Cooperative Coverage Extension for Relay-Union Networks

Transcription

1 1.119/TPDS , IEEE Transations on Parallel and Distributed Systems IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 1 Cooperative Coverage Extension for Relay-Union Networks Yong Cui, Xiao Ma, Xiuzhen Cheng, Minming Li, Jianghuan Liu, Tianze Ma, Yihua Guo, and Biao Chen Abstrat Multi-hop overage extension an be utilized as a feasible approah to failitating unovered users to get Internet servie in publi area WLANs. In this paper we introdue a Relay-Union Network (RUN), whih refers to a publi area WLAN in whih users often wander in the same area and have the ability to provide data forwarding servies for others. We develop a RUN framework to model the ost of providing forwarding servies and the utility obtained by gaining servies. The objetive of the RUN is to maximize the total Quality of Cooperation (QoC) of users among RUN. Two optimal bandwidth alloation shemes are proposed for both free and dynami bandwidth demand models. To make our sheme more pragmati, we then onsider a more pratial senario in whih the bandwidth apaity of the relays and the minimum demand of the lients are bounded. We prove that the problems under both the single relay and the multi-relay senario are NP-hard. Three heuristi algorithms are proposed to deal with bandwidth alloation and relay-lient assoiation. We also propose a distributed signaling protool and divide the entralized MRMC algorithm into three distributed ones to better adapt for real network environment. Finally, extensive simulations demonstrate that our RUN framework an signifiantly improve the effiieny of ooperation in the long term. Index Terms Coverage extension, relay-union network, bandwidth alloation, assoiation, ooperative. 1 INTRODUCTION APubli area WLAN often has a relatively fixed user group suh as students of a lassroom building. Sometimes a user does not have Internet aess due to limited AP overage, poor signal strength, or authentiation failure. Multi-hop aess is a feasible approah to failitate these users to employ other online users as relays for data forwarding [1] [5]. In this paper, we propose a Relay-Union Network (RUN), whih ontains a union of lients that often wander in the same publi area and sometimes provide data forwarding for others. In a RUN, at any moment, a fration of the union members with diret AP onnetions play the role of relays and offer forwarding servies to others. In RUN, servie demands of the lients may be different from eah other and vary from time to time. To haraterize the satisfation degree of a lient on the obtained forwarding servie, we employ a utility funtion as a metri in our model. Sine providing forwarding servies for others may have negative impat on the relay s own Yong Cui, Xiao Ma, Tianze Ma and Yihua Guo are with the Department of Computer Siene and Tehnology, Tsinghua University, Beijing, P. R. China. uiyong@tsinghua.edu.n (Yong Cui), max11@mails.tsinghua.edu.n (Xiao Ma), mtz4@mails.tsinghua.edu.n (Tianze Ma), guo-yh8@mails.tsinghua.edu.n (Yihua Guo). Xiuzhen Cheng is with the Department of Computer Siene, The George Washington University, Washington, DC 252, USA, and College of Computer and Information Sienes, King Saud University, Riyadh, Saudi Arabia. heng@gwu.edu. Minming Li is with the Department of Computer Siene, City University of Hong Kong. minming.li@ityu.edu.hk. Jianghuan Liu is with the Shool of Computing Siene at Simon Fraser University, British Columbia, Canada. jliu@s.sfu.a. Biao Chen is with the Department of Computer Information Siene, University of Maau, Maau, P. R. China. bhen@uma.mo. This work is supported by the 973 Program of China (29CB3253,211CB328), the NSF of China ( ), the NSF of the United States (CNS ), and the NPST program by King Saud University (Projet No. 1-INF1184-2). performane (e.g. battery power, CPU resoure), we also onsider a relay ost funtion in our RUN framework. As all the members in a RUN take the role of relay from time to time, all users mutually benefit from eah other in the long term. In this paper, we first propose a Quality of Cooperation (QoC) model that inludes a lient utility funtion and a relay ost funtion, based on whih the QoC of a relay and a lient an be well defined. Next we point out that the utoff bandwidth alloation is a ruial issue in our strategy through analyzing the relationship between the bandwidth and the QoC. Optimal bandwidth alloation shemes are then proposed for two bandwidth demand models. Following that we onsider a more pratial senario in whih the relay s bandwidth apaity and the lient s minimum bandwidth demand are respetively upper and lower bounded. We then propose three heuristi algorithms, with two targeting on Single- Relay Multi-Client (SRMC) for bandwidth alloation, and the other one targeting on Multi-Relay Multi-Client (MRMC) for both lient-relay assoiation and bandwidth alloation. Finally we introdue a distributed dynami mehanism of MRMC (D 2 MRMC), whih onsists of a distributed signaling protool and several distributed algorithms to handle the dynami senarios of MRMC. Finally, extensive simulation study is performed, and the results indiate that our framework an signifiantly improve the total QoC of RUN. The rest of the paper is organized as follows. Setion 2 presents the related researh. Setion 3 introdues the QoC model and the related definitions. The solutions for single-relay multi-lient and multi-relay multi-lient are investigated in Setion 4 and 5, respetively. The distributed MRMC mehanism and the omparison between MRMC and D 2 MRMC are proposed in Setion 6. The simulation study is inluded in Setion 7. Finally in () 213 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See

2 1.119/TPDS , IEEE Transations on Parallel and Distributed Systems IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2 Setion 8 we onlude the paper. 2 RELATED WORK There has been an inreasing interest in enhaning the overage and onnetivity of wireless networks [1], [2], [5] [9]. Multihop-relaying is usually employed to enhane the transmission performane of primary users (PUs) by seleting seondary users (SUs) as relays in Cognitive Radio Networks (CRNs) [1], [2]. Wang et al. [5] investigate a onnetivity-enhaning mehanism for large-sale wireless sensor and ad ho networks by introduing k-hop lustering. Syue et al. [7] investigate radio overage extension in physial layer, and fous on finding the impat of physial-layer ooperation on the network-layer routing design. Guizani et al. [8] leverage a ross-layer approah to enourage potential relaying nodes to provide servies for others. These existing mehanisms not only extend the wireless overage area, but also aim to enhane the QoS by inreasing the average throughput and dereasing the delay. However, the ost of relays aused by providing servies is not perfetly onsidered in their solutions. To better utilize the forwarding apability of eah node in RUN, resoure (e.g. bandwidth, wireless hannel) alloation and relay-lient assoiation are two key issues that need to be investigated. Several works have been proposed to maximize the revenue of ISP and address the ongestion ontrol issue in infrastruture networks. Non-ompetitive priing has been extensively employed as a tool to handle resoure alloation in the literature ( [1] [12]). Hande et al. [1], as a representative ontribution, present an ISP revenue maximization and ongestion management sheme for the appropriate hoie of the aess prie for broadband servies offered by a monopoly ISP. However, the existing priing-based solutions mainly fous on maximizing servie providers revenue in infrastruture networks without onsidering end users profit and somehow fail to apture the full harateristis of RUN (e.g. role exhange). In this paper, We try to explore an appliable solution to guarantee the soial welfare of RUN. On the other hand, relay-lient assoiation is similar to AP assoiation that has been widely studied in reent ten years ( [13] [17]). Referene [13], as one of the representative literature, propose a distributed aess point seletion arhiteture onsidering both throughput and fairness. Dawei Gong et al. [14] explore AP assoiation for 82.11n with heterogeneous lients (82.11a/b/g/n) and onsider the problem as a MAC layer utility maximization problem. The frame aggregation feature of 82.11n is onsidered in their solution to avoid poor lient throughput and overload APs. Different from them, Niholson et al. [16] propose a measurement-based solution named Virgil. It performs fast onnetion and tests on all the available APs to hoose the best one (maximum bandwidth, best signal strength, et.) when servie unavailability ours. In general, the QoS metris employed in these solutions usually lak of onsiderations for various user demands. Serving urgent users in priority may gain more soial welfare from the entire network perspetive. Resoure alloation and relay-lient assoiation for ooperative multi-hop aess in RUN has not been widely investigated yet, whih is the main fous of our paper. 3 MODELS AND DEFINITIONS In our RUN mehanism, the servie that the lient obtains is the most important fator related to QoC maximization. We employ aess bandwidth of a lient as a metri to measure the servie it reeives. Note that in our analysis, we fous on one unit time whenever an amount is involved for simpliity. For instane, the utility funtion of a lient defined in Definition 2 refers to the satisfation degree orresponding to the amount of aess bandwidth it reeives per unit time. Definition 1 (Aess bandwidth of a lient): The aess bandwidth of a lient is defined to be the amount of data transmitted by the lient per unit time. The relationship between the aess bandwidth and the user s satisfation should not be a simple linear funtion. Here we introdue a utility funtion to desribe suh a relationship. Definition 2 (Utility funtion of a lient): The utility funtion of a lient i is defined to be f i (B), where B is the lient s aess bandwidth obtained from its relay and f i (B) is the satisfation degree orresponding to the amount of aess bandwidth B. It reflets the urgeny degree of the lient s servie demand. Assumption 1: The utility funtion of a lient is onave. Assumption 1 an be justified as follows. The derivative f i (B) of the funtion f i (B) is equivalent to the marginal utility (MU) of the aess bandwidth. Aording to the Law of Diminishing Marginal Utility [18], MU dereases with the inrease of the aess bandwidth beause a lient s desire of getting more aess bandwidth does not inrease with eah additional unit of bandwidth aquired. Therefore f i (B) is a dereasing funtion. Thus f i (B) should be onave. Definition 3 (Serving bandwidth of a relay): The serving bandwidth of a relay is defined to be the total amount of bandwidth in bits per seond that the relay utilizes as its forwarding servie. A relay s serving bandwidth is the summation of aess bandwidth of all its lients. Clients in RUN an ahieve more utility by inreasing the relay s serving bandwidth. However, the forwarding servie may have negative impat on the relay s own transmission. Meanwhile, the energy onsumption and CPU utilization may beome heavier. Therefore, a relay pays a ost when providing forwarding servie, whih is formulated by a ost funtion in our model. Definition 4 (Cost funtion of a relay): Denote the ost funtion of a relay r j by g j (B), where B is the relay s serving bandwidth and g j (B) is the orresponding ost () 213 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See

3 1.119/TPDS , IEEE Transations on Parallel and Distributed Systems IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 3 Assumption 2: The ost funtion of a relay is onvex. Assumption 2 an be justified as follows. The derivative g j (B) of the funtion g j (B) is equivalent to the marginal ost (MC) of the serving bandwidth. MC is inreasing with the inrease of the relay s serving bandwidth. The reason is that when the oupany rates of CPU and bandwidth beome higher, the harm to the performane of the relay aused by forwarding for others beomes heavier. Thereforeg j (B) is an inreasing funtion. Thus g j (B) is assumed to be onvex. Definition 5 (QoC of RUN): The QoC (Quality of Cooperation) Q of a RUN is the metri of the ooperation effiieny among users in RUN and is alulated by the summation of all lients utility minus all relays ost. An example of utility funtion f i (B), ost funtion g j (B) and QoC funtion Q r (B) in a single-relay singlelient senario is illustrated in Fig. 1. QoC fi(b): utility B Cutoff bandwidth B n gj(b): ost fi(b)-gj(b): QoC Bandwidth Fig. 1. An example of utility, ost and QoC funtions. 4 SINGLE-RELAY MULTI-CLIENT We first onsider a relatively simple senario in whih there is only one relay r j serving N lients in RUN. The N lients are denoted by C = { 1, 2,..., N }. Fig. 1 illustrates a simpler ase in whih N = 1. It an be observed that the QoC starts to deline when the serving bandwidth exeeds a threshold. Therefore, the relay should limit eah lient s maximum aess bandwidth by a utoff bandwidth. Definition 6 (Client utoff bandwidth): Define the lient utoff bandwidth of a lient i, denoted by B i 1, to be the maximum aess bandwidth it is allowed to use, whih is limited by its relay. Definition 7 (Relay utoff bandwidth Br j ): Define the relay utoff bandwidth of a relay r j, denoted by Br j, to be the summation of its lient utoff bandwidth. A set of lient utoff bandwidth, denoted by {B i} = {B 1,B2,...BN }, should be determined to maximize the total QoC of RUN. However, the QoC annot be solely determined by the serving bandwidth. It also relates to the aess bandwidth of eah lient that is determined by its bandwidth demand. Definition 8 (Bandwidth demand of a lient): Define the bandwidth demand of a lient to be the bandwidth required for its urrent data transmission. Here we define the ritial marginal utility (MU) of a lient i to bef i (B). i Similarly, ritial MC of a relayr j is 1. For bandwidth notations suh as B,B r,b min and B max, index is the supersript, i.e, B i. But for funtion notations suh as f,g,h,q, index is the subsript, i.e., f i. defined to be g j (Br j ). In the following we disuss how to evaluate the utoff bandwidth of eah lient under different bandwidth demand models. 4.1 Free Bandwidth Demand Model We first onsider an ideal bandwidth demand model, in whih the bandwidth demand of a lient has no onstraint. Therefore, the relay an evaluate an optimal lient utoff bandwidth alloation to maximize the RUN s QoC without onsidering the bandwidth demands of its lients. The total QoC Q of the RUN an be alulated as follows: N Q = f i (B) g(b i r ), (1) i=1 where B r = N i=1 Bi, whih is the serving bandwidth of the relay. Then the optimal lient utoff bandwidth alloation {B i} = {B,B1,...,BN } to maximize the RUN s QoC should be the solution to the following problem. maxq s.t. B i {B i} (2) We have the following theorem: Theorem 1: Under the free bandwidth demand model and the optimal lient utoff bandwidth alloation, the ritial MU of eah lient equals the ritial MC of the relay. It an be formulated by: df i (B i ) db i = dg(b r) db r,1 i N s.t. B i (3) The proof an be found in the supplementary file 2. To make the theorem more omprehensive, we give an easy-to-understand example in setion 4.1 of the supplementary file. In the following part, we utilize this theorem to ompute an optimal bandwidth alloation under free bandwidth demand model. 4.2 Dynami Bandwidth Demand Model We try to onsider a more pratial bandwidth demand model in this setion. In realisti network environments, the bandwidth demand of a lient may vary from time to time. For a lient i, assume that its bandwidth demand is a ontinuous random variable whih follows a ertain distribution with a probability density funtion q i (B) (an be derived aordingly to the historial bandwidth demand). The lient informs the relay of its q i (B), inluding the funtion type and the value of eah oeffiient (the message an be appended to the assoiation request). The relay replies with the lient utoff bandwidthb i. If the lient s bandwidth demand exeeds B i during its data transmission (the probability equals + q B i i (B)dB), its aess bandwidth will be restrited to the lient utoff bandwidth to guarantee soial welfare. 2. For all the theorems in the paper, the detailed proofs an be found in our supplementary file () 213 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See

4 1.119/TPDS , IEEE Transations on Parallel and Distributed Systems IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 4 Under this bandwidth demand model, we evaluate the total QoC from the perspetive of mathematial expetations. The expetation of the utility of a lient i is B i f i (B)q i (B)dB + + B f i i (B)q i i (B)dB. Thus the expetation of the total utility of N lients an be expressed by (4). E utility = N i=1 ( B i B i f i (B)q i (B)dB + + f i (B i )q i (B)dB) (4) Meanwhile (5) gives the expetation of the relay s serving bandwidth. E bs = N i=1 ( B i Bq i (B)dB + + B i B i q i (B)dB) (5) Thus the expetation of the relay s total ost an be evaluated by (6). E ost = g(e bs ) (6) That is to say, the expetation of total QoC is E Q = E utility E ost. (7) Then an optimal lient utoff bandwidth alloation that an maximize the expetation of the total QoC under the dynami bandwidth demand model should be the solution to the following problem. max {B i } E Q s.t. B i (8) The definition of the relay s ritial MC should also be extended from the perspetive of mathematial expetations, i.e., g (E bs ) instead of g (B r ). We have: Theorem 2: Under the dynami bandwidth demand model and the optimal lient utoff bandwidth alloation, the ritial MU of every lient equals the ritial MC of the relay. Theorem 2 an be formulated by: df i (B i ) db i = dg(e bs) de bs,1 i N s.t. B i (9) It an be utilized to ompute an optimal utoff bandwidth alloation under dynami bandwidth demand model from the mathematial expetation perspetive. 4.3 Capaity Limitation and Minimum Bandwidth Demand Model The above investigation implies an assumption that the apaity of a relay is infinite and a lient an aept an infinitesimally small bandwidth. In reality, a relay s apaity is always upper-bounded and a lient s bandwidth demand is always lower-bounded. Therefore a relay an not afford to serve an exessive number of lients and a lient an not aept a relay that ould not supply a minimum bandwidth. Denote by B max the maximum serving bandwidth of the relay and by B i min the minimum bandwidth demand of lient i. These two new restritions make our model more pratial. The problem of optimal lient utoff bandwidth alloation an be formulated by: max {B i } Q s.t. B i B i min and B r B max. (1) We have the following theorem, Theorem 3: Under the single-relay multi-lient senario with the apaity limitation and minimum bandwidth demand model, the bandwidth alloation problem defined by (1) is NP-hard. We prove the theorem by a redution from the wellknown subset sum problem [19] to the above problem. The proof an be found in the supplementary file. We design a heuristi algorithm named SRMC-ES (Single-Relay Multi-Client based on Equation Solving) to ompute a feasible utoff bandwidth alloation. Algorithm 1: SRMC-ES Input: B max, C = { 1, 2,..., N }, {Bmin 1,B2 min,...,bn min }, r, {f 1,f 2,...,f N }, g Output: {B} i 1 B r Infinity 2 while B r > B max do // Optimal alloation 3 {B} i BandAllo(r,C) // Ensure minimum bandwidth demand of every lient 4 for i = 1;i N;i++ do 5 if B i < Bi min then 6 B i Bmin i 7 end 8 end 9 B r N i=1 Bi 1 if B r B max then 11 break 12 end // Selet the lient index with lowest QoC ontribution 13 for eah i in C do 14 δ i ComputeDelta( i ) 15 end 16 index arg min i δ i, i C // Stop serving index 17 B r (B r B index ) 18 B index 19 C (C { index }) 2 end 21 return{b i} The design motivation of Alg. 1 is stated as follows. We first get the optimal bandwidth alloation {B i } without the apaity and demand limitation by solving equations obtained from (3) or (9) (BandAllo(r, C)). If the relay an not afford to serve all the lients while keeping the RUN s QoC as high as possible, the lients with relatively low ontributions to the RUN s QoC will not be served. Here we introdue a metri δ i to quantify i s ontribution to the RUN s QoC. δ i = f i (B i ) (g(b r) g(b r B i )), (11) where g(b r B i ) is part of the relay s ost aused by the lients other than i. Thus δ i stands for i s portion in the RUN s QoC. We denote the time omplexity of BandAllo() by T B (N), whih depends on the approah adopted to solving (3) or (9). BandAllo() is alled at most N times () 213 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See

5 1.119/TPDS , IEEE Transations on Parallel and Distributed Systems IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 5 QoC k 1... kp k 3 k 2 B i min B B max fi(b): utility of lient i g(b): ost of relay Bandwidth (a) Pieewise linearized utility and ost funtions B 1 min B 1 min+ B Client 1... Root B 2 min... B n min B 2 min+ B.... B n min+ B Client 2... Bmax Bmax Bmax Client n (b) Tree-knapsak problem to maximize total utility Fig. 2. Approximation for the SRMC problem. in the main loop of SRMC-ES. Thus the time omplexity of SRMC-ES is T(SRMC-ES) = O(N T B (N)). 4.4 An Approximation Solution for Bandwidth Bounded Model The major ontribution to the running time of Alg. 1 is the time used to solve (3) or (9), i.e. T B (N). It highly relies on the exat forms of utility and ost funtions, as well as the algorithm employed to solve the differential equations. To redue the possible unertainty and instability, we further propose a dynami-programmingbased approximation algorithm that does not need to solve (3) or (9), while ahieving an approximate solution at an aeptable approximation degree. Algorithm 2: SRMC-DP Input: B max, C = { 1, 2,..., N }, {Bmin 1,B2 min,...,bn min }, r, {f 1,f 2,...,f N }, g Output: {B i}, Q 1 B min min i Bmin i 2 Q 3 {B} i 4 for B r = B min ;B r B max;b r = B r + B do // Initialization 5 dp(,j) =, j 6 for i = 1;i N;i++ do 7 for j = Bmin i ;j Br;j = j + B do 8 dp(i,j) = 9 end 1 end // Dynami Programming 11 for i = 1;i N;i++ do 12 for j = Bmin i ;j Br;j = j + B do 13 for k = Bmin i ;k j;k = k + B do 14 dp(i,j) = max k {dp(i 1,j k)+f i (k),dp(i 1,j),dp(i,j)} 15 Reord the k that maximizes dp as k i 16 end 17 end 18 end 19 U max = dp(n,b r) 2 Update {B i } aording to the reorded {k i } 21 if Q < (U max g( N i=1 Bi )) then 22 Update Q and {B i} aordingly 23 end 24 end 25 return {B} i and Q As shown in Fig. 2(a), we leverage pieewise linear funtions to approximate the utility of lients and the ost of relay. Sine the minimum bandwidth demand and the apaity of the relay are the lower bound and upper bound of lient i s utoff bandwidth, respetively, we only disretize the utility and ost funtion of eah lient i from Bmin i to B max. With pieewise granularity being B, the utoff bandwidth of lient i an only be hosen from the set {,Bmin i,bi min + B,...,B max}. The basi idea of the heuristi algorithm is depited as follows. We first maximize the total utility of all lients ( N i=1 f i(b)) with the bandwidth apaity of the relay being B max. Unlike the situation in the NP-hard proof above, the QoC of the RUN will not always be maximized even if the apaity of the relay is used up. Providing more serving bandwidth may ause negative QoC inome with the influene of the ost of the relay. Therefore, we repeat the proess of maximizing the total utility under different relay apaities (B min,b min + B,...,B max ), where B min is the minimum bandwidth demand among the N lients. Then we hoose the maximal QoC from the results obtained under different apaities. First, we propose a dynami programming based algorithm to address the utility maximization problem. As shown in Fig. 2(b), under speifi bandwidth apaity, the problem an be regarded as a 1 knapsak problem on a rooted tree T suh that if a node is seleted into a knapsak, then all nodes on the path from the seleted node to the root node must also be seleted into the knapsak. Here the verties in the tree (the items of knapsak problem) represent the different utoff bandwidth, the prie of eah item is the utility, the N branhes represent N lients, and the weight apaity of the knapsak is the bandwidth apaity of the relay. The Tree-Knapsak Problem (TKP) has been proved to be weakly NP-omplete [2]. In this paper, we employ dynami programming to address the problem in pseudo-polynomial time. In the dynami programming proess of Alg. 2, we assume the total utility in state (i,j) to be dp(i,j), where i represents lient 1 to lient i, and j represents the remaining bandwidth apaity of the relay. The parameter k in lines is the bandwidth alloated to lient i. Note that lient i may not be served by the relay, in whih ase the sub-state is dp(i 1,j). The time omplexity of the dynami programming proess (lines 11-18) is O(NBmax). 2 The proess is invoked under different bandwidth apaities, hene the running time of Alg. 2 is O(NBmax 3 ), whih is pseudopolynomial. 5 MULTI-RELAY MULTI-CLIENT In this setion we study the senario of multiple relays and multiple lients in RUN. The following two issues need to be investigated: how to assoiate lients with relays and how to alloate lient utoff bandwidth. Definition 9 (Cluster): A luster i is defined to be the node set onsisting of relay i and all the lients it serves. The serving relationship may vary from time to time. Assume that there are K relays denoted by R = {r 1,r 2,...,r K }. Define by X = (x ij ) a binary assoiation () 213 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See

6 1.119/TPDS , IEEE Transations on Parallel and Distributed Systems IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 6 matrix with x ij = 1 if and only if r i serves j. Let B = (b ij ) be a lient utoff bandwidth matrix with b ij being the utoff bandwidth assigned to j by r i. If the free bandwidth demand model is utilized, the QoC Q i of eah luster i an be evaluated by Q i = N N x ij f j (b ij ) g i ( x ij b ij ) (12) j=1 j=1 Then the lient-relay assoiation and the lient utoff bandwidth alloation issue an be formulated as follows. s.t. max { K Q i } X,B i=1 K x ij = 1, i=1 N x ij b ij Bmax i, j=1 K x ij b ij B j min, i=1 1 j N 1 i K 1 j N x ij {,1}, 1 i K and 1 j N (13) In (13), the assoiation matrix X and the lient utoff bandwidth matrix B are the variables to be omputed. The objetive funtion is to maximize the summation of all lusters QoC. The first onstraint indiates that every lient an get forwarding servie from one relay; the seond onstraint indiates that the maximum serving bandwidth of the relay r i an not exeed its apaity limitation Bmax; i while the third onstraint indiates that the reeived bandwidth of a lient j should not be smaller than its minimum bandwidth demand B j min. We have the following theorem, Theorem 4: The lient-relay assoiation and the lient utoff bandwidth alloation issue under MRMC is NPhard. The proof an be found in the supplementary file. We propose a greedy algorithm Alg. 3 to ompute a feasible solution for (13). We first examine all possible relay-lient pairs to find out the one with the highest ontribution to the network QoC. Then the lient is assoiated with that relay. Here we use δ ij defined in (11) as a metri to quantify the QoC ontribution of the lient 3. This proess is repeated until all lients are assoiated with relays or all relays are at full apaity. The while-loop of MRMC is exeuted at most N times, assuming N > K. SRMC-ES is alled N K times during the first iteration and at most N times in eah of the other N 1 iterations. Thus the time omplexity of MRMC is T(MRMC) = O(N(N 1) + NK) O(N)T B (N) = O(N 2 (N +K)T B (N)). 3. Note that the algorithm employed to ompute δ ij and {B i } an also be replaed by SRMC-DP (line 7) Algorithm 3: MRMC Input: C = { 1, 2,..., N }, R = {r 1,r 2,...,r K }, {f 1,f 2,...,f N }, {g 1,g 2,...,g K }, {Bmax 1,B2 max,...,bk max }, {Bmin 1,B2 min,...,bn min } Output: X = (x ij ), B = (b ij ) // Define C ri as the set of lients urrently served by r i 1 C ri Φ,i = 1,2,...,K 2 index r,index 3 while C! = Φ and R! = Φ do // Update δ and the bandwidth for eah (,r) pair 4 for eah r i in R do // If i index r, the orresponding δ and the bandwidth alloation does not hange ompared to the last while-loop 5 if index r = or index r = i then 6 for eah j in C do {j } 7 {δ ij,b Cr i } SRMC-ES(r i,c ri {j }, j ) 8 end 9 end 1 end // Selet ( index,r indexr ) with the highest δ 11 {index r,index } arg max i,j δ ij, r i R, j C // Assoiate index with r indexr 12 x indexr,index 1 13 C C { index } // Update C rindexr 14 C rindexr C rindexr {index } 15 Br indexr // Update the orresponding bandwidth alloation 16 for eah k C rindexr do 17 b indexr,k B k 18 Br indexr Br indexr +b indexr,k 19 end // A relay at full apaity should not serve any more lients 2 if Br indexr Bmax indexr then 21 R R {r indexr } 22 end 23 end 24 return{x, B} 6 DISTRIBUTED DYNAMIC MECHANISM OF M- RMC The MRMC algorithm presented in Setion 5 is a entralized one, whih has two limitations. First, the omputation proess should be exeuted on a ertain entralized ontrol node. The overhead of gathering information from the whole network might be quite high and sometimes impratial. Seond, it is diffiult to handle the dynami arrivals and departures of the members in RUN, whih requires the exeution of the algorithm to orrespondingly update the assoiation and bandwidth alloation of the whole network whenever there is a RUN member hange. Therefore, in this setion we propose a distributed dynami mehanism D 2 MRMC for the MRMC senario. D 2 MRMC onsists of a protool that defines the signaling proess between lients and relays, and several modified algorithms to determine relay-lient assoiation and bandwidth alloation. As shown in Fig. 3, we extend the standard AP-STA assoiation protool [21] to handle lient-relay assoiation. The standard beaon frame defined in is extended by appending an additional Cooperation Pa () 213 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See

7 1.119/TPDS , IEEE Transations on Parallel and Distributed Systems IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 7 rameter Set after the IBSS Parameter Set. The Cooperation Parameter Set ontains the ost funtion and the apaity limitation of the relay, and the utility funtions, the minimum bandwidth demands, et.. When a lient moves out of the overage range of any AP and seeks for forwarding servie, it an reeive a list of available relays by listening to their beaon frames. The lient determines whih relay is the most appropriate one, sends an Assoiation Request frame and gets the Assoiation Response frame to/from the relay to omplete the assoiation proedure. Relay Beaon Frame with Cooperation Parameter Set Assoiation Request Frame with Bandwidth Alloation Vetor Assoiation Response Frame with Cutoff Bandwidth Client Algorithm 5: D 2 MRMC: Client Arrival Input: r i, C ri, Br i, Bi max, BCr i, newly arrived lient j Output: The updated C ri and B Cr i 1 if Br i < Bmax i then 2 broadast beaon frames with Cooperation Parameter Set 3 end 4 if j launhes a onnetion then 5 C ri C ri {j } 6 B i r B Cr i // Capaity release 7 if B i r >= B i max then 8 for eah k in C ri do 9 δ k ComputeDelta( k ) 1 end 11 index arg min k δ k, k C ri 12 C ri C ri { index } 13 B Cr i SRMC-ES(r i,c ri ) 14 end 15 for eah lient k C ri do 16 update B k aording to BCr i 17 end 18 end Fig. 3. The signaling proess of lient-relay assoiation We divide our MRMC algorithm into three omponents to meet the requirement of the distributed senario. Alg. 4 is exeuted on eah lient to determine its expeted relay and the lient utoff bandwidth alloated by that relay when it needs the forwarding servie. Alg. 5 and Alg. 6 are exeuted on eah relay, with the former one handling the arrival of lients, and the latter the departure. If a newly arriving lient has a diret aess to an AP, it an work as a relay by broadasting the beaon frames to attrat lients; when it leaves the network, the assoiated lients need to all Alg. 4 to searh for a new relay. Algorithm 4: D 2 MRMC: Client Aess Input: j, R = {r 1,r 2,...,r K }, Cooperation Parameter Set for eah r i // output is the index of the relay that lient j hoose to assoiate with Output: index 1 if j needs forwarding servie but has no relay then 2 for eah r i R do 3 {δ i,b Cr {j } i } SRMC-ES(r i,c ri {j }, j ) 4 end 5 index arg max i δ i, r i {r i } 6 j onnets to r index 7 end Alg. 4 presents the aess proedure exeuted on eah lient j. For eah relay r i, the lient j omputes its QoC ontribution and the orresponding bandwidth alloation based on the Cooperation Parameter Set (line 3). The lient selets the relay whih ontributes the most to the network QoC aording to δ ij defined in (11). Alg. 5 details the proedure of handling the arrival of a lient at eah relay r i. If a lient deides to onnet to r i, r i gets the bandwidth alloation vetor B Cr i from the lient and updates the lient utoff bandwidth of eah lient it urrently serves by sending the Assoiation Response frame. If the apaity of r i is full, it would rejet the assoiation request of any newomers, and stop its broadast of the beaon frames. Capaity release (lines 7-14) is an option to inrease the QoC of the network if a newly arriving lient an bring more QoC than any existing one(s). To alleviate QoC redution aused by the lients that ontribute less and ome earlier, we need to release the apaity of the relay by kiking out these lients (lines 11-13). The lients ould all Alg. 4 again to selet a new relay. Algorithm 6: D 2 MRMC: Client Departure Input: r i, j, C ri Output: The updated C ri and B Cr i 1 if j was served by r i and it leaves the overage of r i then 2 C ri (C ri { j }) 3 B Cr i SRMC-ES(r i,c ri ) 4 for eah lient k C ri do 5 update B k aording to BCr i 6 end 7 end When a lient moves out of the overage area of its relay, the relay should detet this departure event and all Alg. 6 to re-alulate the lient utoff bandwidth for other serving lients. Then it announes the updated bandwidth alloation to its lients through the Assoiation Response frame. This lient-departure handling proedure makes D 2 MRMC more flexible espeially when users frequently move in and out. 7 EVALUATIONS In this setion we evaluate our RUN framework by simulation study. We first onsider the ase of a single relay and multiple lients to evaluate the QoC inome under the optimal alloation, SRMC-ES, and SRMC-DP () 213 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See

8 1.119/TPDS , IEEE Transations on Parallel and Distributed Systems IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 8 QoC of RUN Optimal Average Fixed Number of lients (a) Free model with polynomial utility/ost funtion QoC expetations SRMC ES SRMC DP Average Fixed Number of lients () Bandwidth bounded model Fig. 4. SRMC performane QoC expetations Optimal Average Fixed Number of lients (b) Dynami model with uniform distribution Average Kik Rate Total Client #1 Client #2 Client #3 Client # Number of Clients (d) Average proportions of kiked lients of SRMC-ES Then we evaluate the performane of our MRMC algorithm for the ase of multi-relay multi-lient. Finally, the D 2 MRMC mehanism is implemented and evaluated in the simulated RUN to onsider the distributed senario, demonstrating that the signaling proess between lients and relays works well while ahieving high QoC in the long term. 7.1 SRMC Performane We onsider the ase of single-relay multi-lient first. The results for 1 to 7 lients are reported in Fig. 4(a), 4(b) and 4(). The legend Optimal in Fig. 4(a) and Fig. 4(b) stands for the optimal utoff bandwidth alloation obtained from Theorems 1 and 2, Average and Fixed in Fig. 4() are listed for omparisons, with Average indiating that the relay s serving bandwidth is equally alloated to all lients and Fixed implying that the utoff bandwidth of eah lient is fixed to 2Mbps. The free bandwidth demand model is employed in Fig. 4(a). The utility funtions for the seven lients (from lient #1 to #7) are defined by 2 B,3.5 B,5 B,...,11 B (step 1.5) respetively, while the ost funtion of the relay is.2b 2. It is lear that our alloation sheme leads to a higher network QoC than the other two shemes. The result of the dynami bandwidth demand model is shown in Fig. 4(b). Eah data point is an average over 5 runs to redue randomness. The utility funtions are the same as in Fig. 4(a), and the ost funtion is.4b 2. The bandwidth demand of a lient follows a uniform distribution on [.5, 2.5] Mbps. It an be observed that our sheme still ahieves the maximum QoC, while Fixed performs bad ompared with the other two shemes. The result of the bandwidth bounded model is shown in Fig. 4(), in whih SRMC-ES and SRMC-DP are e- valuated. Eah data point is an average over 5 runs to redue randomness. The bandwidth apaity of the relay is fixed to 7Mbps, while the minimum bandwidth demand of eah lient follows a uniform distribution on [.5, 2.5] Mbps. The utility funtions for the seven lients and the ost funtion for the relay are the same as in Fig. 4(b). Note that our SRMC-DP ahieves a higher QoC ompared to the other three shemes. However, sine the running time of SRMC-DP highly relies on the value of B max and the bandwidth granularity ( B), it may take an unaeptable amount of time on bandwidth alloation ompared to SRMC-ES under speifi irumstanes. During the simulation of SRMC-ES, some of the lients may be kiked out from obtaining relay s servie beause they ontribute relatively little QoC to the network. We also alulate the average proportions of the kiked lients in Fig. 4(d). With the inrease of the total number of lients, the proportion of the relay s serving lients (marked as Total in the figure) beomes smaller. This is reasonable sine relay s apaity is upper-bounded, and the relay has to stop serving these lients to ahieve more utility from the lients with larger ontributions. The statistis of the kik rate of lient #1,2,3,4 also proves it. With the inrease of the total number of lients, the lients with less ontributions (e.g. 2 B for Client #1) will be kiked out with a higher priority. 7.2 MRMC Performane Fig. 5(a) and 5(b) depit the simulation results of MRMC in omparison with Random-Average and Random- Fixed shemes. Random implies that the lients are randomly assoiated with relays. Average implies that the relays alloate its bandwidth apaity to all lients equally, and Fixed implies that the relays alloate fixed bandwidth to eah lient until their bandwidth apaity is used up. The utility funtions of the lients are defined as B,3 B,5 B,...,23 B (step 2) while the ost funtions of the relays are.1b 2,.15B 2,.2B 2,...,.35B 2 (step.5). The bandwidth apaities of the relays follow a uniform distribution on [6,14] Mbps, while the minimum bandwidth demands of the lients follow a uniform distribution on [.5,2.5] Mbps. Fig. 5(a) reports the total QoC under a various number of lients while the number of the relays is 4. Fig. 5(b) shows the result under a various number of relays while the number of the lients is fixed to 8. The result of MRMC is an average over 5 runs while those of Random-Average and Random-Fixed are over 1 runs to redue randomness. It is obvious that MRMC possesses an apparent advantage over the other two shemes. Random-Average has very poor performane when the number of lients is small or the number of relays is large. This is beause eah relay serves few lients in these two irumstanes, and the bandwidth alloated to eah lient may be quite high, whih may ause pretty high relay ost. Next, a small publi area WLAN is simulated in whih 3 users loate in the area and form a RUN (note that here node arrival and departure are not onsidered) () 213 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See

9 1.119/TPDS , IEEE Transations on Parallel and Distributed Systems IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 9 QoC of RUN Average bandwidth(mbps) MRMC Random Fixed Random Average 1 3/4 6/4 9/4 12/4 15/4 Number of lients/number of relays (a) Number of lients varies MRMC Random Average Random Fixed No Run bandwidth ost Proportion of relays () Average bandwidth Relay ost Fig. 5. MRMC performane QoC of RUN Data amount(mb) MRMC Random Fixed Random Average 5 8/2 8/3 8/4 8/5 8/6 Number of lients/number of relays (b) Number of relays varies Average data Average servie Proportion of relays (d) Average data and servie On eah day, these users are randomly divided into 4-8 groups around different APs (i.e. eah group stands for the overage area of one AP). Users of eah group are then randomly divided into relays and lients, and one of them is hosen as the deision node. The proportion of relays in eah group varies from 1% to 6%. An operation of 3 days is simulated. The entralized MRMC algorithm is exeuted on the deision node of eah group to ompute the assoiation and bandwidth alloation. The utility funtions of the lients are defined as B,3 B,...,23 B (step 2) while the ost funtions of the relays are.1b 2,.15B 2,.2B 2,...,.35B 2 (step.5). The bandwidth apaities of the relays follow a uniform distribution on [6,14] Mbps, while the minimum bandwidth demands of the lients follow a uniform distribution on [.5,2.5] Mbps. The simulation results are shown in Fig. 5() and 5(d). We alulate the average aess bandwidth of all users (shown as bar graph) and the ost of all relays (shown as broken line graph) over the 3-day period in Fig. 5(). It an be observed that the average bandwidth is inreased by 4%-9% with our MRMC algorithm ompared with No RUN, whih demonstrates that the users have more hanes to get online by multihop aess and the network QoC is improved. When the proportion of relays is lower, the inrease of the average bandwidth under the RUN mehanism is more obvious. It demonstrates that our solution is more suitable for the publi area WLANs with fewer APs and a larger number of users that are far from any AP. Note that the Random-Average sheme ahieves the maximum average bandwidth, it is reasonable sine the bandwidth apaity of eah relay is over used by lients in this sheme. From the figure we ould see that the ost of relays of Random-Average is nearly 3x larger than that of our MRMC algorithm. It proves that our RUN mehanism an ahieve nearly the same average bandwidth while onsidering servie providers ost simultaneously. A user in RUN both transmits its own data and provides forwarding servie for others. We ompare the average amount of data transmitted by relays and lients (inluding relays own data) and the average amount of servie provided by relays during the 3-day period in Fig. 5(d). The differene between the average amount of data transmitted and the average amount of servie provided beomes larger when the proportion of the relays is higher, whih indiates that more users an onnet to APs diretly under this senario. 7.3 D 2 MRMC Performane To validate D 2 MRMC, we simulate a small publi area WLAN in whih 3 users randomly visit a irular area everyday, making up RUN. There only exists one AP in the enter of the area. On eah day, users arrive at and depart from the area with a preset probability p. Eah user has a random distane from the AP, whih determines whether the user has a diret AP aess or has to obtain forwarding servie from relays. The ratio of the AP overage radius to the radius of the whole irular area, whih is designated as overage ratio, varies from.2 to.7. The ommuniation overhead (lateny) between lients and relays is a fixed value. The relays an obtain 7Mbps bandwidth from the AP. A lient an onnet to a relay only when their distane, whih is determined by their random positions, is smaller than a ertain value. The mobility pattern of eah node follows a random distribution, the x,y oordinates of eah node are generated by a rand() funtion. Other parameter settings are the same as those presented in Setion 7.2 for validating MRMC. The simulation results are reported in Fig. 6. We alulate the average aess bandwidth of all users over the 3-day period and report the results in Fig. 6(a). It an be observed that the average bandwidth inreases by 25%-5% with the RUN mehanism using D 2 MRMC ompared with No RUN. When the overage ratio is lower, the inrease of the average bandwidth under the RUN mehanism is more obvious. The Random-Average ahieves larger average bandwidth than D 2 MRMC, but the ost of relays are also very large just as we have depited in Fig. 5(). Fig. 6(b) illustrates the number of users in 4 different user lasses per unit time under 6 different overage ratios. Potential relay refers to the users having diret AP aess, while Potential lient refers to the users staying out of the overage of the AP. Aordingly, Real relay indiates the users who are forwarding data for others, while Real lient stands for the users who are transmitting data through real relays. The number of potential relays per unit time grows and the number of potential lients per unit time dereases with the inrease of the overage ratio. This is beause a user has a larger possibility to beome a relay rather than a real lient if the AP s overage is beoming larger. Real lients are less than potential lients, espeially when the overage () 213 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See

10 1.119/TPDS , IEEE Transations on Parallel and Distributed Systems IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 1 Average bandwidth(mbps) D 2 MRMC Random Average Random Fixed No RUN Ratios of AP overage radius (a) Average bandwidth of 3 users Number per unit time Potential Relay Real Relay Potential Client Real Client Ratios of AP overage radius (b) Average user number in different user lasses Data amount(mb) Average data exhange Real relay Real lient Day () The average amount of data exhanged and the number of real relays & real lients in 3 days Number Fig. 6. D 2 MRMC simulation on RUN in 3 days. ratio is small. This is reasonable beause the number of potential relays is small so that some lients are even unable to aess to any relay. When the overage ratio is not too small, this problem rarely happens beause the overage range of all relays an possibly over the whole irular area. We also illustrate the average amount of exhanged data between relays and lients and the total numbers of real relays and real lients for the 3-day period in Fig. 6(). We alulate the average result over 1 simulation runs. The overage ratio of eah run is set to.4. We notie that the total amount of data exhanged has a positive orrelation with the number of real relays and lients, in partiular the number of real relays. The reason is that the number of real relays indiates how many users are forwarding data for others, whih determines the amount of data exhanged in the network. 8 CONCLUSION This paper proposes a ooperative overage extension mehanism in Relay-Union Networks. By investigating the relationship among bandwidth, ost, and utility, we present a QoC model and formulate the maximization of network s QoC as an optimal utoff bandwidth alloation problem. We derive the solution to the problem under two different bandwidth demand models. We then extend the problem by taking eah relay s apaity limitation and eah lient s minimum bandwidth demand into aount. We design SRMC-ES and SRMC-DP to evaluate a feasible bandwidth alloation for the singlerelay multi-lient senario and the MRMC algorithm to ompute a relay-lient assoiation and bandwidth alloation for the multi-relay multi-lient ase. Finally we propose an extended MRMC mehanism termed D 2 MRMC, whih onsists of a protool defining the signaling proess, and several algorithms dynamially handling the ooperation problem in a distributed way. Extensive simulation results demonstrate the inrease of the network QoC and the per-user bandwidth of our RUN framework. REFERENCES [1] W. Li, X. Cheng, T. Jing, and X. Xing, Cooperative multi-hop relaying via network formation games in ognitive radio networks, in IEEE INFOCOM, April 213, pp [2] T. Jing, S. Zhu, H. Li, X. Cheng, and Y. 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11 1.119/TPDS , IEEE Transations on Parallel and Distributed Systems IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 11 Yong Cui is a professor in Tsinghua University, Counil Member in China Communiation Standards Assoiation, Co-Chair of IETF IPv6 Transition WG Softwire. Having published more than 1 papers in refereed journals and onferenes, he is also the winner of Best Paper Award of ACM ICUIMC 211 and WASA 21. Holding more than 4 patents, he is one of the authors in RFC 5747 and RFC 5565 for his proposal on IPv6 transition tehnologies. His major researh interests inlude mobile wireless Internet and omputer network arhiteture. Jianghuan Liu is an Assoiate Professor in the Shool of Computing Siene at Simon Fraser University, British Columbia, Canada. He was also a Mirosoft Researh Fellow, and worked at Mirosoft Researh Asia (MSRA) in the summers of 2, 21, 22, 27, and 211. His researh interests are in networking, in partiular, multimedia ommuniations, peer-to-peer networking, loud omputing, soial networking, and wireless sensor/mesh networking. He is a o-reipient of IEEE IWQoS 8 and IEEE/ACM IWQoS 212 Best Student Paper Awards, IEEE Communiations Soiety Best Paper Award on Multimedia Communiations 29, IEEE Globeom 211 Best Paper Award, and ACM Multimedia 212 Best Paper Award. Xiao Ma reeived his bahelor degree in the Department of Computer Siene and Tehnology from Tsinghua University, China in 211. He is pursuing the master degree in the Department of Computer Siene and Tehnology at Tsinghua University, supervised by Prof. Yong Cui. His researh interests inlude mobile loud omputing, wireless networks and omputer network arhiteture. Tianze Ma reeived his bahelor and MS degree in the Department of Computer Siene and Tehnology from Tsinghua University, China, in 28 and 211, respetively. He has published several papers on international onferenes and journals, inluding a full onferene paper in INFOCOM 211. His researh interests mainly inlude wireless mesh networks and omputer network arhiteture. Xiuzhen Cheng is an assoiate professor at the Department of Computer Siene, The George Washington University, Washington DC. Her urrent researh interests fous on ognitive radio networks and wireless mobile omputing. She has served on the editorial boards of several tehnial journals and the tehnial program ommittees of various professional onferenes/workshops. She also has haired several international onferenes. She worked as a program diretor for the US National Siene Foundation (NSF) from April to Otober in 26, and from April 28 to May 21. She reeived the NSF CAREER Award in 24. She is a senior member of IEEE and a member of ACM. Yihua Guo reeived his bahelor degree in the Department of Computer Siene and Tehnology from Tsinghua University, China in 212. He is pursuing the Ph.D degree at University of Mihigan. His researh interests mainly inlude data enter networking, wireless networks and mobile systems. Minming Li reeived the BE and PhD degrees from the Department of Computer Siene and Tehnology, Tsinghua University, Beijing, China, in 22 and 26, respetively. He is urrently an assistant professor in the Department of Computer Siene, City University of Hong Kong. His researh interests inlude wireless ad ho networks, algorithm design and analysis, and ombinatorial optimization. Biao Chen reeived his BS in Computer Siene from Fudan University in China and MS in Mathematis and PhD in Computer Siene from Texas A&M University respetively. After graduation, he joined the Department of Computer Siene in University of Texas at Dallas as assistant professor. Currently, he is a visiting professor in the Department of Computer and Information Siene of University of Maau. His researh interests inlude distributed systems, networking, internet of things, and seurity. He is a member of Sigma Xi, IEEE, and ACM () 213 IEEE. Personal use is permitted, but republiation/redistribution requires IEEE permission. See