Performance Evaluation of Scheduling in IEEE Based Wireless Mesh Networks

Transcription

1 Performace Evaluatio of Schedulig i IEEE Based Wireless Mesh Networks Bo Ha, Fug Po Tso, Lidog Li ad Weijia Jia Departmet of Computer Sciece, City Uiversity of Hog Kog 83 Tat Chee Aveue, Kowloo, Hog Kog {Bo.Ha, Li.Lidog}@studet.cityu.edu.hk, wjia@cs.cityu.edu.hk Abstract-We propose a efficiet cetralized schedulig algorithm i IEEE based Wireless Mesh Networks (WMN) to provide high qualified wireless multimedia services. Our algorithm takes special attetio o the relay fuctio of the mesh odes i a trasmissio tree which is seldom studied i previous research. Some importat desig metrics, such as fairess, chael utilizatio ad trasmissio delay are cosidered i this schedulig algorithm. IEEE employs TDMA ad the selectio policy for scheduled liks i a time slot will defiitely impact the system performace. We evaluated the proposed algorithm with four selectio criteria through extesive simulatios ad the results are istrumetal for improvig the performace of IEEE based WMNs i terms of lik schedulig. I. INTRODUCTION The rapid growth of high-speed multimedia services for residetial ad small busiess customers has created a icreasig demad for last mile broadbad access. Traditioal broadbad access is offered through digital subscriber lie (xdsl), cable or T etworks. Each of these techiques has differet cost, performace, ad deploymet trade-offs. While cable ad DSL are already beig deployed o a large scale, Fix Broadbad Wireless Access (FBWA) systems [, 2] are gaiig extesive acceptace for wireless multimedia services with several advatages. These iclude rapid deploymet, lower maiteace ad upgrade costs, ad graular ivestmet to match market growth [2]. Recetly, study group was formed uder IEEE Project 802 to recommed a air iterface for FBWA systems that ca support multimedia services [3]. I protocol stack, the medium access cotrol layer (MAC) supports both poit-to-multipoit (P2MP) mode ad mesh (multipoit-to-multipoit) mode. All these mesh odes aturally form a WMN [4, 5]. Compared with the traditioal wireless ad hoc etworks, WMN has the followig distict features. First, WMNs are ot isolated self-cofigured etworks ad emerge as a flexible ad low-cost extesio of the existig wired ifrastructure etworks. Geerally, WMNs serve as the access etworks that employ multi-hop wireless forwardig to relay traffic. I such a eviromet, power cosumptio is ot a primary cocer as mesh odes are fixed ad wire-powered. Traffic patters may be asymmetric which mostly ivolve commuicatio to ad from wired gateway (Base Statio), rather tha ivolvig pairs of ed-odes. Moreover, odes i a mesh etwork are either statioary or miimally mobile. Thus, cotrary to routig i ad hoc etworks, the liks i WMNs have much loger duratio times. At last, most applicatios of WMNs are broadbad services with various QoS requiremets [4]. I IEEE mesh mode, schedulig is oe of the most importat problems that will impact the system performace. A schedulig is a sequece of fixed-legth time slots, where each possible trasmissio is assiged a time slot i such a way that the trasmissios assiged to the same time slot do ot collide. Geerally, there are two kids of schedulig broadcast ad lik. I a broadcast schedulig, the etities scheduled are the odes themselves. The trasmissio of a ode is iteded for, ad must be received collisio-free by all of its eighbors. While i a lik schedulig, the liks betwee the odes are scheduled. The trasmissio of a ode is iteded for a particular eighbor, ad it is required that there be o collisio at this receiver. We propose a efficiet cetralized schedulig algorithm for IEEE mesh mode. Compared with the existig schedulig algorithms, the proposed scheme cosiders some distict features of WMNs, such as the fuctio of access etworks ad the iheret relay model. Moreover, this schedulig scheme also cosiders some importat performace metrics, such as, fairess, chael utilizatio ad trasmissio delay. To the best of our kowledge, this is the first cetralized schedulig algorithm i IEEE based WMNs which cosiders the relay model. I what follows, Sectio II itroduces some related work. The schedulig mechaism i the IEEE mesh mode is described i Sectio III. I Sectio IV a efficiet cetralized schedulig scheme for IEEE based WMNs is proposed. Sectio V presets performace evaluatio ad Sectio VI cotais some coclusio remarks. II. RELATED WORK Several IEEE special task groups have bee established to defie the requiremets for mesh etworkig i wireless persoal area etworks (WPANs), wireless local area etworks (WLANs) ad wireless metropolita area etworks (WMANs). Although at differet degrees of maturity, the followig emergig stadards have bee idetified: IEEE 802.s, IEEE , IEEE 802.6a, ad IEEE A brief itroductio of these ope stadards ca be foud i [5]. Most of the existig researches about WMNs are based o IEEE 802. stadard [6 0, 27]. Kyasaur ad Vaidya studied the problem of improvig the capacity of multichael wireless etworks by usig multiple iterfaces [6]. Aguayo et al aalyzed the causes of packet loss i a 38-ode urba multi-hop 802.b mesh etwork [7]. Raiwala ad Chiueh proposed a multi-chael WMN architecture that equips each mesh etwork ode with multiple 802. etwork iterface cards [8]. Draves et al preseted a ew metric, which is a fuctio of the loss rate ad the badwidth of the lik, for routig i multi-radio multi-hop wireless mesh etworks [9]. Gambiroza et al studied fairess ad ed-to-ed performace i multi-hop wireless backhaul etworks through a formal referece model ad a extesive set of simulatio experimets [0]. Tag et al studied iterferece-aware topology cotrol ad QoS routig i IEEE 802.-based multi-chael wireless mesh etworks with dyamic traffic [27]. Little work has bee doe about IEEE based The paper is supported by CityU Strategic grat o

2 wireless mesh etworks. Wei et al adopted a iterfereceaware cross-layer desig to icrease the throughput of WMN []. Cao et al developed a stochastic model for the distributed scheduler of the IEEE mesh mode [28]. Recetly, two cetralized schedulig algorithm were proposed for WMN [32, 33]. However, oe of them cosider the relay model which is very importat i WMN. The geeral schedulig problem has bee extesively studied i Packet Radio Network (PRNET) [2 2]. The work i [2] is maily about the capacity regio of a PRNET which is defied as the set of all origi-to-destiatio (o-d) message rates that are achievable via ay arbitrary protocol. The author showed that the problem of determiig whether a give poit belogs to the capacity regio of a PRNET is NP hard. Nelso ad Kleirock defied a chael access protocol for a PRNET i which the locatios of the odes of the etwork were assumed to be fixed ad kow [3]. A approximatio to the mea system delay of packets i the etwork was developed ad compared to simulatios. Two polyomial time algorithms were proposed for lik schedulig i a spread spectrum radio etwork [4]. Cido ad Sidi itroduced ew distributed dyamic chael assigmet algorithms for a multihop PRNET [5]. The basic idea of the algorithms is to split the shared chael ito a cotrol segmet ad a trasmissio segmet. Ephremides ad Truog provided a comprehesive study of schedulig broadcast trasmissios i a multi-hop, mobile PRNET [7]. Chou ad Li derived a upper boud of the miimum TDMA frame legth of ay collisio-free ode assigmet protocol i a PRNET i which a ode had multiple receptio capacity [8]. Ramaatha ad Lloyd cosidered both lik ad broadcast schedulig i multi-hop PRNETs [9]. I each istace, schedulig algorithms were give that improved upo existig algorithms both theoretically ad experimetally. Grokvist compared broadcast ad lik schedulig ad determied which oe was preferable [20]. They showed that oly the coectivity of the etwork ad the iput traffic load of the etwork were eeded i order to determie whether broadcast or lik schedulig was preferable. Bjorklud et al developed mathematical programmig formulatios for resource optimizatio for both broadcast ad lik schedulig [2]. They further preseted a colum geeratio approach which costatly yielded optimal or earoptimal solutios i umerical experimets. Ufortuately, o extesive experimetal study or oly very simple experimet was give i these existig literatures. Schedulig algorithm is also a importat research topic i the traditioal ad hoc etworks ad Bluetooth scatterets. Rácz et al proposed a pseudo-radom coordiated scatteret schedulig algorithm to perform the schedulig of both itra ad iter-picoet commuicatio i Bluetooth etworks [22]. Kim et al preseted two versios of QoS-aware schedulig algorithms: a perfect assigmet algorithm for bipartite scatteret ad a distributed localized algorithm [23]. Recetly, Saloidis ad Tassiulas preseted a framework for the provisio of determiistic ed-to-ed badwidth guaratees i wireless ad hoc etworks [24]. This framework did ot require ay apriori kowledge o the umber of odes i the etwork or eve etwork-wide slot sychroizatio. Several research works also have bee doe to make ad hoc etworks take the role of wireless access etworks. Hsiao et al described a ew distributed routig algorithm that performed dyamic load-balacig for wireless access etworks [25]. Bejerao cosidered the problem of desigig a efficiet ad low-cost ifrastructure for coectig static multi-hop wireless etworks with wired backboe, while esurig QoS requiremets such as badwidth ad delay [26]. III. BACKGROUND ON IEEE MESH MODE I P2MP operatio, the wireless lik operates amog a cetral Base Statio (BS) ad a set of Subscriber Statios (SSs). The BS is the oly trasmitter operatig i the dowlik (from BS to SS), so it trasmits without havig to coordiate with other statios. Subscriber statios share the uplik to the BS o a demad basis. I the mesh mode, all odes are orgaized i a ad hoc fashio, each ode ca relay traffic for other odes ad QoS is provisioed o a packet-bypacket basis. Withi a mesh etwork, a system that has a direct coectio to backhaul services outside the mesh etwork is termed the Mesh BS. All the other systems of a mesh etwork are termed Mesh SSs. Uplik ad dowlik are defied as traffic i the directio to the Mesh BS ad that away from the Mesh BS, respectively. Mesh differs from P2MP mode i that i the mesh mode, traffic ca be routed through other SSs ad ca occur directly betwee the SSs. Whereas i the P2MP mode, traffic oly occurs betwee the BS ad SSs. Moreover, ulike the P2MP mode, the mesh mode oly supports Time Divisio Duplex (TDD) for uplik ad dowlik traffic [3]. For the trasmissio, several SSs share the chael i a TDMA (Time Divisio Multiple Access) fashio. I what follows, uless specified otherwise, we will refer to BS ad SS as Mesh BS ad Mesh SS. Ad we will use the terms SS ad ode iterchageably. A ew SS, say u, eterig IEEE based WMN obeys the followig procedures. At first u scas for MSH-NCFG (Mesh Network Cofiguratio) messages to establish coarse sychroizatio with the etwork (the cost of sychroizatio phase is beyod the scope of this paper). The u shall build a physical eighbor list from the acquired iformatio. From this list, u selects a Sposorig Node (SN) accordig to some policy. A sposorig ode is defied as a eighborig ode that relays MAC messages to ad from the BS for u. That is, it is a upstream ode that is closer the BS. Registratio is the process where u is assiged its ode ID. After eterig the etwork, a ode ca also establish the liks with other odes. Fig. gives a example of etwork topology which is composed of oe BS ad SSs. There is a lik betwee two SSs if they are withi the trasmissio rage of each other. Fig. 2 shows the correspodig schedulig tree that oly cotais the trasmissio liks betwee a ode ad its SN. We refer the omitted liks i Fig. 2 (compared with Fig. ) as the iterferece liks. BS will periodically broadcast MSH-CSCF (Mesh Cetralized Schedulig Cofiguratio) messages that iclude the complete topology of schedulig tree to the odes. Due to the cetralized ature of the schedulig algorithm, there are o hidde termial problems here. I IEEE based WMNs, commuicatio i all the liks shall be cotrolled by a schedulig algorithm. There are three kids of schedulig i IEEE mesh mode: cetralized, coordiated distributed ad ucoordiated distributed schedulig. We will brief the geeral idea of cetralized schedulig below. For distributed schedulig, we refer the iterested readers to [3]. I cetralized schedulig, the BS shall gather resource requests through MSH-CSCH (Mesh Cetralized Schedulig) messages from all the SSs withi a certai hop rage. The BS determies the flow assigmets from these resource requests ad commuicates

3 Figure. Network Topology Figure 2. Schedulig Tree these assigmets to all the SSs. Subsequetly, the SSs determie their ow trasmissio opportuities i a distributed fashio, usig a commo predetermied algorithm with the same iput iformatio. The SSs will let the BS kow their chages of resource request through MSH-CSCH messages. The the BS will rebroadcast the adjusted flow assigmet ad the SSs ca recalculate their trasmissio opportuities. To quote the IEEE stadard [3], the advatage of cetralized schedulig is that it is typically used i a more optimal maer tha distributed schedulig for traffic streams, which persist over a duratio that is greater tha the cycle time to relay the ew resource requests ad distribute the updated schedule. IV. QOS-AWARE SCHEDULING SCHEME A. Problem Defiitios ad Modelig As metioed above, the cosidered traffic i IEEE based WMNs is maily to ad from the BS, thus we focus o lik schedulig i this paper. I mesh mode, the uderlyig TDMA commuicatio is structured ito frames, each composes of several equal duratio time slots. A TDMA scheme makes a cosiderable effort at maximizig the spatial reuse of the available badwidth while at the same time elimiatig the possibility of collisio [6]. We defie the closed oe-hop eighbor set of ode u as Nei[u] ad the set of ode v s sposored odes is represeted as Sos(v). The cycle of a lik schedulig is the time eeded to trasmit all the traffic to/from the BS i the WMN, uder certai traffic model. The legth of a lik schedulig is the umber of time slots i the cycle. The cycle keeps repeatig util the ext schedulig update. The chael utilizatio ratio (CUR) is defied as the ratio betwee the umber of occupied time slots ad the umber of available time slots (the legth of schedulig multiplied by the umber of odes). Note that, the resulted CUR is, i fact, the average CUR for all SSs. The average trasmissio delay is the umber of time slots betwee the time slot whe a packet is trasmitted by the source SS ad the time slot whe the same packet arrives at the destiatio. Suppose a packet is set out i time slot 2 ad arrives to the destiatio i time slot 7, the trasmissio delay is the calculated as 5 time slots. Here, we cosider the followig special schedulig problem: how to assig time slots to trasmissio liks i IEEE based WMNs so as ) to reduce the legth of schedulig; 2) to improve the chael utilizatio ratio ad 3) to decrease the trasmissio delay, subjected to some costraits that are preseted below. I particular, depedig o the sigalig mechaism, trasmissios may collide i two ways i wireless etworks: primary ad secodary iterferece [9]. Primary iterferece occurs whe a ode has to do more tha oe thig i a sigle time slot. The reaso for this costrait is that the odes caot trasmit ad receive simultaeously ad caot trasmit/ receive more tha oe packet at the same time. Thus, this costrait is also referred to as the trasmissio/receptio costrait. Secodary iterferece occurs whe a receiver R tued to a particular trasmitter T is withi the rage of aother trasmitter whose trasmissios, though ot iteded for R, iterfere with the trasmissios of T. This costrait is also referred to as the iterferece-free costrait. We ca use the partial topology i Fig. 3 to illustrate the iterferece more clearly. I this figure, two odes that are withi the trasmissio rage of each other are coected by a lik. The solid lies represet the trasmissio liks i the schedulig tree ad the dashed lies represet the iterferece liks. We stress that although there is o traffic trasmitted over iterferece liks ad these liks do ot have to be scheduled, they may iduce coflicts betwee liks that must be scheduled. Suppose the ode i the higher part of the figure is closer to the BS ad the lik from ode A to B (uplik) is scheduled i the curret time slot. Due to these two kids of iterferece, odes B, C, E, F, N ad P caot trasmit through their upliks i the same time slot. I fact, these iterfered odes ca be divided ito two types: ) Nei[B] {A}, such as odes B, C ad P ad 2) Sos(Nei[A] {B}), such as odes E, F ad N. For example, if ode P is scheduled to trasmit to Q, B will receive packets from both A ad P. If ode N is scheduled to trasmit to M, M will receive packets from both A ad N. Thus, these trasmissios will collide. Note that, there is o differece i the mechaisms for the schedulig of dowlik ad uplik. I IEEE mesh mode, uplik ad dowlik are scheduled separately. Thus, for the limited space, we oly describe the schedulig algorithm for uplik ad it ca be easily exteded to the case of dowlik. Figure 3. Iterferece Model

4 B. Trasmissio-Tree Schedulig (TSS) Algorithm I the proposed algorithm, the SS is assiged service toke based o its traffic demad. We use service toke to allocate time slots to each lik proportioally accordig to the required badwidth of the lik s trasmitter, thus, the fairess is guarateed (o odes will be starved). Suppose there are totally SSs ad the traffic demad of SS i is tr i. The the service toke assiged to SS i will be toke i = tr i /g, where g is the greatest commo divisor (GCD) of tr, tr 2, tr. We divide the traffic demads by their GCD to reduce the legth of schedulig. For example, if the traffic demads of the SSs are 2Mbps, 8Mbps, 6Mbps ad 4Mbps. The service tokes assiged to the SSs will be, 4, 3 ad 2. Compared with the service toke assigmet 2, 8, 6 ad 4, the legth of resulted schedulig is reduced to half. Here, we ame the set {toke i } as ST. Each time after a lik is assiged a time slot, the service toke of its trasmitter is decreased by oe ad that of the receiver is icreased by oe. Therefore, usig the chage of service toke, we ca easily itegrate the hop-by-hop relay model of WMN ito our algorithm. Fig. 4 gives the details of the algorithm. Suppose the legth of the resulted schedulig is k. The iputs of this algorithm are the schedulig tree T ad the service toke set ST, ad the output is a k schedulig matrix S. If ode i is scheduled i time slot j, S ij =, otherwise, S ij = 0. Iitially, all the elemets i S are 0. I each roud (for the while loop), iitially, if the service toke of the trasmitter of a lik is o zero, this lik is marked as available, otherwise, it is marked as idle. A available lik satisfied with some selectio criterio (to be discussed later) is scheduled i the curret time slot. The selected lik is marked as scheduled ad all the coflictig eighborig liks of this selected lik are marked as iterfered. The service tokes of the trasmitter ad receiver of this scheduled lik are also adjusted. The, the ext scheduled lik is selected based o the same rule. The selectio is repeated util oe of the liks are marked as available. The same procedure is repeated util the service tokes of all these SSs are decreased to 0. The implemetatio of fuctio select_oe_lik() is determied by differet selectio criteria. I this paper, we cosider four kids of criteria: radom, mi iterferece, earest to BS (hop cout) ad farthest to BS. I radom selectio, each time the scheduled lik is selected radomly. I the mi iterferece selectio, the lik whose trasmitter iterferes the miimal umber of other SSs is chose for Algorithm TSS Iput : Schedulig tree T = (V, E ) ad service toke set ST Output : A time slot assigmet S : k = ; 2: assig service toke to each SS 3: while tokei 0 do 4: iitialize the status of all trasmissio liks i E 5: while e E ad status (e) = available do 6: m = select_oe_lik(); 7: status (m) = scheduled ; 8: adjust_service_toke (m); 9: Smk = ; 0: mark_iterferece (m); : ed while 2: k ++; 3: ed while Figure 4. Pseudo code for the proposed schedulig algorithm schedulig. While i the earest to BS ad farthest to BS selectios, the lik whose trasmitter has the miimal or maximal hop cout to the BS is scheduled. If two SSs have the same umber of iterfered eighbors or the same hop cout to the BS, we use the ode ID to break the tie ad choose the SS with the smaller ode ID. Note that, whe the service toke of odes with smaller ID is decreased to 0, odes with higher ID will get the chace to be scheduled, thus will ot be starved forever. Moreover, the trasmissio slots assiged to a ode is determied by the umber of its server tokes. The odes with smaller ID ca ot always trasmit more frequetly tha odes with higher ID. C. Performace Aalysis This sectio aalyzes the time complexity of the proposed schedulig algorithm ad gives some bouds o the legth of schedulig. Propositio. Usig hop i to represet the hop cout of SS i to BS, the legth of schedulig k is at most O(). Proof: The total umber of occupied time slots is toke i hop i. Thus, we ca get k toke i hop i. The worst case occurs whe there is oly oe lik ca be scheduled i each time slot. As metioed above, the BS shall gather resource requests from all the SSs withi a certai hop rage HR threshold, therefore hop i HR threhold. I a real IEEE based WMN, the traffic demad of each SS will also have the maximal value which should be a costat. Thus, k O(). Propositio 2. The time complexity of the proposed schedulig algorithm is of O( 2 ). Proof: From the pseudo code i Fig. 4, we ca see that the proposed algorithm TSS cosists of two loops with executios of at most k times ad times respectively. Therefore, the time complexity is O(k). Based o Theorem, we have that k O(), thus, this theorem is proved. Propositio 3. The chael utilizatio ratio CUR = toke i hop i /k. The proof of Theorem 3 is straightforward by the defiitio of CUR. V. SIMULATION A. Performace Metrics As metioed above, three metrics are set up for the performace evaluatio. They are the legth of schedulig k, CUR, ad the average trasmissio delay. The legth of schedulig is the most importat measure of the performace of a schedulig algorithm, ad it is cosidered i most of the previous literatures. I may applicatios, the trasmissio schedule is costructed oly whe the etwork is iitialized ad the data commuicatio is doe accordig to this schedule for as log as the etwork remais up. Due to the shared ature of wireless chael, CUR is aother sigificat performace metric that we must cosider. Higher CUR will improve the effect trasport capacity of WMNs. Sice CUR = toke i hop i /k, we ca see that give the schedulig tree ad service toke set, CUR is

5 legth of schedulig Chael umber of odes i the etwork (a) r = 5 uits, toke i = ad is from 50 to 20 legth of schedulig Chael umber of odes i the etwork (b) r = 20 uits, toke i = ad is from 20 to 00 legth of schedulig Chael trasmissio rage of odes legth of schedulig Chael umber of odes i the etwork (c) = 20, toke i = ad r is from 20 uits to 65 uits (d) r = 5 uits, toke i [0, 3] ad is from 50 to 20 Figure 5. Legth of the schedulig iverse proportioal to the legth of schedulig k. That is, smaller k will lead to a better CUR. Moreover, sice IEEE based WMN is used to provide broadbad wireless multimedia services, we also aim to reduce the trasmissio delay usig the proposed schedulig algorithm. Because each SS ca trasmit oly oe packet i a time slot, packets will be buffered i the itermediate SS. The buffer maagemet policy will defiitely impact the trasmissio delay. I the simulatio, we give priority to packets from odes that are further away from the BS. B. Simulatio Setup As metioed above, to the best of the author s kowledge, this is the first schedulig algorithm i IEEE mesh mode that cosiders the relay model. Therefore, o compariso ca be made with existig schemes. A C-coded custom simulator is used for the performace evaluatio of the proposed schedulig algorithm. We aim to ivestigate the impact of differet selectio criteria o above metioed performace metrics. For simplicity, i the followig we call the schedulig algorithms usig the above four selectio criteria as, Chael, ad, respectively. I the simulatio, a give umber of SSs were radomly ad uiformly distributed i a square simulatio area of size 00 by 00 uits. The BS is placed atthe ceter of the simulatio area. Each SS has a fixed trasmissio rage r. The SS s movemet is ot cosidered. Thus, two SSs are eighbors whe their distace is smaller tha their trasmissio rage. All the simulatio results preseted i this sectio were obtaied by ruig these algorithms o 300 coected graphs. We obtai the simulatio results for both homogeeous (the service toke umber of odes is ) ad heterogeeous (the service toke umber of odes is radomly selected from 0 to 3) traffic demads. C. Simulatio Result For the limited space, we oly preset the results about the legth of schedulig i Fig. 5. We show the results for average trasmissio delay ad chael utilizatio ratio i [3]. The cofiguratios of simulatio for Fig. 5 (a), (b), (c) ad (d) are as followig: (a) the ode s trasmissio rage is 5 uits, the umber of odes i the etwork rages from 50 to 20 with icremet step of 0 ad the service toke of odes is ; (b) the ode s trasmissio rage is 20 uits, the umber of odes i the etwork rages from 20 to 00 with icremet step of 0 ad the service toke of odes is ; (c) the umber of odes i the etwork is 20, the ode s trasmissio rage rages from 20 to 65 uits with icremet step of 5 ad the service toke of odes is ad (d) the ode s trasmissio rage is 5 uits, the umber of odes i the etwork rages from 50 to 20 with icremet step of 0 ad the service toke of odes is radomly selected from 0 to 3. As metioed above, we use the umber of time slots to measure the legth of schedulig ad average trasmissio delay. Therefore, the uit of the y- axis i Fig. 5 is the umber of time slots. From Fig. 5 (a), (b) ad (d), we otice that whe the ode s trasmissio rage is fixed, the icrease of the umber of odes i the etwork will icrease the legth of schedulig. Whe the umber of odes is fixed, the icrease of ode s trasmissio rage will decrease the legth of schedulig as show i Fig. 5 (c). Comparig Fig. 5 (a) with Fig. 5 (d), we fid that the icrease of average service toke will lead to loger schedulig legth. From Fig. 5 (c), we ca see that whe the ode s trasmissio rage icreases to be larger tha 55 uits, the schedulig legth decreases to 20 which is the same as the umber of the odes. The reaso is that uder this etwork topology, almost all the SSs are oe hop away from the BS ad the mesh etwork degrades to P2MP etwork, so every SS eeds oly oe time slot to trasmit its ow data to the BS.

6 Amog these four algorithms, performs best, followed by ad Chael (these two algorithms perform very closely) ad the performace of is the worst. The reaso is that whe the mesh etwork is used as access etwork, the odes which locate earer to the BS will become the bottleeck i the schedulig tree ad thus givig higher priority to these odes will reduce the umber of eeded time slots. VI. CONCLUSION We proposed a efficiet cetralized schedulig algorithm for IEEE based WMNs. I this algorithm, we cosider some particular features of WMNs, such as the fuctio of access etworks. The relay model is also itegrated ito this schedulig algorithm. The schedulig scheme takes fairess, chael utilizatio ad delay requiremets for all traffic ito cosideratio. I the proposed algorithm, the selectio policy for scheduled odes will impact the algorithm s performace. We use the legth of schedulig, trasmissio delay ad chael utilizatio ratio to evaluate the performace of the proposed schedulig algorithm. Our comprehesive simulatio studies show that givig higher priority to the odes earer to the BS will reduce the legth of schedulig ad trasmissio delay ad improve the chael utilizatio ratio. Our curret work icludes ivestigatig the impact of differet buffer maagemet policy o the trasmissio delay ad further research o the computatio complexity of the proposed schedulig problem. REFERENCES [] W. Webb, Broadbad Fixed Wireless Access as a Key Compoet of the Future Itegrated Commuicatios Eviromet, IEEE Commuicatio Magazie, vol. 39, o. 9, pp. 5 2, Sep [2] H. Bolcskel, A.J. Paulraj, K.V.S. Hari, R.U. Nabar ad W.W. Lu, Fixed Broadbad Wireless Access: State of the Art, Challeges, ad Future Directios, IEEE Commuicatio Magazie, vol. 39, o., pp , Ja [3] IEEE Std 802.6TM-2004, IEEE Stadard for Local ad Metropolita Area Networks Part 6: Air Iterface for Fixed Broadbad Wireless Access Systems, Oct., [4] I. F. Akyildiz, X. Wag ad W. 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