QoS-Driven MAC-Layer Resource Allocation for Wireless Mesh Networks with Non-Altruistic Node Cooperation and Service Differentiation

Transcription

1 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 2, DECEMBER 2009 QoS-Driven MAC-Layer Resource Aocation for Wireess Mesh Networks with n-atruistic de Cooperation and Service Differentiation Ho Ting Cheng, Student Member, IEEE, and Weihua Zhuang, Feow, IEEE Abstract de cooperation has been demonstrated promising in system performance improvement for wireess networks. To effectivey provision packet-eve quaity-of-service (QoS) in wireess mesh networks (WMNs) supporting heterogeneous traffic, medium access contro (MAC) with service differentiation is imperative. In this paper, we study the probem of non-atruistic non-reciproca node cooperative resource aocation for WMNs with QoS support, taking subcarrier aocation, power aocation, partner seection/aocation, service differentiation, and packet scheduing into account. Due to the NP hardness of our resource aocation probem, we propose two ow-compexity yet effective approaches based on the Karush-Kuhn-Tucker (KKT) interpretations, taiored for WMNs with QoS assurance and MAC-ayer service differentiation. Further, simuation resuts show that both proposed approaches can effectivey provision packet-eve QoS and enhance system performance. Our study aso sheds some ight on the question of whether and when non-atruistic node cooperation is beneficia to WMNs. Index Terms Karush-Kuhn-Tucker (KKT), non-atruistic node cooperation, quaity-of-service (QoS) provisioning, resource aocation, service differentiation, wireess mesh network (WMN). I. INTRODUCTION WIRELESS mesh networking has emerged as a promising soution for future broadband wireess access [2]. Wireess mesh networks (WMNs) generay comprise gateways, mesh routers, and mesh cients, organized in a three-tier hierarchica architecture [2]. Recenty, wireess mesh networking for suburban/rura residentia areas has been attracting a ot of attentions (e.g., Wray WMNs [3]). Mesh routers can be set up at premises in a neighborhood, forming a resiient mesh backbone and providing an a-wireess environment [3]. As increasing throughput in a WMN is the key to the success of providing an a-wireess environment, different resource aocation strategies have been proposed to provide a high-speed mesh backbone with quaity-of-service (QoS) assurance (e.g., [4]). To further enhance the system performance, cooperative diversity or node cooperation can be empoyed to Manuscript received May 7, 2009; revised September 8, 2009; accepted October 5, The associate editor coordinating the review of this paper and approving it for pubication was J. M. Shea. This research was supported by research grants from the Natura Science and Engineering Research Counci (NSERC) of Canada. This research is presented in part in a paper accepted for presentation in IEEE Gobecom 2009 []. The authors are with the Centre for Wireess Communications, Department of Eectrica and Computer Engineering, University of Wateroo, 200 University Avenue West, Wateroo, Ontario, Canada N2L 3G (e-mai: {htcheng, wzhuang@bbcr.uwateroo.ca). Digita Object Identifier 0.09/TWC /09$25.00 c 2009 IEEE achieve a spatia diversity gain by way of a virtua antenna array formed by mutipe wireess nodes in a distributed fashion [5]. In fact, node cooperation has been demonstrated promising in improving the spectra and power efficiency of wireess networks without additiona compexity of mutipe antennas [6]. The basic idea behind node cooperation rests on the observation that the signa transmitted by a source node can be overheard by other nodes in a wireess environment. The source and its partner(s) can jointy process and transmit their information, thereby creating a virtua antenna array and achieving a desired diversity-mutipexing tradeoff [7]. Compared to traditiona co-ocated muti-antenna techniques, node cooperation can provide a comparabe spatia diversity gain without imposing extra hardware compexity. Athough there exists a rich body of research work on node cooperation in the iterature [6] [7], packet-eve scheduing is mosty negected, and the issue of QoS support and provisioning has not been carefuy addressed. This phenomenon stems from the fact that previous research work mainy focuses on issues reated to the physica ayer. In this work, our goa is to devise an efficient and effective node cooperative resource aocation strategy taiored for WMNs with heterogenous traffic. In particuar, we focus on medium access contro (MAC)- ayer resource aocation in WMNs with QoS assurance and service differentiation. We consider regenerative mesh nodes and non-atruistic node cooperation, meaning that there is no pure reay in the system. Further, the node cooperation of interest is non-reciproca, meaning that one node assists its neighbor but does not necessariy receive hep from that neighbor. We aso consider prioritized node cooperation so as to reaize the notion of service differentiation. The main contributions and significance of our work are two-fod: ) We study the probem of non-atruistic node cooperative resource aocation for WMNs with QoS support, taking subcarrier aocation, power aocation, partner seection/aocation, service differentiation, and packet scheduing into account. Thanks to the Karush-Kuhn- Tucker (KKT) interpretations, we propose two resource aocation approaches taiored for the WMN of interest. Both approaches are shown to be effective in providing QoS assurance and service differentiation. Further, our approaches are of ow compexity, eading to viabe candidates for practica impementation; 2) Simuation resuts show that both proposed approaches are effective in packet-eve QoS provisioning and system

2 2 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 2, DECEMBER 2009 performance enhancement over their counterparts. Our resuts demonstrate that the proposed approaches are ess vunerabe to the changes in the system parameters such as the accuracy of traffic oad estimates. Further, our study reveas a critica principe that whether node cooperation is beneficia depends upon the nature of node cooperation, the mode of network operation, and the traffic pattern. The remainder of this paper is organized as foows. Reated work is given in Section II. The system mode is described in Section III. The probem of non-atruistic node cooperative resource aocation for WMNs with QoS support is described in Section IV. Two proposed QoS-driven resource aocation approaches with node cooperation are presented in Section V. Performance evauation is given in Section VI. Finay, concusions are presented in Section VII. Fig.. Mountains Wireine gateway Mesh router Mesh router Mesh cient Wireine gateway Mesh router Mesh cient Custer An iustration of a typica WMN for suburban/rura residentia areas. II. RELATED WORK In the iterature, there exists a rich body of research work on node cooperation [6] [7]. Besides information-theoretic studies [7], most recent work on the topic of node cooperation can be cassified into two groups: ) distributed space-time coding design; and 2) resource aocation with reay seection. The first group focuses on the design and performance evauation of distributed space-time coding (e.g., [6,8]). Spectra efficiency can be further improved by means of dirty paper coding appied at the transmitters [9]. With appropriate detection techniques, an additiona diversity order can be attained in time-varying wireess channes [0]. However, most node cooperation strategies based on distributed space-time coding conceive the existence of pure reay nodes, which is not aways feasibe in practica WMNs. The second group aims at reay seection and resource aocation. Partner matching agorithms based on graph theory are proposed in [], the objective of which is to optimize the energy efficiency; however, energy consumption is not a concern in WMNs. In [2], a distributed cooperative MAC protoco for muti-hop networks is proposed for reay seection. Game theory and auction theory are aso empoyed to derive node cooperation strategies and cooperative resource aocation soutions (e.g., [3,4]). The performance resuts of the aforementioned approaches can be appeaing; however, powerfu centra controers are mosty required to execute those agorithms. In the case of austere suburban and rura environments, distributed contro is preferred, yet directy appying those approaches to WMNs with decentraized contro can be ineffective or inefficient. On the other hand, many of the existing partner seection schemes consider ony measured (instantaneous) signa-tonoise ratios in choosing a partner (e.g., [7]), and most of the existing approaches focus on atruistic node cooperation. In the context of non-atruistic node cooperation, the avaiabiity of a potentia partner and its QoS requirement shoud aso be taken into account. In [5,6], the probem of partner seection for non-atruistic node cooperation is studied. Three partner seection schemes with power contro are proposed in [5] for baancing transmit power and system performance, whereas two partner seection schemes are proposed in [6] so as to minimize the average outage probabiity. However, MAC-ayer service differentiation is not addressed, for ony a singe cass of traffic is considered in the aforementioned work. In [7], Zhang et a. propose a simpe two-step scheme for the system throughput maximization probem with physica-ayer QoS assurance. Without considering beneficia node cooperation, however, system performance can be undermined. In addition, both packet scheduing and packet-eve QoS support are not taken into consideration, pausiby eevating the packet dropping rates for rea-time traffic. In this work, we propose two ow-compexity QoS-driven node cooperative resource aocation approaches taiored for WMNs with heterogeneous traffic. Our proposed approaches are demonstrated efficient yet effective in providing packeteve QoS assurance and faciitating MAC-ayer service differentiation. III. SYSTEM MODEL A. Network Mode We consider an orthogona frequency division mutipexing (OFDM)-based WMN for suburban or rura residentia areas, consisting of wireine gateways attached to the Internet backbone and a number of mesh routers and mesh cients scattered around, rendering a hierarchica muti-hop network (see Fig. ). In specific, mesh routers mounted on the rooftops of the premises comprise a wireess mesh backbone, whie mesh cients (e.g., aptops) associated with their cosest mesh router constitute various access networks. The system mode takes account the austere suburban and rura networking environments, which thwarts one-hop direct communications as opposed to muti-hop transmissions, providing ease of depoyment and offering greater coverage of wireess access [2]. Mesh routers are assumed stationary and hence the channe gains can be estimated accuratey. We consider that traffic traverses from mesh cients to mesh routers to the gateway ony. Each mesh node is equipped with one transceiver having an omni-directiona antenna, so that it cannot transmit and receive at the same time. To provide network stabiity and increase throughput, we assume that there is an efficient node custering agorithm in pace for the wireess mesh backbone [4], so that the notion of frequency reuse is taken into consideration, the cochanne interference eve is bounded,

3 CHENG and ZHUANG: QOS-DRIVEN MAC-LAYER RESOURCE ALLOCATION FOR WIRELESS MESH NETWORKS WITH NON-ALTRUISTIC... 3 and each custer is assigned a set of subcarriers. Consider a synchronized WMN, in which time is partitioned into frames, each containing a number of DATA sots. Two casses of traffic are considered, namey ) rate-guaranteed (RG) traffic and 2) best-effort (BE) traffic. In particuar, the RG traffic has a minimum data rate requirement and a deay bound requirement, whereas the BE traffic has no QoS requirement. Ca admission contro (CAC) is assumed in pace such that the QoS requirements of an admitted RG traffic fow can be met. de cooperation is considered and triggered as ong as it is feasibe and beneficia for system performance. In fact, there are many pausibe node cooperation scenarios in the WMN of interest; however, in this work, we focus on a node cooperation scenario where custermembers cooperativey transmit their packets to a custerhead. B. de Cooperation Consider a transmission scenario invoving three wireess nodes, namey de S, de R, and de D. de S is to transmit data to de D, whie de R is viewed as a reay to hep de S forward the data to de D. WeempoytheCooperation Protoco I suggested in [5] as our node cooperation strategy throughout this paper, and consider the decode-andforward (DF) mode of cooperation (i.e., regenerative mesh nodes). In the first timesot, de S transmits a packet to both de R and de D. In the second timesot, de R forwards the packet received from de S to de D, whie de S transmits another packet to de D. tice that, in this cooperation protoco, de D receives two copies of the first packet and one copy of the second packet in two timesots. In traditiona cooperative networks with nodes empoying fu transmit power, the achievabe throughput per timesot due to cooperative transmissions can be higher than direct transmissions, thanks to both spatia mutipexing gain and power gain. Unike symbo-eve cooperation where continuous symbo transmissions can be feasibe, continuous packet transmissions are ess reaistic. Thus, in this work, we consider that a potentia packet-eve cooperation opportunity arises in every two timesots. Foowing the anaysis in [7] for a frequency-fat Rayeigh fading environment, the channe capacity C DF achieved by the DF mode with perfect) decoding is given by C DF = 2 og 2 (( + γ SD ) 2 + γ RD, where γ XY = E XY h XY 2 /σ 2 with E XY ( 0) being the received average energy at de Y from de X, X, Y {S, R, D, h XY the Rayeigh fading coefficient for the X Y ink modeed as an independent zero-mean compex Gaussian random variabe with unit variance, and σ 2 the noise-pus-cochanne interference power eve. In the case of non-atruistic node cooperation, due to the necessity of spitting the transmit power, ) C DF is given by C DF = 2 og 2 (( + a S γ SD ) 2 + a R γ RD, where a X is the scaing factor for the transmit power of de X, i.e.,0 a X. Foowing the anaysis given in [7], it can be proved that arbitrariy positive power aocation has no impact on the diversity performance in the DF cooperation mode with perfect decoding. By the same token, it can be further proved that, with m potentia reays, choosing the singe best reay is sufficient to achieve the fu diversity order in the DF cooperation mode with perfect decoding and arbitrariy positive power aocation. It is noteworthy that the case of a S =corresponds to the scenario of atruistic node cooperation. Compared to the channe capacity achieved by ordinary direct transmissions, denoted by C d =og 2 (+γ SD ), we can envision that a non-atruistic cooperative transmission may not aways be advantageous over an ordinary direct transmission. Therefore, for the sake of overa system performance, node cooperation among mesh nodes shoud be considered in a hoistic manner, to be discussed in Section V. IV. QOS-DRIVEN NON-ALTRUISTIC NODE COOPERATIVE RESOURCE ALLOCATION There are various system constraints associated with the non-atruistic node cooperative resource aocation probem for WMNs. Let M, N, andl denote the number of mesh nodes, the number of subcarriers avaiabe, and the number of timesots (i.e., DATA sots) in a frame, respectivey. The sum of the (non-negative) transmit power of each mesh node on the (aocated) subcarriers is bounded by a maximum power eve: N n= p m,n P m max, m, and p m,n 0, m, n, () where p m,n is the transmit power of the mth node over the n th subcarrier on the th timesot and Pm max is the maximum power constraint of the m th node. With the hep of node custering, a number of subcarriers are aocated to each custer. Here, we consider the case where each subcarrier can ony be aocated to one transmission ink without cooperation or at most two transmission inks with node cooperation (i.e., a direct ink and an assisted ink) in a custer. If node cooperation is empoyed, both a source node and its partner transmit data over the same subcarrier(s). In addition, since choosing the best partner is sufficient in terms of diversity performance [7], a node can have at most one partner at a time on condition that the node cooperation is favorabe. The aforementioned constraints can be formuated as foows: M c m,n + z mu, n, and c u,n = c m,n,,m u u=,u m when z mu =, m, u, n, (2) z mu, u and z mu, m (3) u=,u m c m,n {0,, m, n, and z mu {0,, m, u (4) where c m,n is an indicator of aocating the nth subcarrier to the m th node on the th timesot and z mu is the indicator of node cooperation offered to the m th node by the u th node. tice that, in genera, z yx z xy, x, y, as the node cooperation considered in this work is non-reciproca (i.e., asymmetric). For the sake of notationa convenience, we set z mm =, m. Provided that node cooperation is in pace, the transmit power of a node is spit into two segments, one dedicated to its direct transmissions and the other to the

4 4 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 2, DECEMBER 2009 assisted transmissions for its partner: z mu a mu =, u and 0 a mu, m, u (5) with a mu being the normaized portion of the tota transmit poweroftheu th node for assisting the m th node s transmissions. Let M and M 2 be the set of RG nodes and that of BE nodes, respectivey, i.e., M = M + M 2. In our probem formuation, we take the minimum rate requirements of the RG nodes in the current frame, if any, into account: R m (c, p, a, z) R d m, m (6) where R d m is the (instantaneous) transmission rate demand of the m th node in the current frame (i.e., R d m > 0, m M and R d m =0, m M 2 )andr m (c, p, a, z) is the achievabe data rate of the m th node, which can be computed by [6] R m (c, p, a, z) = N L ( (+amm 2 c m,n og 2 gmm,np m,n + z mu a mu gmu,np u,n. (7) u=,u m In (7), c = [ ] c m,n, p = [ ] p M N L m,n, a = M N L [a mu ] M M, z = [z mu ] M M, and gmu,n = ϕg mu,n/σn, 2 where ϕ is a bit-error-rate (BER) measure, G mu,n the channe gain from the u th node to the receiver of the m th node s transmissions over the n th subcarrier on the th timesot, and σn 2 the aggregate noise-pus-cochanne interference power on the n th subcarrier. tice that constraint (2) is impicity incorporated in (7). With the aforesaid system constraints, different objective functions can be considered. Here, we empoy the we-known utiity maximization framework to abstract our objective function. Let U m (R m (c, p, a, z) Θ) denote the utiity function of the m th node and Θ {, 2 the utiity seector. The objective function is given by U m (R m (c, p, a, z)) Θ) { M = R m (c, p, a, z), when Θ = [ ( )] κ M n Rm(c,p,a,z) A, when Θ =2 (8) where A is a sufficienty arge constant such that 0 <R m /A <, m [8]. Thus, the objective function is to maximize the system throughput when Θ =, to achieve proportiona fairness when Θ = 2 and κ =, and to achieve maxmin fairness when Θ = 2 and κ, respectivey. In practice, the choice of Θ is contingent on the purpose of the networking appication and/or the prerogative of a system designer. Other system performance can aso be optimized by means of utiity functions (e.g., a tradeoff between throughput and fairness [9]). In ight of the fact that traffic demands and interference eves vary over time, we need to update our resource aocation soution from time to time. Therefore, we consider that the node cooperation between a source node and its partner is committed merey for an active resource aocation interva. ) 2 Probem Formuation: Consider the foowing nonatruistic node cooperative resource aocation optimization probem (NCRAOP) { M max c,p,a,z U m (R m (c, p, a, z) Θ) subject to (), (3), (4), (5), (6), and c m,n (9), n, where c, p, a, and z are the optimization variabes. By reducing the we-known NP-compete number partitioning probem to the NCRAOP, it can be proved that the NCRAOP is an NPhard probem. A summary of important symbos used in this paper is given in Tabe I for easy reference. V. PROPOSED RESOURCE ALLOCATION APPROACHES WITH NODE COOPERATION A. KKT Interpretations In genera, soving the NP-hard NCRAOP requires exponentia time compexity [20]. To design an efficient and effective resource aocation approach to sove the NCRAOP, we consider the Lagrangian of the NCRAOP and the KKT conditions. Due to space imitations, we ony present some key resuts here. ) Subcarrier Aocation Criterion: For the n th subcarrier and the th timesot, choose m {( =argmax U m m (R m (c, p, a, z) Θ)+ξ () ) m R m (c, p, a, z) c m,n (0) where ξ () m is the Lagrange mutipier for constraint (6), and set c m,n =. 2) Partner Aocation Criterion: For the u th node, choose m such that m =argmax m u { U m (R m (c, p, a, z) Θ) a mu R m (c, p, a, z) z mu () and set z m u =. 3) Partner Seection Criterion: For the m th node, choose u such that u =argmax u m { U m (R m (c, p, a, z) Θ) a mu R m (c, p, a, z) z mu (2) and set z mu =. tice that, in genera, the resuts obtained from the partner seection criterion and that from the partner aocation criterion are not the same. The partner seection criterion refers to choosing the best reay for a particuar source node, whereas the partner aocation criterion refers to aocating a reay node to the best source node. In a nutshe, the partner seection criterion is to maximize the node-wise utiity, whie the partner aocation criterion is to maximize the network-wise utiity.

5 CHENG and ZHUANG: QOS-DRIVEN MAC-LAYER RESOURCE ALLOCATION FOR WIRELESS MESH NETWORKS WITH NON-ALTRUISTIC... 5 Symbo M N L p m,n Pm max c m,n z mu a mu R m( ) R d m U m( ) Θ ρ Nm T λ TABLE I SUMMARY OF IMPORTANT SYMBOLS. Definition number of mesh nodes in the WMN number of avaiabe subcarriers in the WMN number of timesots (i.e., DATA sots) in a frame transmit power of the m th node over the n th subcarrier on the th timesot maximum power constraint of the m th node indicator of aocating the n th subcarrier to the m th node on the th timesot indicator of node cooperation offered to the m th node by the u th node normaized portion of the tota transmit power of the u th node for assisting the m th node achievabe data rate of the m th node (instantaneous) transmission rate demand of the m th node utiity function of the m th node utiity seector tunabe system parameter to baance cooperation and non-cooperation set of subcarriers aocated to the m th node on the th timesot poing time interva Poisson arriva rate for BE traffic B. Exampes To better understand the conceptua impications of our subcarrier aocation criterion and partner seection/aocation criterion, we consider the foowing three objective functions, namey ) system throughput maximization, 2) proportiona fairness, and 3) max-min fairness. For presentation carity, we assume ξ () m =0. ) System Throughput Maximization (Θ = ): U m (R m ( ) Θ) = R m ( ) and hence U m (R m ( ) Θ) = ; therefore, the subcarrier aocation criterion given in (0) and the partner seection criterion given in (2) become { ( (+amm m =argmax og m 2 gmm,n ) 2 p m,n + z mu a mu gmu,np u,n u=,u m (3) and u =argmax u m { N L c m,ng mu,np u,n ( +amm gmm,npm,n) 2 + u m z mua mu gmu,np u,n (4) respectivey. Thus, given the power aocation (i.e., a, p) and partner seection (i.e., z), the condition (3) impies that the arger throughput the m th node can contribute over the n th subcarrier on the th timesot, the better the n th subcarrier on the th timesot is assigned to the m th node (i.e., c m,n =, m,n, ). Likewise, given the power aocation and subcarrier aocation, the condition (4) indicates that we shoud choose a partner who can contribute the argest margina increase in the achievabe data rate. Therefore, both criteria agree with the notion of throughput maximization. tice that in the case of non-cooperation (i.e., z mu =0), the condition (3) reduces to the we-known subcarrier aocation criterion for throughput maximization [2]. 2) Proportiona Fairness ( )(Θ = 2 and κ = ): U m (R m ( ) Θ) =n Rm( ) A and hence U m (R m ( ) Θ) = /R m ( ); therefore, the conditions (0) and (2) become { ( (+amm m =argmax m R m ( ) og 2 gmm,np ) 2 m,n + z mu a mu gmu,np u,n u=,u m (5) and u =argmax u m { R m ( ) N L c m,n g mu,n p u,n ( +amm g mm,n p m,n) 2 + u m z mua mu g mu,n p u,n (6) respectivey. As seen, it is more ikey for a mesh node to get an extra subcarrier and/or a partner if its data rate obtained is sma, whereas it is ess ikey to assign an extra subcarrier or a partner to a node whose data rate obtained is aready very high. Thus, both criteria match with the notion of proportiona fairness. 3) Max-min Fairness [(Θ = 2 and κ ): U m (R m ( ) Θ) = n ( Rm(c,p,a,z) A )] κ, and hence U m (R m ( ) Θ) =κ [ n (R m ( )/A)] κ /R m ( ). Since0 < R m ( )/A <, [ n (R m ( )/A)] κ becomes a dominant term as κ. Hence, the conditions (0) and (2) become m =argmin R m( ) and u =argmin R m( ) (7) m u m respectivey. Thus, we tend to assign subcarriers and partners to the nodes which have minima achievabe data rates, reaizing the notion of max-min fairness. In the foowing subsections, we propose a centraized resource aocation approach and a distributed resource aocation approach to sove the NCRAOP in Section V-C and Section V-D, respectivey.

6 6 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 2, DECEMBER 2009 C. Proposed Approach with Centraized Contro In order to obtain the goba optima soutions to the NCRAOP, subcarrier aocation, partner seection/aocation, and power aocation shoud be jointy considered, which brings about very high computationa cost. To devise an efficient yet effective node cooperative resource aocation strategy with centraized contro, we propose a four-phase resource aocation approach with QoS assurance and service differentiation. Specificay, in Phase, we fix the power aocation and then sove the NCRAOP without considering node cooperation; In Phase 2, we perform water fiing for power aocation to improve the system performance; In Phase 3, we aow node cooperation, if feasibe and favorabe, so as to add an additiona performance gain to the system; In Phase 4, we perform water fiing for power aocation again providing the soutions of subcarrier aocation and partner aocation, thereby further improving the system performance. Consider a simpe MAC protoco to iustrate the notion of packet scheduing for our proposed approach. Time is partitioned into frames, each of which is further divided into a beacon sot, a contro sot, and L DATA sots. Each RG node estimates the traffic oad (i.e., both the oca traffic oad and the reay traffic oad) by averaging the rate requirement over a fixed estimation window (e.g., 00ms) on a reguar basis. In the contro sot, a custerhead coects the traffic demand from its custermembers at the beginning of each active resource aocation interva (i.e., by poing periodicay). Then, the custerhead executes the proposed centraized resource aocation and announces a resource aocation decision in the next beacon sot. In the DATA sots, nodes transmit their information according to the resource aocation decision. Phase-: With uniform power aocation and no node cooperation (i.e., z mu = 0 and a mu = 0, m u), the NCRAOP can be reduced to the foowing resource aocation optimization probem { M max U m (R m (c) Θ) (8) c subject to (6), c m,n, n,, and c m,n {0,, m, n, (9) and the subcarrier aocation criterion given in (0) is as foows. For the n th subcarrier and the th {( timesot, choose m such ( that m = arg max m U m (R m (c) Θ)+ξ m) () og2 +g mm,n pm,n). The variabe ξ () m is updated iterativey by ξ () m =max{ 0,ξ () m s(k) m d m, with s (k) m being the step size at the k th iteration for the m th node and d m = R m (c) R d m. With CAC in pace, the approach terminates when a the subcarriers are aocated and a the rate requirements are met (i.e., ξ () m =0, m), and the subcarrier aocation soution c is obtained such that M c m,n =, n,. Phase-2: Perform water fiing for optima power aocation on the aocated subcarriers for each mesh node. Let R m (ˆp) and R m (p ) be the achievabe data rate obtained of the node with uniform power aocation (i.e., ˆp) andthat with optima power aocation (i.e., p ), respectivey. Since m th R m (p ) R m (ˆp) [22], the QoS demands of the mesh nodes can sti be met after transmit power is aocated according to water fiing. In a nutshe, Phase-2 resource aocation further improves the Phase- resource aocation soutions by empoying optima power aocation, conducing to improved system performance. Phase-3: Here, we investigate the performance gain due to feasibe and favorabe node cooperation. tice that partner aocation is feasibe in our centraized approach, for a custerhead can have compete knowedge on which mesh nodes can be the potentia partners for a particuar mesh node. With the subcarrier aocation soution obtained in Phase and the power aocation soution obtained in Phase 2, the NCRAOP becomes { M max a,z U m (R m (a, z) Θ) (20) subject to (3), (5), (6), and z mu {0,, m, u. (2) Denote ρ ( 0) as a tunabe system parameter to baance node cooperation and node non-cooperation, i.e., a mu = ρa uu, m u. In fact, ρ indicates the wiingness of a node to assist another mesh node s transmissions, i.e., the smaer the vaue of ρ, the ess eager is a node to assist the m th node for some m. For some u, if m u z mu =, then a mu = ρa uu (> 0), m u; otherwise, a uu = and a mu =0, m u. On the other hand, in the case of nonatruistic node cooperation, it is conceivabe that the vaue of ρ shoud be upper bounded (e.g., ρ 0.5), as a the mesh nodes have their own data to transmit. Suppose the u th node is to assist the m th node, i.e., z mu =. Then, the transmit power of the u th node eft for cooperation, denoted by Pu eft,isgivenby Pu eft = Pu max N a uu n= p u,n, wherep u,n is obtained from Phase-2. Let Nm be the set of subcarriers aocated to the m th node on the th timesot. If the transmit power of the u th node dedicated to node cooperation is uniformy distributed over the subcarriers aocated to the m th node on the th timesot, then ˆp u,n = P u max / n N c m m,n. Thus, the portion of the transmit power of the u th node in assisting the m th node s transmissions is a mu n N ˆp m u,n. In the presence of the two casses of traffic, service differentiation is indispensabe for effective QoS provisioning, where RG nodes are assigned higher priority over BE nodes. As a consequence, node cooperation shoud aso be prioritized. In particuar, we consider that ony RG nodes can receive assistance from either BE nodes or other RG nodes. Here, we further divide our Phase-3 resource aocation into two steps, namey ) BE-assisting-RG and 2) RG-assisting-RG. Step : In the case of BE-assisting-RG, aow BE nodes to { assist RG nodes whenever favorabe. Let A = m m M, j m z mj =0 and B = { u u M 2, i u z iu =0.SetA consists of RG nodes which do not receive any assistance from any other nodes, whereas set B consists of BE nodes which do not offer any assistance to any nodes. The partner aocation criterion is as foows. For the u th node, { u B, choose m that m U =argmax m (R m(a,z) Θ) m A a mu such R m(a,z) z mu.

7 CHENG and ZHUANG: QOS-DRIVEN MAC-LAYER RESOURCE ALLOCATION FOR WIRELESS MESH NETWORKS WITH NON-ALTRUISTIC... 7 R m (a, z) = R m (ã, z) = R u (a, z) = R u (ã, z) = N L N L N L N c ( m,n og 2 +g m m,np ) m,n ( (+g 2 c m,n og 2 m m,np ) 2 m,n + am ugm u,n ˆp u,n) >R m (a, z) (23) c u,n og ( 2 +g uu,n p ) u,n L c u,n og ( 2 +auu guu,n u,n) p <Ru (a, z) (25) (22) (24) Then, check if this partner aocation process can hep enhance the tota utiities. Let R m (a, z) and R m (ã, z) be the achievabe data rate obtained of the m th node without node cooperation and that with node cooperation, respectivey. We have (22)- (25) shown at the top of this page. Since Ru d = 0, u M 2, the soutions obtained by considering node cooperation are aso feasibe to the NCRAOP. Set z m u =and remove the m th node from A (i.e., A A {m ) if the foowing condition is vaid: U m (R m (ã, z) Θ)+U u (R u (ã, z) Θ) >U m (R m (a, z) Θ)+U u (R u (a, z) Θ). (26) If (26) is satisfied, it means that assigning the u th node to the m th node as its partner can increase the tota utiities, thereby improving the network-wise system performance. The u th node is removed from B (i.e., B B {u), and the process repeats unti A = {φ or B = {φ. Step 2: In the case of RG-assisting-RG, aow an RG node to assist other RG nodes whenever favorabe. Partner aocation in this step becomes convouted, for an RG node decreases its achievabe data rate and pausiby voids its own rate constraint (given { in (6)) when assisting other nodes. Let C = m m M, j m z mj =0 and D = { j j M, i j z ij =0.SetC consists of the RG nodes which do not receive any assistance from any other nodes, whereas set D consists of the RG nodes which do not offer any assistance to any RG nodes. For j { D, choose m such that m U m =argmax (Rm(a,z) Θ) R m(a,z) m C\{j a mj z mj. Then, check if the new resource aocation soutions are sti feasibe for the NCRAOP and can increase the tota utiities. Let (a, z) and (ã, z) denote the current node cooperative resource aocation soution and the new node cooperative resource aocation soution, respectivey. We have (27)-(30) shown on the next page. Set z m j =and remove the m th node from C (i.e., C C {m )ifthefoowing two conditions are vaid: U m (R m (ã, z) Θ)+U j (R j (ã, z) Θ) >U m (R m (a, z) Θ)+U j (R j (a, z) Θ) (3) R j (ã, z) Rj d. (32) Since Rj d > 0, j M, we have to ensure that the rate constraints for a the RG nodes are not vioated due to the aforesaid partner aocation (i.e., condition (32)). Condition (3) refers to the case where aocating the j th node as a partner to the m th node can increase the tota utiities. The j th node is removed from D (i.e., D D {j), and the process repeats unti C = {φ or D = {φ. With effective node cooperation, Phase-3 resource aocation improves the Phase-2 resource aocation soutions, thereby giving rise to higher tota utiities. Phase-4: The introduction of partner aocation (i.e., (a, z)) in Phase 3 changes the achievabe rate function. Thus, the power aocation soution obtained in Phase 2 is no onger optima. With the known soutions for subcarrier aocation and partner aocation, carry out water fiing for power aocation again so as to further improve the system performance. Suppose the u th node is to assist the m th node, i.e., z mu =. For the sake of optimaity, water fiing for the u th node shoud be performed over both Nu and Nm; however, procuring the optima power aocation soutions requires a considerabe number of recursive computations. Here, to baance the computationa compexity and the system performance, we make use of water fiing for power aocation for the m th node over Nm ony, m,. Lemma : With the subcarrier aocation soution and the partner aocation soution, denoted by c and (ã, z), respectivey, the power aocation soution obtained from water fiing, denoted by p,isgivenby ( ) p m,n = c 2ξ (2) m Υã mmgmm,n m,n 2ξ (2) mã mmgmm,n + Υ 2 (ã mm) 2 (gmm,n) 2 4(ξ (2) m) 2 Γ m +, m, n, 2ξ (2) mã mmgmm,n (33)

8 8 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 2, DECEMBER 2009 R m (a, z) = R m (ã, z) = R j (a, z) = R j (ã, z) = N L c ( m,n og 2 +am m g m m,np ) m,n N L ( (+am 2 c m,n og 2 m g m m,np ) 2 m,n + am jgm j,n ˆp j,n) >R m (a, z) (28) N L 2 c j,n og 2 ( +gjj,np ) 2 j,n + z ji a ji gji,nˆp i,n (29) = i j N L 2 c j,n og 2 ( +a jj gjj,np ) 2 j,n + z ji a ji gji,nˆp i,n <R j (a, z) (30) n= i j (27) where Υ = U m (R m(p) Θ) + ξ () m, Γ m = u m z muã mu gmu,n ˆp u,n, and ξ (2) m is the Lagrange mutipier for the constraint N n= p m,n P m max, m,. Proof: We omit the proof as it is simiar to the one given in [22]. With the aforementioned optima power aocation, Phase- 4 resource aocation further enhances the Phase-3 resource aocation soution, eading to higher tota utiities. The fowchart of our proposed centraized approach is depicted in Fig. 2. D. Proposed Approach with Distributed Contro When custerheads are not avaiabe, distributed node cooperative resource aocation is essentia. We consider that each mesh node can communicate with a other mesh nodes in the same custer. Here, we propose a two-phase distributed node cooperative resource aocation approach with QoS support and service differentiation. We consider that an active resource aocation interva consists of two phases, namey contention phase and transmission phase. In the contention phase, the approach of Back-burst can be used for subcarrier contention [2]. In the transmission phase, mesh nodes transmit their data with the consideration of node cooperation, if feasibe and favorabe. ) Contention Phase: A contention phase consists of a number of contention periods. For each contention period, the Back-burst (BB) methodoogy is used for the subcarrier contention to achieve service differentiation [2]. Let E = { { m m M,R m ( ) <Rm d and F = m m M,R m ( ) Rm d {m m M2.SetE consists of the RG nodes whose QoS demands are not satisfied, whereas set F consists of both the BE nodes and the RG nodes whose QoS demands are met. Each contention period is further divided into two mini-periods, where the first miniperiod is for the contention among the nodes in E, whie the second mini-period is for the contention among the nodes in F. Fig. 3(a) depicts the dynamics of a contention phase. At the beginning of each contention period, every node is in a istening mode and waits for a period of time before transmitting its BB signa. In the first mini-period, the waiting time of an RG node in E is inversey proportiona to its minimum required rate. Therefore, the node with the highest minimum required rate sends its BB signa earier than the other RG nodes in E so as to win the contention. Other nodes which detect the BB signa remain in the istening mode. An RG node becomes a winner for this contention if it senses an ide channe after transmitting a BB signa. To ensure that each contention period resuts in ony one winner, we assume that the ength of a BB signa sent from a node is proportiona to its network ID (e.g., MAC address). The winner of this contention period then seects the best subcarriers according to the subcarrier aocation criterion given in (0) so as to meet its QoS demand. tice that uniform power aocation is empoyed when the subcarriers are seected. After the subcarrier seection is finished, the winner transmits a BB signa over the aocated subcarriers so that the other nodes in a istening mode can detect and record which subcarriers have been chosen. Then, a the other RG nodes wait for the next contention and this process repeats unti a the RG nodes in E have seected their subcarriers. Since we assume that CAC is in pace, a the QoS requirements of the RG nodes in E can be met at the end of this phase. Subcarrier contention among the nodes in F (i.e., satisfied RG nodes and BE nodes) occurs ony if there is some unaocated subcarrier(s). If there is no BB detected in the first mini-period, meaning that the subcarrier contention among the RG nodes in E is compete, every node in F waits for a period of time in the second mini-period before sending out its BB signa, where the waiting time is inversey proportiona to its margina utiity increase when choosing the best avaiabe U subcarrier (i.e., m(r m( )) ). Thus, the arger the margina c m,n utiity increases, the more ikey that the node wi be the winner. The winner then seects the best subcarrier according to the subcarrier aocation criterion given in (0). The process repeats unti a the subcarriers are used. Simiar to the centraized resource aocation approach, after the subcarrier aocation is determined, each mesh node performs water fiing for power aocation independenty to further increase both its utiity and the system performance. 2) Transmission Phase: A transmission phase consists of a number of frames, where each frame consists of L DATA sots. Each DATA sot is further divided into two (identica) minisots. Fig. 3(b) depicts the frame structure used for a transmission phase. Fig. 4 iustrates a typica (non-atruistic)

9 % % % % % % % % % % CHENG and ZHUANG: QOS-DRIVEN MAC-LAYER RESOURCE ALLOCATION FOR WIRELESS MESH NETWORKS WITH NON-ALTRUISTIC... 9 Start Phase Fix (p,a,z) and sove M M Um Rm cm n cm n c m= m= ( ( c ) Θ),, { max s.t. (6),, and 0, Phase 2 Perform water fiing for power aocation over Ν, m, m Phase 3 For u B, choose m * s.t. ' U m ( Rm ( a,z) Θ ) Rm ( a,z) = m A amu z mu m* argmax For j D, choose m * s.t. ' Um( Rm( a, z) Θ) Rm ( a, z) m* arg max m C\{ j a z = mj mj ( ( a, z) Θ ) + ( ( a, z) Θ ) > m* ( m* ( a, z) Θ ) + u( u( a,z) Θ) U R U R m* m* u u U R U R? Yes set z m * u = & A A { m* U ( Rm ( a, z) Θ ) + U j( Rj( a, z) Θ ) > m* * U ( Rm ( a,z) Θ ) + U j( Rj( a,z) Θ) m* * & Rj( a,z) R? d j Yes set z m * j = & C C { m* B B { u D D { j A = { φ or B = {? φ YES C = { φ or D = {? φ Yes Phase 4 Perform water fiing for power aocation over Ν, m, m End Fig. 2. Fowchart of the proposed centraized approach. node cooperation scenario in the transmission phase. In Fig. 4(a), the m th node (i.e., an RG node) is transmitting data to its destination node (i.e., the d th node) in the first minisot. The m th node s transmission can be overheard by the u th node in the first minisot if the u th node is in the istening mode. The u th node then checks if it can decode the m th node s transmissions successfuy. If the u th node fais to decode the m th node s transmissions, the u th node wi not hep reay the m th node s data (see Fig. 4(b)). On the other hand, if the u th node can decode the m th node s transmissions reiaby, the u th node then becomes the partner of the m th node if condition (26) is vaid with the u th node being a BE node or conditions (3) and (32) are vaid with the u th node being an RG node (see Fig. 4(c)). As a matter of fact, the m th node can have more than one partner at a time (e.g., the i th node and u th node in Fig. 4(c)). In the presence of mutipe potentia partners, we empoy the partner seection scheme proposed in [2] to choose the best partner for the m th node with respect to our partner seection criterion given in (2). We aso assume that a signa capture mechanism is in pace so that a potentia partner can ony overhear the strongest neighboring node s transmission [23]. This node cooperation between a source node and its partner sustains unti the next active interva. E. Compexity Anaysis The time compexity of the proposed four-phase centraized approach is O(bMNL + M M), where b is a constant. For the proposed two-phase distributed approach, since each mesh node behaves independenty, the time compexity is O(kNL + M), where k is a constant. It is noteworthy that the difference in time compexity between the two approaches stems from different modes of network operation (i.e., centraized contro or distributed contro) and different methodoogies of resource aocation (i.e., partner aocation or partner seection). For comparison, the time compexity of a Hungarian approach is O( M M 2 + MN 2 L 2 ). Despite a pausiby improved system performance, appying a Hungarian approach can be inefficient in the WMNs without powerfu centraized controers. In contrast, our proposed approaches are of ow compexity and more suitabe for the ow-cost mesh nodes. F. Discussion In game theory, efficient resource utiization is determined by the concept of Pareto optimaity [24]. On the other hand, network stabiity can be achieved when a resource aocation soution attains an Nash equiibrium [24]. Foowing the definitions of Pareto optimaity and Nash equiibrium, we can show that the partner aocation/seection soutions in our proposed node cooperative resource aocation approaches

10 0 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 2, DECEMBER 2009 Contention Phase Contention Period st Mini-period BB 2 nd Mini-period st Mini-period 2 nd Mini-period BB Wait time before transmitting a BB signa Wait time before transmitting a BB signa (a) An iustration of the subcarrier contention phase among RG nodes and BE nodes. Transmission Subcarrier N Phase Frame L DATA sots 2... L st 2nd Minisot (b) The structures of a frame and a DATA sot empoyed in the transmission phase. Fig. 3. The phase structures of the proposed two-phase distributed node cooperative resource aocation approach. are Pareto optima. Further, modeed by a round-robin game payed by the RG nodes (potentia partners), the partner seection (aocation) soutions attain an Nash equiibrium. The proof for our proposed partner aocation achieving Pareto optimaity is reported in []. Other game-theoretic evauation resuts can be proved directy by first principes. Therefore, our proposed approaches not ony can make efficient use of scarce network resources but aso can faciitate network stabiity. The fowchart of our proposed distributed approach is depicted in Fig. 5. m i (a) u d m m i i (b) u d d VI. PERFORMANCE EVALUATION A. Packet-Leve QoS Provisioning In the MAC ayer, to streamine QoS provisioning and provide service differentiation, packet prioritization is imperative [25]. We conceive that the priority of RG traffic (packets) is reated to the performance of their packet dropping rates. In this work, we ony take the packet dropping due to the deay bound vioation into account. The higher the packet dropping rate that an RG traffic fow suffers from, the higher the priority of the packets associated with that fow. In the centraized approach, after gathering the transmission requests in the contro sot, a custerhead grants the requests Fig. 4. phase. Exampe of a typica node cooperation scenario in the transmission of transmitting higher-priority packets first. In the distributed approach, we consider that the RG node with the highest packet dropping rate transmits its BB signa earier than the other nodes in the contention phase. If two or more RG nodes have the same packet dropping rate, the node with the highest minimum required rate wi win the contention of interest. In (c) u

11 CHENG and ZHUANG: QOS-DRIVEN MAC-LAYER RESOURCE ALLOCATION FOR WIRELESS MESH NETWORKS WITH NON-ALTRUISTIC... Contention phase Transmission phase Start QoS demands of RG nodes met? Yes Any unused subcarriers? The m th node s transmission in the st minisot Can the u th node overhear and decode the transmission? Yes Conditions for partner seection satisfied? Yes Cooperative transmission in the 2 nd minisot Yes Subcarrier aocation for unsatisfied RG nodes in the st mini-period Subcarrier aocation for satisfied RG nodes and BE nodes in the 2 nd mini-period Ordinary direct transmission by the m th node s transmission in the 2 nd minisot ms and that of the subsequent frames (with L DATA sots) is 5L ms in the proposed centraized approach, with a 5ms DATA sot. We consider that the poing is done in every T ms, meaning that the node cooperative resource aocation soution is updated every T ms. Here, both the poing and the beacon packet transmissions are assumed to be error-free. For fair comparison, we consider that the duration of an active interva in the proposed distributed approach is T ms, where the first 0ms is dedicated to the contention phase whie the remaining time period is dedicated to the transmission phase. We perform the simuations for 0,000 runs and average the resuts, where each simuation run sustains 5,000 frames. Concerning the traffic modes, the RG traffic is generated according to a two-state ON-OFF mode. In the ON state, a fixed-size packet arrives in every 20ms with rate demand 384kb/s, whereas in the OFF state, no packet is generated. We consider that the duration of an ON period and that of an OFF period are independent, both foow an exponentia distribution, where the mean ON period and the mean OFF period are s and.2s, respectivey. The deay bound of RG traffic is assumed to be 5L ms. The required packet dropping rate is ess than %. On the other hand, the BE traffic does not have any QoS requirements. BE packet arrivas foow a Poisson process with mean rate λ packets/second, where the packet size foows a Weibu distribution (i.e., Weibu(2,2)). To mimic the mixed traffic in a WMN, we assume that an RG node has one RG traffic fow and one BE fow, whie a BE node has one BE fow. Fig. 5. End Fowchart of the proposed distributed approach. other words, our QoS provisioning strategy for the RG traffic hinges upon the packet dropping rate. To further augment the effectiveness of QoS provisioning, the partners, timesots, and subcarriers aocated to or chosen by a particuar mesh node are reserved for packet transmissions unti the next active resource aocation interva (e.g., next poing). B. Simuation Environment Consider a custer with a number of wireess mesh nodes randomy ocated in a km x km coverage area. We adopt the path-oss mode suggested in [26] (i.e., hiy/moderateto-heavy tree density). Consider an OFDM-based wireess environment with N avaiabe subcarriers. We assume that a subcarriers exhibit frequency-fat Rayeigh fading. The maximum transmission rate over each subcarrier is considered to be 200kb/s. We further assume that the routing is predetermined so that the transmission source and destination pair of an incoming packet is known in advance. Other simuation parameters are chosen as foows: Pm max =W, σ2 n =0 2 W, N = 00, L =4, ρ =/3, ϕ =,andθ =. Since our resource aocation soutions sustain for an active resource aocation interva, the duration of the first frame (with beacon sot, contro sot and L DATA sots) is 5(L +2) C. Simuation Resuts We evauate the system performance of the proposed node cooperative resource aocation approaches versus M, T, M, and λ in terms of throughput, resource utiization, packet dropping rate, and node cooperation gain (i.e., normaized throughput gain due to node cooperation). The standard deviations of the resuts are aso potted for reference. For performance comparison, we consider two baseine approaches and an approach suggested in [7]: ) a centraized baseine approach which is the same as the proposed centraized approach without Phase-3 and Phase-4 resource aocation; 2) a distributed baseine approach which is the same as the proposed distributed approach without considering node cooperation in the transmission phase; and 3) the Zhang s approach proposed in [7] which first aocates the subcarriers with no QoS consideration to maximize throughput and then re-aocates the subcarriers trying to satisfy the QoS demands of the nodes without considering node cooperation. te that the performance degradation due to signaing overhead is not taken into account in evauating the system performance. An upper bound for average throughput performance is aso potted for reference. ) Effect of M: For M 2 = 2 M, T = 50ms, and λ = 50 packets/second, Fig. 6 shows the throughput performance versus the number of mesh nodes. We can see that the throughputs of a considered approaches increase with We anayticay obtain an upper bound for average throughput performance under the assumptions of no packet dropping for the RG traffic and perfect statistica traffic mutipexing.

12 2 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 2, DECEMBER 2009 TABLE II RELATIONSHIP BETWEEN THE NUMBER OF MESH NODES, M, AND THE NODE COOPERATION GAIN (NCG) (I.E., NORMALIZED THROUGHPUT GAIN DUE TO NODE COOPERATION) FOR THE PROPOSED APPROACHES (WITH M 2 =2 M, T = 50MS, AND λ =50PACKETS/SECOND) M NCG for the proposed centraized approach (in %) NCG for the proposed distributed approach (in %) Throughput (Mb/s) Proposed centraized Proposed distributed Centraized baseine Distributed baseine Zhang s Upper bound Packet dropping rate (in percentage) Proposed centraized Proposed distributed Centraized baseine Distributed baseine Zhang s Number of mesh nodes, M Fig. 6. Comparison of the throughput performance of the proposed fourphase centraized approach, the proposed two-phase distributed approach, the centraized baseine approach, the distributed baseine approach, and the Zhang s approach [7] vs. the number of mesh nodes (with M 2 =2 M, T = 50ms, and λ =50packets/second) Number of mesh nodes, M Fig. 7. Comparison of the RG packet dropping rates of the proposed fourphase centraized approach, the proposed two-phase distributed approach, the centraized baseine approach, the distributed baseine approach, and the Zhang s approach [7] vs. the number of mesh nodes (with M 2 =2 M, T =50ms, and λ =50packets/second). M, since the system is not saturated. As expected, the centraized approaches (i.e., the proposed four-phase centraized approach and the centraized baseine approach) outperform their distributed counterparts (i.e., the proposed two-phase distributed approach and the distributed baseine approach) due to the merit of the existence of a custerhead. However, the Zhang s approach achieves the highest throughput among a considered approaches, reaizing the goa of throughput maximization. On a different note, our proposed four-phase centraized (two-phase distributed) approach outperforms the baseine centraized (distributed) approach, which stems from an additiona performance gain due to beneficia node cooperation. The node cooperation gain (NCG) is given in Tabe II. As anticipated, the more the mesh nodes, the more the potentia hepers and hence the higher the NCGs. In genera, the NCG obtained in our proposed centraized approach is higher than that obtained in our proposed distributed approach. The rationae is mainy due to the partner aocation empoyed in our proposed centraized approach yet the partner seection in our proposed distributed approach. Another reason is that node cooperation in the proposed distributed approach can ony be triggered when some mesh nodes are ide in the first minisot, thereby curbing some potentia and favorabe node cooperation opportunities. The gain in our proposed centraized approach is roughy eveed off from M = 30 onward, which is ascribed to the imited avaiabe resources (i.e., subcarriers). We expect that the NCG can be higher with a arger vaue of N. We observe that, as the number of mesh nodes increases from 6 to 48, the resource utiization of the proposed four-phase centraized approach increases from 9% to 4%, that of the proposed two-phase distributed approach from 7% to 30%, that of the centraized baseine approach from 8% to 3%, that of the distributed baseine approach from 6% to 28%, and that of the Zhang s approach from 0% to 44%, respectivey. The ow resource utiization is due to ow traffic oad and resource reservation. We observe that the resource utiization (and throughput) for our proposed approaches can be improved when the traffic oad increases and the RG traffic demand is ess stringent. In Fig. 7, the RG packet dropping rates are depicted. The packet dropping rates for RG traffic in our proposed approaches and two baseine approaches are we beow % due to effective packet-eve QoS provisioning. On the other hand, the RG packet dropping rate of the Zhang s approach increases and reaches 20% as M increases. Fig. 7 shows that the Zhang s approach is ineffective in supporting the QoS requirements of RG traffic at the packet eve. netheess, the Zhang s approach aims at maximizing the (network-wise) throughput in ieu of focusing on (nodewise) QoS satisfaction. The resuts aso assure the fact that provisioning QoS and increasing throughput are conficting performance measures [9].

13 CHENG and ZHUANG: QOS-DRIVEN MAC-LAYER RESOURCE ALLOCATION FOR WIRELESS MESH NETWORKS WITH NON-ALTRUISTIC... 3 TABLE III RELATIONSHIP BETWEEN THE VALUE OF T AND THE NODE COOPERATION GAIN (NCG) (I.E., NORMALIZED THROUGHPUT GAIN DUE TO NODE COOPERATION) FOR THE PROPOSED APPROACHES (WITH M =30MESH NODES, M 2 =2 M, AND λ =50PACKETS/SECOND) T (in ms) NCG for the proposed centraized approach (in %) NCG for the proposed distributed approach (in %) Throughput (Mb/s) Proposed centraized Proposed distributed Centraized baseine Distributed baseine Zhang s Upper bound Packet dropping rate (in percentage) Proposed centraized Proposed distributed Centraized baseine Distributed baseine Zhang s Poing time, T (ms) Fig. 8. Comparison of the throughput performance of the proposed fourphase centraized approach, the proposed two-phase distributed approach, the centraized baseine approach, the distributed baseine approach, and the Zhang s approach [7] vs. the poing time (with M = 30 mesh nodes, M 2 =2 M,andλ =50packets/second). 2) Effect of T : For M =30mesh nodes, M 2 =2 M, and λ = 50 packets/second, we study the impact of the poing time (or the ength of an active interva) on the system performance measures. Fig. 8 shows the throughput performance versus the vaue of T. The throughputs obtained in a considered approaches decrease with the vaue of T. The arger the vaue of T, the ess accurate the traffic oad estimate and hence the weaker the throughput performance. In particuar, even though our proposed distributed approach maintains its NCG against T (see Tabe III), its throughput drops significanty from 3.0Mb/s to.9mb/s. On the contrary, with the hep of a custerhead, not ony does our proposed centraized approach effectivey sustain its throughput performance, but its NCG aso ramps up consideraby from 2% to 54% when T increases (see Tabe III). As a resut, the proposed four-phase centraized approach is shown to be ess vunerabe to poor traffic oad estimates. As to the Zhang s approach, however, its throughput obtained pummets sharpy as T increases. The decine is due to the absence of effective packet-eve QoS provisioning mechanism in pace and, therefore, once the traffic oad estimates are ess accurate, the system performance deteriorates dramaticay. This phenomenon can aso be expained in Fig. 9. Simiar to Fig. 7, the RG packet dropping rates of our proposed approaches and two baseine approaches are capped by %. In contrast, the packet dropping rate of the Zhang s approach increases from Poing time, T (ms) Fig. 9. Comparison of the RG packet dropping rates of the proposed fourphase centraized approach, the proposed two-phase distributed approach, the centraized baseine approach, the distributed baseine approach, and the Zhang s approach [7] vs. the poing time (with M = 30 mesh nodes, M 2 =2 M,andλ =50packets/second). 0% to 43%, resuting in the worst RG packet dropping rate performance. In short, resource aocation approaches without considering packet-eve QoS provisioning are susceptibe to the accuracy of traffic oad estimates. For resource utiization, we observe that the trends of a curves are simiar to those in Fig. 8. 3) Effect of M : For M =30mesh nodes, T = 50ms, and λ = 50 packets/second, we study the impact of RG traffic (i.e., the vaue of M ) on the system performance measures. In Fig. 0, the throughput performance versus the vaue of M is depicted. Since the network is not saturated, in genera, a the curves go up with the number of RG nodes, M.From M =20onward, the throughputs of our proposed distributed approach and the distributed baseine approach begin to eve off, resuting from the effect of resource reservation for the RG traffic. By the same token, the rates of the throughput increment in our proposed centraized approach and the centraized baseine approach decrease from M = 25 onward. The throughput performance of the Zhang s approach first rises from M =0to 20 and then decines afterwards. Simiar to the previous discussions, as the number of RG nodes increases, the Zhang s approach fais to effectivey provision packet-eve QoS, thereby increasing its RG packet dropping rate and decreasing its throughput. At M = 30, the throughput obtained in the Zhang s approach is even ower than that in the proposed four-phase centraized approach. The resource utiizations attained by a the approaches have the trends simiar to those in Fig. 0.

14 4 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 8, NO. 2, DECEMBER Throughput (Mb/s) Proposed centraized Proposed distributed Centraized baseine Distributed baseine Zhang s Upper bound Throughput (Mb/s) λ = 50 λ Number of RG nodes, M 0 Proposed centraized Proposed distributed Centraized baseine Distributed baseine Zhang s Fig.. Comparison of the throughput performance of the proposed fourphase centraized approach, the proposed two-phase distributed approach, the centraized baseine approach, the distributed baseine approach, and the Zhang s approach [7] vs. the vaue of λ (with M = 30 mesh nodes, M 2 =2 M,andT = 50ms). Fig. 0. Comparison of the throughput performance of the proposed fourphase centraized approach, the proposed two-phase distributed approach, the centraized baseine approach, the distributed baseine approach, and the Zhang s approach [7] vs. the number of RG nodes (with M =30mesh nodes, T =50ms, and λ =50packets/second). We observe that the NCGs of our two proposed approaches stay more or ess the same against M. It shows that the node cooperation opportunities of both proposed approaches are amost independent of the number of RG nodes in the system. It is noteworthy that, in Fig. 0, there is an obvious performance gap between the throughputs obtained from the considered approaches and the upper bound at a arge M. This gap is mainy ascribed to the resource reservation for RG traffic. Concerning the RG packet dropping rates, the trends of the considered approaches are simiar to the ones shown in Fig. 9. In a nutshe, with the virtue of node cooperation, our four-phase centraized approach can achieve better system performance and provide more effective QoS provisioning than its throughput-oriented counterpart when there is a arge number of RG nodes in the network. 4) Effect of λ: For M =30mesh nodes, M 2 =2 M, T = 50ms, and ρ =/3, we study the impact of BE traffic (i.e., the vaue of λ) on the system performance measures. Here, we consider two cases: ) λ = 50 packets/second (i.e., bursty data traffic) and 2) λ packets/second (i.e., background data traffic). Fig. shows the throughput performance for λ = 50 and λ. It is cear that the throughputs in the presence of background data traffic (i.e., λ ) are higher than in the case of Poisson arrivas (i.e., λ =50). We aso observe that the NCGs obtained drop from 23.4% to 9.0% in the proposed centraized approach and from 7.59% to 0% in the proposed distributed approach, respectivey, when the data traffic changes from bursty (i.e., λ = 50) to background (i.e., λ ). Concerning our proposed centraized approach, since the rate function is a concave function and the throughput obtained by Phase- and Phase-2 resource aocation is aready high in the case of λ, the room for further throughput increment due to node cooperation is reativey smaer than in the case of λ =50. As a resut, the performance gain of the proposed four-phase centraized approach over the centraized baseine approach is ess substantia. On the other hand, it is notabe that the NCG of our proposed distributed approach vanishes in the case of λ, the rationae for which is that a the mesh nodes are busy a the time and no mesh nodes are ide in the first minisot in the transmission phase. Thus, there is no partner avaiabe, wiping out the effectiveness of node cooperation. In other words, if a WMN with decentraized contro is saturated (with background data traffic), the benefits of non-atruistic node cooperation cannot be expoited. In a nutshe, when designing and depoying an efficient and effective WMN in practice, we shoud take notice of the nature of node cooperation (i.e., non-atruistic or atruistic), the traffic pattern (i.e., bursty traffic or background traffic), and the mode of network operation (i.e., centraized contro or distributed contro). As regards the packet dropping rate of the RG traffic, we observe that the resuts are neary the same as the ones shown in Fig. 7. A in a, the BE packets are assigned the ower priority and hence the change in the vaue of λ has amost no infuence on the packet dropping rate performance of RG traffic. VII. CONCLUSIONS In this paper, we propose two non-atruistic node cooperative resource aocation approaches taiored for WMNs with QoS support and service differentiation. Both the proposed four-phase centraized approach and the proposed two-phase distributed approach are shown to be effective in QoS provisioning for RG traffic and system performance improvement. Simuation resuts demonstrate that our proposed approaches achieve satisfactory system performance as the number of mesh nodes changes and are ess susceptibe to the inaccuracy of traffic oad estimates. Our study reveas a crucia design principe that whether or not node cooperation is usefu depends upon the nature of node cooperation, the traffic pattern, and the mode of network operation. Further, our approaches

15 CHENG and ZHUANG: QOS-DRIVEN MAC-LAYER RESOURCE ALLOCATION FOR WIRELESS MESH NETWORKS WITH NON-ALTRUISTIC... 5 are of ow compexity, eading to a viabe candidate for practica impementation. REFERENCES [] H. T. Cheng and W. Zhuang, QoS-driven node cooperative resource aocation for wireess mesh networks with service differentiation, in Proc. IEEE GLOBECOM, 2009, accepted for presentation. [2] H. T. Cheng, H. Jiang, and W. Zhuang, Distributed medium access contro for wireess mesh networks, Wireess Commun. and Mobie Computing, vo. 6, no. 6, pp , Sep [3] J. Ishmae, S. Bury, D. Pezaros, and N. Race, Depoying rura community wireess mesh networks, IEEE Internet Computing, vo. 2, no. 4, pp , Juy-Aug [4] H. T. Cheng and W. Zhuang, Pareto optima resource management for wireess mesh networks with QoS assurance: joint node custering and subcarrier aocation, IEEE Trans. Wireess Commun., vo. 8, no. 3, pp , Mar [5] R. U. Nabar, H. Bcskei, and F. W. 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Whitehouse, A. Woo, F. Jiang, J. Poastre, and D. Cuer, Expoiting the capture effect for coision detection and recovery, IEEE EmNetS-II, pp , May [24] G. Owen, Game Theory, 3rd Ed. Academic Press, 200. [25] H. T. Cheng and W. Zhuang, ve packet-eve resource aocation with effective QoS provisioning for wireess mesh networks, IEEE Trans. Wireess Commun., vo. 8, no. 2, pp , Feb [26] IEEE Broadband Wireess Access Working Group, Channe modes for fixed wireess appications, [Onine]. Avaiabe: Ho Ting Cheng (S 05) received the BEng and MPhi degrees in Information Engineering from The Chinese University of Hong Kong in 2003 and 2005, respectivey. He is a research assistant and currenty working toward his Ph.D. degree at the Department of Eectrica and Computer Engineering, University of Wateroo, Canada. His research interests incude distributed resource aocation, quaity-of-service provisioning, medium access contro, scheduing, ca admission contro, wireess mesh networking, and communication theory. Weihua Zhuang (M 93-SM 0-F 08) received the B.Sc. and M.Sc. degrees from Daian Maritime University, China, and the Ph.D. degree from the University of New Brunswick, Canada, a in eectrica engineering. Since October 993 she has been a facuty member in the Department of Eectrica and Computer Engineering, University of Wateroo, where she is currenty a professor. Her current research focuses on resource aocation and QoS provisioning in wireess networks She is a coauthor of the textbook Wireess Communications and Networking, and a co-recipient of a Best Paper Award from IEEE ICC 2007, a Best Student Paper Award from IEEE WCNC 2007, and the Best Paper Awards from QShine 2007 and She received the Outstanding Performance Award in 2005, 2006, and 2008 from the University of Wateroo for outstanding achievements in teaching, research, and service, and the Premier s Research Exceence Award in 200 from the Ontario Government for demonstrated exceence of scientific and academic contributions. Dr. Zhuang is the Editor-in-Chief of IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, and an Editor of IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, EURASIP JOURNAL ON WIRELESS COMMUNICATIONS AND NETWORKING,andINTERNATIONAL JOURNAL OF SENSOR NETWORKS. She is a Feow of IEEE and an IEEE Communications Society Distinguished Lecturer.