInterference-aware routing for multi-hop wireless mesh net-worksrdquo Computer Communications vol 33 no 16 pp 1961ndash1971 2010

[12] V C M Borges D Pereira M Curado and E MonteiroldquoRoutingmetric for interference and channel diversity inmulti-radio wireless mesh networksrdquo in Ad-Hoc Mobile and WirelessNetworks vol 5793 of Lecture Notes in Computer Science pp55ndash68 Springer Berlin Germany 2009

[13] S Roy D Koutsonikolas S Das and Y C Hu ldquoHigh-throughput multicast routing metrics in wireless mesh net-worksrdquo Ad Hoc Networks vol 6 no 6 pp 878ndash899 2008

[14] P M Ruiz and A F Gomez-Skarmeta ldquoApproximating optimalmulticast trees in wireless multihop networksrdquo in Proceedings ofthe 10th IEEE Symposium on Computers and Communications(ISCC rsquo05) pp 686ndash691 June 2005

[15] H L Nguyen and U T Nguyen ldquoBandwidth efficient multicastrouting in multi-channel multi-radio wireless mesh networksrdquoin Proceedings of the International Conference on Ultra Modern

Telecommunications and Workshops (ICUMT rsquo09) pp 1ndash8October 2009

[16] G Zeng B Wang Y Ding L Xiao and M Mutka ldquoEfficientmulticast algorithms formultichannel wireless mesh networksrdquoIEEE Transactions on Parallel and Distributed Systems vol 21no 1 pp 86ndash99 2010

[17] H S Chiu K L Yeung and K-S Lui ldquoMaximizing broadcastload in multi-channel Multi-interface wireless mesh networksrdquoin Proceedings of the IEEE Global Telecommunications Confer-ence (GLOBECOM rsquo08) pp 533ndash537 December 2008

[18] F Li Y Fang F Hu and X Liu ldquoLoad-aware multicast routingmetrics in multi-radio multi-channel wireless mesh networksrdquoComputer Networks vol 55 no 9 pp 2150ndash2167 2011

[19] P A K Acharya and E M Belding ldquoMARS link-layer rateselection for multicast transmissions in wireless mesh net-worksrdquo Ad Hoc Networks vol 9 no 1 pp 48ndash60 2011

[20] A Avokh and G Mirjalily ldquoInterference-aware multicast andbroadcast routing in wireless mesh networks using both rateand channel diversityrdquo Computers amp Electrical Engineering2013

[21] T Kim Y Yang J C Hou and S V Krishnamurthy ldquoResourceallocation for QoS support in wireless mesh networksrdquo IEEETransactions on Wireless Communications vol 12 no 5 pp2046ndash2054 2013

[22] W Kocay and D Kreher Graphs Algorithms and Optimiza-tion Discrete Mathematics and Its Applications Chapman ampHallCRC Boca Raton Fla USA 2005

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of