A Queue-aware Scheduling Algorithm for MultihopRelay Wireless Cellular Networks

Haining Chen, Xiaojuan Xie and Hongyi Wu

Abstract—This work centers on the downlink scheduling al-gorithm for such cellular wireless networks with relays as IEEE802.16j. We propose an efficient algorithm to discover concurrenttransmission scenarios under a multihop relay environment,while applying the back-pressure flow control mechanism toreflect the dynamic queue status of each relay station. Then, wedevelop a linear programming algorithm for scheduling, aimingat maximizing network throughput and achieving fairness. Inthis linear programming model, we consider the frame-basedtransmission in wireless cellular networks and the queue dy-namics at the relay stations. Simulations are carried out basedon IEEE 802.16 OFDMA mode for performance evaluation andcomparison in terms of throughput and fairness. The results showthe effectiveness of our proposed scheduling algorithm againstother scheduling schemes.

I. INTRODUCTION

Wireless cellular networks have undergone rapid develop-ment over the past several decades, evolving from the firstgeneration [1], [2], to the second generation [3], [4], and to thethird generation systems [5], [6]. WiMAX (Worldwide Inter-operability for Microwave Access) along with other emergingtechnologies [7], [8] are being actively considered as the newadditions to this family, aiming to provide anytime, anywheresolution that supports voice, data and streamed multimedia athigher data rates than previous generations.

The growth of wireless cellular networks shows that thequest for higher network throughput, wider network coverage,larger network capacity, and better network quality never stops.To achieve such goals, a variety of approaches, including mod-ulation and coding, seamless handoff, and efficient frequencyreuse, have been developed during the past evolution. Besidesthe aforementioned technologies, an architectural enhancementcalled relay network have been proposed for wireless cellularnetworks to achieve better throughput, coverage, capacity, andquality. In the relay network, one or multiple Relay Stations(RS) are deployed between a Base Station (BS) and an MobileStation (MS) for data relaying, thus creating a multihopwireless network. An example of such relays is illustrated inthe recent WiMAX draft standard, IEEE 802.16j [9].

The benefit of using RS in the wireless network is multifold.First, RS can expand the coverage area of wireless cellular

This work is supported in part by National Science Foundation CAREERAward under Award Number CNS-0347686 and by U.S. Department ofEnergy (DoE) under Award Number DE-FG02-04ER46136.

Haining Chen is with Computer Information Technology Division, BethelCollege, Mishawaka, IN, 46545. Email: haining.chen@bethelcollege.edu.

Xiaojuan Xie and Hongyi Wu are with the Center for Advanced Com-puter Studies, University of Louisiana at Lafayette, Lafayette, LA, 70504.Email:{xxx7680,wu}@cacs.louisiana.edu.

networks. It is obvious that the radius of the cellular cell canbe extended since RS adds its own coverage into the reachablerange of the cellular cell. Besides, RS can help to reach areaswhere there is no direct link available. For example, someshadow areas behind high and dense buildings are difficultto reached by direct link from BS, but are easily reachablewith RS placed at suitable location. Second, RS can increasethe capacity of wireless cellular networks. It is indicated in[10] that RS enables neighboring cells to borrow channelsfrom each other so that when one cell is congested with highvolume of traffic, the borrowed channels from its neighboringcell can help relieve the congestion and thus increase networkcapacity and reduce packet dropped rate. Third, RS canimprove the signal-to-noise ratio (SNR) and accordingly thenetwork throughput. Compared to direct link between BS andMS, the distance of relay link is shorter resulting in lesssignal attenuation in transmission path and improved SNR.Fourth, relay network enables concurrent transmission andhelp increase network throughput.

Nevertheless, the use of RS may result in negative effect,since multihop transmission over relay links increases trans-mission time and can potentially decrease network throughput.In this paper, we propose a scheduling algorithm for multihoprelay wireless cellular networks, and we take into considera-tion both positive and negative factors of relay on throughput,aiming at improving network throughput.

The rest of the paper is organized as follows. Section IIdiscusses related work. Section III proposes our schedulingalgorithm for multihop relay networks. Section IV presentssimulation results. Section V summarizes the paper.

II. RELATED WORK

Several schemes that employs ad hoc RS with distributedrouting and scheduling have been proposed in the literatures[11]–[15]. While such ad hoc solution enjoys great flexibilityin RS deployment, it faces significant signaling overhead andhigh complexity and low reliability in routing (especiallywhen quality-of-service is required). In contrast to the ad hocimplementation of relay network, recent development leansto well-controlled RS, which can be incorporated into thecurrent network with insignificant architecture modificationand small implementation overhead. One such attempt isthe development of a WiMAX draft standard, IEEE 802.16j[9], which is a revision of WiMAX for incorporating relayinto WiMAX networks. In 802.16j, BS runs the schedulingalgorithm and maintains full control over RS, while RS is fortraffic relay only and uses the same spectrum as BS and MS.

2009 IEEE Mobile WiMAX Symposium

978-0-7695-3719-1/09 $25.00 © 2009 IEEE

DOI 10.1109/MWS.2009.13

63

No ad hoc relay routing is needed in 802.16j since centralizedscheduling is implemented in BS.

[16] studies the scheduling algorithm in 802.16j, wheredirectional antennas are used to exploit the space reuse offrequency resources under a Manhattan-like environment. Al-though scheduling algorithm is provided to enhance networkthroughput, how to determine concurrent transmissions in re-lay network is not addressed therein. [17] assumes a multihopwireless mesh backhaul network with in-band relay. Each RSaggregates traffic for nearby MS. A linear programming modelis then developed to calculate the minimum time to transmita fixed data load from BS to every RS over possibly multiplehops. Since the transmission time is minimized for the fixeddata load, throughput is maximized. However, this approachdoes not address the varying traffic load (or queue size) ofeach RS, neither does it consider the frame-based feature ofWiMAX network or other wireless networks.

III. PROPOSED SCHEDULING ALGORITHM FOR MULTIHOP

RELAY WIRELESS CELLULAR NETWORKS

In this section, we first introduce wireless relay networkarchitecture and challenges. Then we present a linear program-ming model developed for scheduling algorithm in multihoprelay networks, followed by a discussion of how to findconcurrent transmission scenarios in relay networks.

A. Architecture and Challenges

Fig. 1 illustrates the architecture of wireless cellular relaynetwork such as IEEE 802.16j [9]. The key characteristicsof such cellular relay network are described below. It is acellular network with frame-based transmissions. BS connectsto RS and/or MS, and each RS can connect further to other RSand/or MS. RS only forwards traffic to/from MS and generateno traffic of its own. RS is transparent to MS, and MS doesnot involve in routing packets for other MS. BS, RS, andMS all share the same spectrum, thus no additional hardwaresuch as a second physical interface is needed. BS needs togather the downlink realtime queue size of its associatedRS and this queue information is sent to BS using uplinkbandwidth. The resulting signaling change due to uplink queuestatus report is insignificant, and the corresponding uplinkbandwidth consumption is neglectable. After gathering RSqueue information, BS run the scheduling algorithm to obtainthe downlink scheduling results and broadcasts the results toRS and MS.

In contrast to the ad hoc architecture discussed in Sec. II,this centralized approach of building a cellular relay networklet BS have full control of its associated RS and MS. Thesignaling and architecture change due to the introduction ofRS is limited. No software or hardware upgrade is needed inMS, and the signaling change of reporting RS queue size isrestricted between RS and BS. Hence this centralized approachis deemed a feasible solution and will not be considered as aburden by cellular network operator.

Scheduling in cellular relay networks is challenging. First,as the input for the scheduling algorithm, concurrent trans-

mission scenarios need to be determined in an efficient way.When adding a link candidate into a concurrent transmissionscenario, it must be guaranteed that adding this link will notdecrease the total throughput of this scenario. However, itis not practical to traverse all possible links searching forconcurrent scenarios due to the non-linear growth of links withrespect to number of MS and RS. The second challenge isdue to fact that wireless cellular networks are predominantlyframe-based, and the corresponding scheduling algorithm musttake this factor into consideration. In each frame, differentconcurrent scenarios must share this frame duration. Thusarises the issue of fair allocation of time resources amongvarious MS who share one frame, while still achieving the goalof achieving max network throughput. The third challenge isto let the scheduling algorithm adjust to the realtime queuesize change in RS.

Although we use 802.16j [9] as an example in our discus-sions throughout the paper, our proposed scheduling algorithmcan be readily applied to other types of wireless cellularnetworks such as WCDMA [5] or LTE [7].

B. Linear Programming Model for the Scheduling Algorithm

Now we present a linear programming model to implementthe scheduling algorithm for wireless cellular multihop relaynetwork. An example of the cellular relay network is shownin Fig. 1, which has M mobile stations and R relay stationsunder the control of one BS. The downlink frame duration is Tseconds, and the frames are indexed by t in the time domain.We consider the one-to-M downlink data transmission, withBS serving as the single source, and the M MS serving asdestinations. The transmission can be accomplished by a directlink from BS to MS, or by relay links via the RS. In each RS,a designated queue is maintained for each MS. The dynamicqueue information of each RS is sent to BS in the uplinkframe that precedes each downlink frame, and based on thesequeue information, BS makes the scheduling decision for thedownlink frame. For the convenience of discussion, each nodeincluding BS, RS and MS is assigned a unique node ID andeach link is given a unique link ID, as indicated in Fig. 1.

We define a concurrent transmission scenario as a set ofall links that can transmit at the same time, i.e., no twolinks in a concurrent transmission scenario can share the sametransmitter or receiver. For example, in Fig. 1, l1, l8 andl12 forms a concurrent transmission scenario and these threelinks can happen simultaneously, while l4 and l8 cannot forma transmission scenario. Let K denote the total number ofconcurrent transmission scenarios, and Sk represents the kthtransmission scenario with 1 ≤ k ≤ K . In each frame t, alltransmission scenarios share the frame duration T in TimeDivision Multiplexing (TDM) manner, and the time portionoccupied by scenario Sk at frame t is denoted by Tk(t).

Let xmij (k, t) denote the number of bits transferred from

node i to node j destined for MS node m in scenario Sk atframe t, given that there is a direct link lij from node i tonode j. We name node i the upstream node of node j, andnode j the downstream node of node i. Let Rij(k, t) denote

64

TABLE ILP MODEL FOR SCHEDULING IN CELLULAR RELAY NETWORKS.

Object Function: maximize∑m am(t);

INPUT VARIABLES:1: MS index m;2: frame index t;3: frame duration T ;4: RS node i’s queue status Qmi (t);5: a set of concurrent transmission scenarios Sk , 1 ≤ k ≤ K;6: power used from node i to j, Pij ;7: distance between node i to j, dij ;

OUTPUT VARIABLES:1: xmij (k, t), scheduled packets transmitted from node i to node j

over link lij in Sk at frame t, destined for MS node m;2: Tk(t), scheduled time duration for scenario Sk;

CONSTRAINTS:1: am(t) =

∑Kk=1

∑n xnm(k, t), where n is m’s upstream node;

2: Qmi (t) +∑Kk=1

∑s x

msi(k, t) =

∑Kk=1

∑r x

mir(k, t) +

Qmi (t + 1), where s and r are RS node i’s upstream anddownstream nodes, respectively;

3:∑m xmij (k, t) ≤ Rij(k, t) × Tk(t), for link lij ;

4: Rij(k, t) = w log2(1 +Pij/d

αij

N0+∑

(x,y)∈Sk,(x,y)�=(i,j) Pxy/dαxj

),

where α is the path loss exponent, N0 is noise power;5:

∑Kk=1 Tk(t) = T ;

the data rate of link lij , and the upper bound of Rij(k, t) canbe calculated according to Shannon’s theorem. The actual datasent over lij in Sk at frame t,

∑m xm

ij (k, t), should be lessthan Rij(k, t) × Tk(t), which is the maximum possible bits.This capacity constraint indicates that a link’s data load in ascenario is subject to the data rate and the scheduled time forthis scenario.

Since each RS node i has a queue for every MS nodem, and we let Qm

i (t) denote the size of this queue at thebeginning of downlink frame t. Since MS consumes onlythe packets destined for itself and MS does not relay packet,there is no need for MS to maintain any queue. The flowconstraint for each RS requires that the sum of Qm

i (t) andthe packets arrived from node i’s upstream nodes destinedfor MS node m in frame t, be equal to the packets destinedfor MS node m that are forwarded to node i’s downstreamnodes, plus the remaining packets in this queue of RS, whichbecome the outstanding packets Qm

i (t+1) at frame t+1. Thisflow constraint reflects dynamic queue change in each RS. Letam(t) denote the packets arrived in MS node m at frame t.Apparently, am(t) =

∑Kk=1

∑n xnm(k, t), where node n and

m has a link lnm between them. Packets arriving in MS nodem at frame t is the sum of packets sent by its neighboringnodes over all scheduled transmission scenarios at frame t.

With the goal of maximizing total network throughput, thescheduling algorithm need to determine Tk(t) and xm

ij (k, t) foreach Sk, given the input of each RS’s queue size, each link’stransmission power, distance between two end nodes of eachlink, and the set of Sk. The proposed scheduling algorithm issummarized by the linear programming (LP) model in Table I.

The characteristics of the proposed scheduling algorithmare highlighted by constraints in in Table I. Constraint 1derives the throughput for MS node m in frame t, revealing

the concurrent transmission nature of the multihop cellularnetworks. Constraint 2 indicates the queue awareness of theproposed scheduling algorithm by monitoring the dynamic RSqueue status, and this queue awareness is not addressed by therelated work discussed in Section II. Constraint 3 illustratesthe capacity constraint of a link in scenario Sk. Constraint 4applies Shannon’s Theorem to calculate the upper bound oflink data rate with consideration of the interference causedby concurrent transmissions. Constraint 5 states the timeconstraint of all concurrent scenarios in a frame, signifyingthe frame-based feature of this approach.

C. Finding Concurrent Transmission Scenarios

Notice that in Table I, input item 5 is a set of concurrenttransmission scenarios Sk, 1 ≤ k ≤ K , and each Sk is derivedbased on current network topology. Since the number of linksgrows non-linearly with the number of nodes in the network,it is unpractical to use an exhaustive algorithm to search for allpossible scenarios. Thus we use a greedy algorithm to derivea subset of all scenarios, as illustrated in Algo. 1.

Algorithm 1 Greedy Algorithm to Find Concurrent Scenarios1: Object Function: maximize F (Sk) =

∑(i,j)∈Sk

wijRij , 1 ≤ k ≤ K2: for k = 1 to K do3: if k = 1 or |ψk| < Lmin then4: set ψk = {(i, j) : (i, j) is an allowed link};5: end if6: Set Sk = φ;7: Set (p,q) = a single link chosen at random from ψk;8: while F (Sk ∪ {(p, q)}) > F (Sk) do9: Set Sk = Sk ∪ {(p, q)};

10: Set ψk = ψk \ ⋃(i,j)∈ψk

{(i, j) : {(i, j)} ∩ {(p, q)} �= φ};11: Find out (p, q) = arg max(i,j)∈ψk

F (Sk ∪ {(i, j)});12: end while13: Set ψk+1 = ψk ;14: end for

When designing the objective function of the greedy al-gorithm, we apply the back pressure flow control mechanism[18]. This mechanism states that in order to maximize the end-to-end throughput in multihop wireless network, the selectedconcurrent transmissions must be able to maximize the objectfunction defined as F (S) =

∑(i,j)∈S wijRij , where S is a

set of multiple links that can form a concurrent transmissionscenario; (i, j) is a data link in S with sender node i andreceiver node j; Rij is the data rate of link (i, j); wij is theweight of link (i, j). wij is also called the back pressure oflink (i, j), since it is defined as wij = maxm(Qm

i − Qmj ),

where Qmi and Qm

j are the queue length destined for node min sender node i and receiver node j, respectively.

In order to maximize objection function F (S), links withhigh back pressure are favored. Intuitively, selecting linkswith higher back pressure for transmission help to relievenetwork traffic bottleneck and increase network throughput,observing the fact that traffic bottleneck occurs where backpressure is high. In addition, applying back pressure flowcontrol mechanism also help to achieve fairness among links.The reason is that once a link is selected for transmissionin the current round and has its back pressure reduced, other

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TABLE IIRELATION OF DATA RATE TO SNR IN OFDMA

Modulation Coding rate SNR(dB) Data rate(Mbps)BPSK 1/2 6.4 4.1558QPSK 1/2 9.4 8.3117QPSK 3/4 11.2 12.4675

16-QAM 1/2 16.4 16.623416-QAM 3/4 18.2 24.935164-QAM 2/3 22.7 33.246864-QAM 3/4 24.4 37.4026

links will have better chances to be selected for transmissionin the next round and have their back pressure reducedaccordingly. Thus the back pressure flow control mechanismtries to deliver traffic for all links, not just favoring anyspecific link, which proves its fairness. Since back pressureflow control mechanism promotes both network throughputand fairness, we apply it to define the object function of thegreedy algorithm.

The greedy algorithm of finding concurrent scenarios havebeen studied extensively, and our greedy algorithm is similarto those in [17] and [12]. During the process of finding Sk,a candidate link is added into Sk when the object functioncan be maximally increased by adding this candidate link.This process is repeated until no more candidate link can beadded into Sk. In Algo. 1, Lmin is a chosen threshold, whichstands for the minimum number of candidate links on whichthe current searching process for Sk can still continue. If thenumber of candidate links is less than Lmin, all links will beadded into the candidate links pool.

In summary, our proposed scheduling algorithm can bedivided into two steps. In step 1, we use a greedy algorithmstated in Algo. 1 to derive a set of concurrent transmissionscenarios, with the back pressure flow control mechanismincorporated into the greedy algorithm; in step 2, we usea linear programming model stated in Table I to calculatethe transmission schedules for all concurrent transmissionscenarios, aiming at maximizing the throughput in each frame.

IV. SIMULATIONS AND DISCUSSIONS

We carry out extensive simulations to evaluate the proposedscheduling algorithm and study the effectiveness of deployingrelay stations in cellular networks. We also compare theperformance of our approach with that of other approaches.

The default simulation setup consists of 1 BS, 3 RS, and 20MS. The 20 MS are deployed randomly in a cell with radius1km, and random way point model is used for MS’s mobilitywith moving speed randomly chosen from 0 to 5m/s. The 3RS are placed in fixed positions, with distance from BS toeach RS set to 600m, and the angle between two neighboringRS set to degree 120o. Traffic is generated in BS on a perframe basis with Poisson distribution. Notice that the relaypath from BS to MS may consist of one or more RS.

We use path loss models in [19]. Specifically, type D pathloss model is used for BS and RS, since type D requires theantennas of both sender and receiver above the roof, whiletype E path loss model applies between BS/RS and MS, since

type E requires only sender’s antenna above the roof. Let PLD

and PLE denote the path loss for type D and type E models,respectively, as indicated below:

PLD = 46.3 + 33.9 log10(fc) − 13.82 log10(ht)−[1.1 log10(fc) − 0.7]hr + [15.6 log10(fc) − 0.8]+[44.9− 6.55 log10(ht)] log10(d/1000) + δ1 (1)

PLE = 20 log10(4πd0/λ)+10(4− 0.0065ht + 17.1/ht) log10(d/d0)+6 log10(fc/2000)− 10.8 log10(hr/2) + δ2 (2)

where fc is radio carrier frequency set to 3.5GHz; λ = C/fc

is radio wavelength; d is distance between sender and receiver;d0 is reference distance set to 100m; ht, hr are transmitterand receiver antenna height, respectively. We set the heightof BS, RS and MS to 50m, 30m, and 1.5m respectively.δ1, δ2 are log-normal shadow with standard deviation of 3dB.We set the transmission power of BS and RS to 30dBm and27dBm, respectively. Using the above path loss models, wecan calculate the received signal strength and the interferencegenerated by concurrent transmissions. Then we can derivethe corresponding Signal-to-Noise Ratio (SNR), given noisepower equals to −100dBm. In our simulation, we use IEEE802.16 OFDMA physical layer model and the parametersare set according to IEEE 802.16 standard [20], [21]. Thebandwidth is set to 10MHZ and the relation of data rate andSNR is depicted in Table II, in order to achieve 10−6 bit errorrate. The frame duration is 20ms.

We compare our proposed scheduling algorithm with directtransmission. For direct transmission, we still run the linearprogramming model in Table I, while the corresponding con-current transmission scenarios only include direct links. Thescheduling algorithm in [17] does not assume buffering inintermediate RS nodes, therefore, we compare our approachwith no buffering in RS. The scheduling algorithm must bechanged accordingly by removing Qm

i (t) and Qmi (t+1) from

Constraint 2 of the LP model in Table I. The greedy algorithmin Algo. 1 also need to be changed due to no buffer in RS,and a link candidate is added into a concurrent transmissionscenario if adding this link can improve the total networkthroughput, and the weight factor wij in Algo. 1 is set to1 correspondingly.

We study the MS throughput averaged over all MS andover 60000 frames, and the result is shown in Fig. 2. Whenthe downlink traffic request for each MS is below 0.4Mbps,all three scheduling algorithms can satisfy the request. Wheneach MS’s request increases from 0.4Mbps to 1.4Mbps, onlythe queue-aware scheduling algorithm can satisfy the request.This proves that relay links help improve network throughputcompared to direct links. Also proven is the benefit of havingbuffer in RS, which allow RS to store remaining packets ofthe current frame, and have them ready for delivery for thenext frame.

We use Jain’s Fairness Index [22] to measure fairness,

66

defined as f(x1, x2, ..., xn) = (∑n

i=1 xi)2

n∑

ni=1 x2

i, where xi is the nor-

malized throughput of MS i, and n is the total number of MSs.We define xi = Thi

Reqi, and Thi and Reqi stand for the actual

data rate and the request date rate of MS i, respectively. Jain’sFairness Index ranges from 0 to 1, and the more close to 1, thebetter the fairness. If Thi = Reqi for all i, or in other words,every MS obtains its requested data rate, then xi = 1 for alli, resulting in Jain’s Fairness Index equals to 1. The fairnesscomparison result is shown in Fig. 3, and the queue-awareapproach has the best fairness performance. One reason is thatwe apply the back pressure flow control mechanism in findingconcurrent scenarios and it helps to remove traffic bottleneckin the network, hence achieving fairness. The other reasonis that relay links can improve the data rate of MS whosedirect link has low data rate, and improve fairness. Directtransmission has the worst fairness performance among thethree scheduling algorithms since links with higher data ratesare always favored by the scheduler. Also shown in Fig. 3 isthat all three scheduling algorithms have fairness performancesdegraded, if request data rate exceeds a certain threshold, anddifferent scheduling algorithms have different thresholds. If weexamine the corresponding throughput performance in Fig. 2,it shows that throughput can not catch up with the data requestafter request data rate exceeds a certain threshold.

It is worthy to study whether using relay links is alwaysbeneficial. We reduce the distance between BS and RS andthe distance between BS and MS, and investigate its impact onnetwork throughput. The result is shown in Fig. 4, with x-axisrepresenting the distance scale factor, and y-axis representingaverage MS throughput. With the reduction of distance scale,all scheduling algorithms increase their throughput perfor-mance, but the differences between queue-aware approach andthe other two approaches also decrease gradually. One reasonis that when MS is close enough to BS, direct transmissionalready has high throughput, thus limited room is left forrelay link to improved the throughput. The other reason isthat when nodes are close to each other, concurrent links mayinterfere with each other and have negative effects on networkthroughput. The SNR of each data link network is related notonly to link distance, but also to the interference generated byother concurrent transmissions.

We also study the impact of K , the total number ofconcurrent transmission scenarios, on network throughput forthe proposed queue-aware scheduling algorithm, as shown inFig. 5. With the increase of K , network throughput increases,and intuitively this is reasonable since larger K enable linearprogramming model to yield result more close to the optimumsolution. When K reaches a certain value, the improvementin throughput is marginal. For example, when K goes from40 to 45, there is no significant increase in throughput, asshown in Fig. 5. This is due to the fact that larger K may haveincluded all the scenarios that will benefit network throughput,thus adding more concurrent scenarios will not increase thenetwork throughput. In practice, we apply a reasonably largevalue to K to achieve near optimal result.

We also increase the number of MS, and study its impact

on throughput. We calculate two throughput ratios, and oneis the throughput ratio of queue-aware scheduling over directtransmission, and the other is the throughput ratio of non-queue-aware scheduling over direct transmission. The resultis shown in Fig. 6. The throughput ratios increase whenthe number of MS increases, and this is because moreMS brings more concurrent transmissions with more spatialreuses. The scheduling algorithm with queue awareness hashigher throughput than the scheduling algorithm without queueawareness with the increase of MS, since buffer in RS canaccommodate more packets in the queue. We also notice thatwhen the average request per MS increases from 1.5Mbpsto 2Mbps, throughput ratios also increase, which implies thatthe proposed scheduling algorithm can adjust itself to catchthe increasing downlink data demand.

V. CONCLUSION

We have proposed a scheduling algorithm for such multihoprelay wireless cellular networks as IEEE 802.16j. A set ofconcurrent transmission scenarios is derived based on back-pressure flow control mechanism, which are used as inputfor a linear programming model that determines the trans-mission schedules for multihop relay networks. The linearprogramming model maximizes the overall throughput, whiletaking into consideration the frame-based nature of cellularnetworks and the queue dynamics at the relay stations. Simu-lations based on IEEE 802.16 OFDMA mode have measuredperformance metrics such as throughput and fairness of theproposed scheduling algorithm, showing the effectiveness ofour approach compared to other scheduling algorithms.

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L12

MS3(6)

L9 L10

L11 L8 L5

L6

L7

L4

L2 L3

L1

MS2(5) MS1(4)

RS3(3) RS2(2)

RS1(1)

BS(0)

Fig. 1. Architecture of cellular relay networks.

0 0.5 1 1.5 20

0.5

1

1.5

2

Average MS request data rate(Mbps)

Ave

rage

MS

thro

ughp

ut (

Mbp

s)

Direct transmissionNon−queue−aware scheduling alg.Queue−aware scheduling alg.

Fig. 2. Throughput comparison.

0 0.5 1 1.5 20

0.2

0.4

0.6

0.8

1

Average MS request data rate(Mbps)

Fai

rnes

s

Direct transmissionNon−queue−aware scheduling alg.Queue−aware scheduling alg.

Fig. 3. Fairness comparison.

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

Distance scale

Ave

rage

MS

thro

ughp

ut (

Mbp

s)

Average request data rate = 2 Mbps

Direct transmissionNon−queue−aware scheduling alg.Queue−aware scheduling alg.

Fig. 4. Impact of distance.

0 0.5 1 1.5 20

0.5

1

1.5

2

Average MS request data rate(Mbps)

Ave

rage

MS

thro

ughp

ut (

Mbp

s)

K=30K=35K=40K=45

Fig. 5. Impact of number of scenarios.

5 10 15 20 25 30 350

0.5

1

1.5

2

Number of MS

Thr

ough

put r

atio

Queue−aware scheduling alg., avg req = 2.0 MbpsNon−queue−aware scheduling alg., avg req = 2.0 MbpsQueue−aware scheduling alg., avg req = 1.5 MbpsNon−queue−aware scheduling alg., avg req = 1.5 Mbps

Fig. 6. Impact of number of MS.

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