Joint QoS-aware Node Clustering and Tax-basedSubcarrier Allocation for Wireless Mesh Networks

Ho Ting Cheng†, Weihua Zhuang†, and Aladdin Saleh∗†Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Email: {htcheng, wzhuang}@bbcr.uwaterloo.ca∗Wireless Technology Department, Bell Canada, 5099 Creekbank Road, Mississauga, ON, Canada L4W 5N2

Email: aladdin.saleh@bell.ca

Abstract— In this paper, we propose a novel node clusteringalgorithm with effective tax-based subcarrier allocation tailoredfor wireless mesh networks with quality-of-service support. Witheffective frequency reuse, our proposed approach is shownto achieve a higher system throughput than a conflict-graphapproach and a baseline approach. Also, our approach is demon-strated promising in performance tradeoff between packet delayand end-to-end transmission rate.

I. INTRODUCTION

Wireless mesh networking has emerged as a promising tech-nology for future broadband wireless access [1,2]. Wirelessmesh networks (WMNs) generally comprise gateways, meshrouters, and mesh clients, organized in a three-tier hierarchi-cal architecture [2]. Recently, wireless mesh networking forsuburban residential areas has been attracting a plethora ofattentions, where mesh routers can be set up at premises inthe neighborhood, rendering a resilient mesh backbone, andproviding an all-wireless ambience.

Concerning the capacity of a wireless network, the through-put of a node decreases with the number of wireless nodes.The implication is that a node should only communicatewith nearby nodes, thereby favoring clustering [3]. In fact,clustering is an effective way to manage a large wirelessnetwork [4]. Although clustering has been researched in thecontext of sensor networks and mobile ad hoc networks(MANETs) in recent years, applying the existing clusteringschemes to WMNs may not be efficient or effective due todifferent networking characteristics and design objectives. Thegoal for establishing WMNs is to provide an all-wireless envi-ronment, rendering a high-speed and efficient mesh backboneoffering broadband wireless access with quality-of-service(QoS) support [2], while the primary purpose for deployingsensor networks is to offer environmental monitoring (e.g.,temperature, pressure, etc) and/or surveillance (e.g., militaryfield surveillance) [5]. Mobility and energy efficiency are themajor concerns in MANETs [4], where the nodes are mobileand have power constraints, but there are no such limitationsin WMNs. Further, the deployment of WMNs is relativelypermanent, giving rise to the requisite of high efficiency ofWMNs with QoS support. Thus, a new clustering approachspecifically tailored for QoS-sensitive WMNs is indispensable.

1This research was supported by research grants from the Natural Scienceand Engineering Research Council (NSERC) of Canada and the Bell Univer-sity Labs (BUL) at Waterloo.

In order to efficiently support multimedia services andameliorate system capacity, effective channel assignment andhence interference control are imperative to facilitate QoS pro-visioning and frequency reuse [6]. In the literature, there existsa wide range of channel assignment schemes for wirelessnetworks [7]–[10]. However, most of the existing approachesare not QoS-aware. An interference conflict graph is usuallyadopted to devise a collision-free scheduling in a two-hopneighborhood [8,9]. Yet, packet scheduling deduced by theinterference conflict graph may not guarantee collision-freetransmissions in a large-scale WMN, where the aggregateinterference coming from the transmissions outside the neigh-borhood can be very large. Combining topology control withchannel assignment is vital for better network management.TiMesh is proposed to avoid a ripple effect [10], but hampersthe notion of frequency reuse, underutilizing the scarce radioresources. Therefore, a novel distributed channel allocationstrategy tailored for a clustered mesh backbone is crucial.

With clustering, interference control and hence frequencyreuse can be facilitated by channel allocation via clusterheads.In a cluster, collision-free scheduling is feasible, to satisfyvarious QoS demands. Resource allocation can be carried outin a hybrid centralized-distributed fashion (i.e., centralizedintra-cluster and distributed inter-cluster resource allocation)[6]. In this paper, we propose a QoS-aware clustering algo-rithm with tax-based subcarrier allocation tailored for WMNs.Our proposed approach is shown to achieve a high systemthroughput, and provide a good performance tradeoff betweenpacket delay and end-to-end transmission rate for real-timetraffic.

II. SYSTEM MODEL

Consider a WMN for suburban residential areas, consistingof one wireline gateway attached to the Internet backboneand a number of mesh routers scattered around, renderinga multi-hop network (see Fig. 1). The system model takesaccount that suburban environments are usually austere, whichthwarts one-hop direct communications as opposed to multi-hop transmissions, providing ease of deployment and offeringgreater coverage of wireless access [2]. A gateway can be setup at one side of the suburban residential area of interest.We assume that mesh routers are non-mobile and the channelgains can be estimated accurately. Traffic is assumed to bevertical, where traffic flows are traversed from mesh routers

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Wireline

gateway

Mesh

router

Internet

backbone

Node A

Node B

Fig. 1. System model.

to the gateway, and vice versa. In this work, we considerthe upstream traffic from the mesh routers to the gateway.Three types of traffic are considered, namely voice, video,and data. Voice traffic and video traffic are considered asreal-time traffic, while data traffic is considered as non-real-time traffic. Time is partitioned into frames, each of whichis further divided into a beacon slot, a control slot, and LDATA slots. Note that how to perform intra-cluster resourceallocation to an individual node (e.g., packet scheduling [6]) isbeyond the scope of this paper. Call admission control (CAC)is assumed in place such that the QoS requirements of anadmitted call (flow) can be satisfied. With a physical layerbased on orthogonal frequency division multiplexing (OFDM)technology, each router can choose a set of subcarriers forDATA transmissions and/or receptions, allowing simultaneoustransmissions over different subcarriers in the mesh backbone.

III. JOINT QOS-AWARE CLUSTERING AND TAX-BASED

SUBCARRIER ALLOCATION

We propose a QoS-aware clustering algorithm with tax-based subcarrier allocation tailored for WMNs. As ameliorat-ing throughput in a mesh backbone is the key to the successof providing an all-wireless ambience, the objective for thejoint QoS-aware clustering and subcarrier allocation problemis chosen to maximize the system throughput. Notice that theobjective function can be modified to optimize other systemperformance measures (e.g., a tradeoff between throughput andfairness with QoS support [11]). However, the node clusteringproblem and the subcarrier allocation problem are coupled. Toreduce the computational complexity, our approach is to solvethe clustering problem and to allocate subcarriers in successionalternatively (as discussed in Section III-D).

Considering the factors of system capacity, QoS provision-ing, burden on clusterheads, delay of packet delivery, andthe austere suburban environment, we formulate the clusteringproblem by setting an upper bound on the subcarriers allocatedto a cluster. Denote Bmax as the upper bound of allocatedchannels in a cluster. The bound caps the maximum traffic loadin a cluster and hence the burden on a clusterhead, controls the

cluster size to a certain extent, and facilitates packet schedulingassisted by clusterheads. The proposed approach for the jointnode clustering and subcarrier allocation problem includes:1) neighbor discovering; 2) initial route establishment; 3)traffic load estimation; 4) node clustering; and 5) subcarrierallocation.

A. Neighbor Discovering

A mesh router can discover its neighbor(s) via any routingprotocol. As mesh routers are assumed to be stationary, allthe possible paths of a mesh router to the gateway can bepre-determined.

B. Initial Route Establishment

Establishing an initial route is imperative to facilitate trafficload estimation and hence QoS-aware node clustering. Denotepe

m as the eth link along the pth shortest path of the mth

node to the gateway. The initial route of a mesh router to thegateway is determined by the following condition:

max∀p

{min∀e∈p

{R̃m(pem)}},∀m (1)

where R̃m(y) = ln(1 + G̃m(y)Pmax

m /η)

can be viewed as a

data rate obtained at the mth node on the yth link with G̃m(y)being the (constant) channel gain on the link, Pmax

m being themaximum power constraint of the mth node, and η being thenoise power. The effect of co-channel interference is discussedin Section III-E. The objective given in (1) is to maximize theminimum of all link rates (i.e., maximize the end-to-end rate)along the shortest path of a node to the gateway. This initialpath establishment criterion ends in a tree architecture for aWMN (See Fig. 1).

C. Traffic Load Estimation

To facilitate resource allocation at the medium access con-trol (MAC) layer, traffic load estimation is necessary [2]. Eachnode estimates the traffic load of real-time traffic by averagingthe rate requirement over a fixed observation window (e.g.,100ms). The sum of the local traffic load estimate of anode and the relay load received is forwarded to its next-hop neighbor (toward the gateway) determined by its initialestablished path. Let Xm be the local traffic load estimateat the mth node, and Ym be the relay load received by themth node. Then, Yu = Xw + Yw, where the uth node is thenext-hop neighbor (toward the gateway) of the wth node. Weassume that there is no local traffic generation at the gateway.Such traffic load estimation is also crucial for supporting QoSin intra-cluster resource allocation [6].

D. Node Clustering Algorithm

We assume that clusterheads can operate in a dual-powermode [5], where higher power levels are reserved for inter-cluster signaling2 whereas lower power levels are for intra-cluster communications. Define an I-tier cluster as a cluster

2In case direct inter-cluster transmissions fail (e.g., due to path loss), weassume that cooperative communications [12] are in place such that the inter-cluster signaling is always feasible.

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formed at the Ith clustering level from the gateway. Theproposed clustering algorithm is described as follows:

Step 1: All nodes are set to be unassigned (i.e., neitherclusterheads nor clustermembers). The gateway is setto be the default clusterhead. Set I=1.

Step 2: The clusterhead of interest selects one of its 1-hopunassigned nodes and collects its QoS requirement(i.e., traffic load demand). If no neighbors can beselected, go to Step 5.

Step 3: The clusterhead of interest chooses the best availablesubcarrier(s) for the selected node based on thesubcarrier allocation criterion given in (5), to bediscussed in Section III-E. If the QoS demand ofthe selected node cannot be satisfied, go to Step 6.

Step 4: If the total number of subcarriers acquired is lessthan or equal to Bmax in the cluster of interest,the selected node becomes a clustermember of thatcluster, the chosen subcarriers are recorded in a tablestored at the cluster of interest, and go back Step 2.

Step 5: An I-tier cluster is created. The clusterhead of inter-est keeps selecting the best available subcarrier(s), iffeasible, until the total number of chosen subcarriersis Bmax.

Step 6: Repeat Steps 2-5 with another I-tier clusterheadelected randomly by the (I-1)-tier clusterhead(s), ifany.

Step 7: The I-tier clusterhead(s) is/are to signal its/theirclosest unassigned neighbor(s) (e.g., 1-hop or 2-hop neighbors) and to elect the clusterhead(s) at the(I+1)-tier. If a clusterhead can be elected, set I=I+1and go back to Step 2.

Step 8: Any unassigned node joins its closest clusterhead(s).Any node that is a 1-hop neighbor of a clusterheadautomatically becomes a clustermember of that clus-ter. Any node that is a 1-hop neighbor of more thanone clusterhead can be viewed as a clustergateway.

Clusters closer to the gateway have higher priority, whereasthe ones farther away from the gateway have lower priority.The rationale is that traffic bottlenecks are usually found at(and near) the gateway and hence those clusters close to thegateway are assigned higher priority in the proposed resourceallocation approach. In this work, for simplicity, clusterheadsonly select their 1-hop nodes as their clustermembers. Thus, aclustered WMN will consist of 1- and/or 2-clusters3, and dif-ferent clusters may have different sizes. Further, clusterheadsform a connected graph.

E. Subcarrier Allocation

Without any effective subcarrier allocation, it is plausiblethat large co-channel interference is introduced by unfavorablesimultaneous transmissions. Consider the case where clus-terheads do not exchange any information and myopicallymaximize the aggregate throughput in their clusters. Since

3A k-cluster is defined as a subset of nodes which are mutually reachableby a path of length at most k-hops for an integer k.

there is no penalty for a cluster to use all the (chosen)subcarriers for its intra-cluster communications, the resultantco-channel interference generated to other clusters can be verylarge, decreasing system capacity. Hence, the above solutioncan be far from the optimal solution(s). In the following, weview a clusterhead as the representative of its cluster.

We propose a novel subcarrier allocation scheme motivatedby Karush-Kuhn-Tucker (KKT) optimality conditions [13].Denote M as the number of clusterheads, N as the number ofavailable subcarriers (i.e., Bmax ≤ N ), and L as the number oftimeslots (i.e., DATA slots) in a frame. Consider the followingpayoff function of the mth clusterhead over the nth subcarrieron the lth timeslot

Slm,n

(al

m,n, plm,n

)= al

m,nrlm,n − pl

m,n

M∑k �=m

alk,nT l

km,n (2)

where rlm,n = ln(1+γl

m,n) represents the obtained data rate ofthe mth clusterhead over the nth subcarrier on the lth timeslotwith the received signal-to-interference-and-noise ratio (SINR)γl

m,n, alm,n is the indicator of allocating the nth subcarrier to

the mth clusterhead on the lth timeslot, i.e., alm,n ∈ {0, 1},

plm,n is the transmit power, and T l

km,n is tax paid by the mth

clusterhead for generating interference to the kth node overthe nth subcarrier on the lth timeslot, defined as

T lkm,n = −∂Uk(a,p, Rd

k)∂pl

m,n

(3)

where Uk(a,p, Rdk) is the utility function of the kth cluster-

head with Rdk being the QoS demand of the kth clusterhead,

a = [alk,n]M×N×L, and p = [pl

k,n]M×N×L. The SINR of themth clusterhead over the nth subcarrier on the lth timeslot isgiven by γl

m,n = ϕGmm,nplm,n

σ∑

k �=m alk,nGmk,npl

k,n+η, where Gmk,n is the

channel gain from the kth clusterhead to the mth clusterheadover the nth subcarrier, ϕ is a bit-error-rate measure, and σis the cross-correlation factor between any two signals. Theutility function of the kth clusterhead is defined as

Uk(a,p, Rdk)

=

{∑Ll

∑Nn al

k,nrlk,n − Rd

k,∑L

l

∑Nn al

k,nrlk,n − Rd

k ≥ ε

0,∑L

l

∑Nn al

k,nrlk,n − Rd

k < ε

(4)

where 0 < ε � 1. Notice that T lkm,n can be interpreted

as the marginal decrease in the utility obtained by the kth

clusterhead per unit increase in the transmit power of the mth

clusterhead over the nth subcarrier on the lth timeslot. Thus,T l

km,n is always non-negative. With the tax interpretation ofthe KKT conditions, each clusterhead, therefore, essentiallymaximizes the difference between its throughput obtainedminus its lump-sum tax paid to the other clusterheads inthe mesh backbone due to the induced interference. Eachclusterhead is to optimize al

m,n and plm,n such that its own

payoff function is maximized. Overall, a and p are theoptimization variables. The proposed subcarrier allocationstrategy is more suitable and applicable than a traditional

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coloring approach to WMNs, mesh routers of which are notevenly distributed. More importantly, with the tax information,subcarrier allocation and hence frequency reuse can be carriedout in a distributed manner.

In this work, we only focus on the subcarrier allocationby fixing power allocation (i.e., uniform power distribution),though subcarrier allocation and power allocation should bejointly considered for the sake of optimality [6]. Thus, thecriterion of subcarrier allocation can be deduced as follows:For the mth node on the lth timeslot, choose n∗ such that

n∗ = arg maxn

{Sl

m,n

(al

m,n

)}(5)

and set alm,n∗ = 1. Note that information exchange among

clusterheads is triggered whenever there is any change insubcarrier allocation.

F. Complexity

Assume that message signaling among clusterheads is per-fect such that they have complete knowledge of their lump-sum tax. Since each clusterhead behaves individually in se-quence, the time complexity of the proposed subcarrier allo-cation is on the order of O(NL). Thus, The time complexity ofthe proposed clustering algorithm given in Section III-D is onthe order of O(MNLBmax). With the help of effective datastructure (e.g., binary tree implementation), the complexitycan be further reduced to the order of O(MLBmax log2 N).

IV. PERFORMANCE EVALUATION

We consider a WMN with mesh routers randomly locatedin a 3km x 3km coverage area. A routing protocol is assumedin place such that the neighbors of each node can be identifiedin advance. Parameters for performance evaluation are chosenas follows: ϕ = 1, σ = 1, η ∼ N(0, 10−12W), Pmax

m = 1W,∀m, N = 25M , L = 4, and Bmax = N/4. The maximumtransmission rate of each subcarrier is 100Kbps. We adopt thechannel model suggested in [14].

We use the traffic models for voice, video, and data, theMAC protocol, and CAC as described in [6]. Here, we usethe MAC protocol for both intra-cluster and inter-clustercommunications. The duration of a timeslot is 5ms, and hencethe duration of a frame is 5(2+L)ms. For intra-cluster MAC,the clusterhead collects the transmission requests and trafficdemands from its clustermembers by polling them periodicallyin the control slot, and announces the resource allocation inthe subsequent beacon. The polling is done in every 100ms.Similarly, for inter-cluster MAC, a clusterhead collects the thetransmission requests from its neighboring clusterhead(s) inthe control slot, and announces the transmission schedule inthe subsequent beacon. The timeslots and subcarriers allocatedto a particular node are reserved for packet transmissions inthe DATA slots until the next polling. Moreover, for real-timetraffic (i.e., voice and video), the higher the packet droppingrate that a traffic flow experiences, the higher the priority ofthe packets associated with that flow. A clusterhead grantsthe requests of those higher-priority packets first, facilitating

Internet

backbone

Clustermember

Clusterhead

Cluster

Initial established path

Node A

Node B

Fig. 2. An illustration of a clustered WMN with 24 mesh routers.

1.5 2 2.5 3 3.5 4 4.5 515

20

25

30

35

40

45

50

55

60

End−to−end throughput (in Mb/s)

Del

ay (

in m

s)

Node A (voice packets)Node B (video packets)

random

proposed

max−rate

random

proposed

max−rate

Fig. 3. Comparison of the real-time packet delay of the proposed scheme,the random scheme, and the max-rate scheme vs. the end-to-end throughputfor Node A and Node B shown in Fig. 2.

QoS provisioning. Both the polling and the beacon packettransmissions are assumed error-free.

The performance measurements are defined as follows:• System throughput – the sum of the throughputs

obtained in the entire WMN.• Frequency reuse ratio – the average number of times

that a subcarrier is used simultaneously per DATA slot.• Packet delay – the interval between the instant that a

packet is generated at a source node and the instant thatpacket is successfully received by the gateway.

A. QoS-aware Clustering

We first study the performance of our proposed QoS-aware clustering algorithm. After discovering the neighbors,every node establishes an initial shortest route to the gatewayaccording to the condition given in (1). With CAC in place,each node can estimate the traffic load. The proposed nodeclustering algorithm is then carried out. An illustration of thecluster structure of a WMN with 24 mesh routers is depicted inFig. 2. The WMN consists of 1- and 2-clusters, and differentclusters may have different sizes.

We then compare the system performance in terms of packetdelay and throughput of the proposed scheme for initial pathestablishment (named proposed) with the scheme for randomshortest path establishment (named random) and the schemefor path establishment that gives the maximum end-to-endrate (named max-rate). The delay-throughput performancecomparison of the three schemes for Node A and Node B

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0 20 40 60 80 1000

200

400

600

800

1000

1200

Number of clusterheads, M

Sys

tem

thro

ughp

ut (

in M

b/s)

tax−based (proposed)conflict−graphbaseline

Fig. 4. Comparison of the system throughput of the proposed approach,the conflict-graph approach, and the baseline approach vs. the number ofclusterheads.

0 20 40 60 80 1000

1

2

3

4

5

6

7

Number of clusterheads, M

Fre

quen

cy r

euse

rat

io

tax−based (proposed)conflict−graph

Fig. 5. Comparison of the frequency reuse ratio of the proposed approachand the conflict-graph approach vs. the number of clusterheads.

(in Fig. 2) is depicted in Fig. 3. Notice that the same nodeclustering algorithm with subcarrier allocation is employed forthe three schemes. As seen, using the max-rate scheme forpath establishment, both voice packets at Node A and videopackets at Node B attain the largest end-to-end throughputat the cost of packet delay. Although both the proposed andrandom schemes result in the smallest packet delays, theproposed approach achieves higher end-to-end throughputs.The improvement of the proposed approach over the randomapproach, however, is not substantial because routing is nottaken into consideration. The improvement is expected to belarger if node clustering, subcarrier allocation, and routingare jointly considered. Other system performance (e.g., packetdropping rates) in regards to intra-cluster resource allocationis reported in [15].

B. Tax-based Subcarrier Allocation

Here, we evaluate the performance of the proposed tax-based subcarrier allocation in terms of system throughput andfrequency reuse ratio. For comparison, we consider a baselineapproach where there is no frequency reuse and an approachusing an interference conflict graph [9]. Fig. 4 shows thesystem throughput versus the number of clusterheads. Thestandard deviations of the results are also plotted for reference.Clearly, our proposed approach achieves a significantly higher

system throughput than the other two approaches. The systemthroughput of all the approaches increases with the number ofclusterheads, for the number of available subcarriers increases.The system throughput procured in our approach to subcarrierallocation, however, rises almost exponentially with the num-ber of clusterheads. The rationale of our proposed approachbeing superior to the conflict-graph approach stems from thefact that the interference conflict graph merely yields a condi-tion that adjacent vertices cannot use the same subcarrier(s),thereby suppressing the potential and favorable concurrenttransmissions over the same subcarrier(s). In contrast, thetax-based subcarrier allocation fosters frequency reuse to agreater extent. We also observe that, on average, our proposedapproach conduces to a higher frequency reuse ratio than theconflict-graph approach (see Fig. 5). The results confirm thefact that employing the notion of frequency reuse is imperativefor increasing the system throughput. Our proposed tax-basedsubcarrier allocation, therefore, can better utilize the networkresources, giving rise to a radio spectrum efficient WMN.

V. CONCLUSION

In this paper, we have proposed a novel QoS-aware clus-tering algorithm with effective tax-based subcarrier allocationtailored for WMNs. The proposed taxation method is shownto be vital to bolster frequency reuse, effectively amelioratingthe system throughput for a mesh backbone. In addition,our proposed scheme provides a good performance balancebetween packet delay and end-to-end data rate for real-timetraffic, leading to a viable candidate for QoS provisioning.Further work includes study of multi-path transmissions andinvestigation of optimal Bmax value(s).

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