A Game Theory based Contention Window Adjustment for IEEE under Heavy Load

Transcription

1 93 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 5, No. 2, August 203 A Game Theory based Contenton Wndow Adjustment for IEEE 802. under Heavy Load Mahdeh Ghazvn, Naser Movahedna 2, Kamal Jamshd 2 Computer Engneerng Department, Shahd Bahonar Unversty of Kerman, Kerman, Iran 2 Computer Engneerng Department, Unversty of Isfahan, Isfahan, Iran ghazvn@eng.u.ac.r, naserm@eng.u.ac.r, jamshd@eng.u.ac.r Abstract: The 802. famles are consdered as the most applcable standards for Wreless Local Area Networks (WLANs) where nodes make access to the wreless meda usng random access technques. In such networks, each node adjusts ts contenton wndow to the mnmum sze rrespectve to the number of competng nodes. So n the case of large number of nodes, the network performance s reduced because of rasng the collson probablty. In ths paper, a game theory based method s beng proposed to adjust the users contenton wndow n mprovng the network throughput, delay and packet drop rato under heavy traffc load crcumstances. The system performance, evaluated by smulatons, shows some superortes of the proposed method over 802.-DCF (Dstrbute Coordnate Functon. Keywords: Contenton wndow, Game theory, 802., MAC (Meda Access Control) layer, Transmsson probablty.. Introducton MAC protocols are classfed nto two general classes: determnstc and random (based on competton). In determnstc meda access methods reservaton mechansms are used n central or dstrbuted fashons. In random access methods, channel access tme s not predctable. In IEEE 802. DCF mode, wreless nodes compete to access the shared wreless medum. The most mportant problem n such networks s the way n whch a node s selected to access the channel. The MAC layer s responsble for optmal and far channel assgnment, whle preventng collson whch occurs f two or more nodes sent frames smultaneously. Many studes are conducted on the applcaton of game theory n medum access control. Game theory examnes the decson makng process n a common envronment wth several decson makers, who have varous objectves n mnd. So the nodes of 802. based wreless networks are good examples of such a stuaton and game theory s hghly applcable n the wreless networks. Desgnng a payoff functon, ncludng utlty and cost functons s an mportant challenge n usng game theory. In most random access games, payoff functons have been defned heurstcally wthout enough explanaton. But, n the present study, a reasonable payoff functon from analytcal aspects of DCF s suggested. In the proposed method, an nfrastructure-less network, consstng of N smlar nodes s consdered. The nodes have the same rado range and hear each other. It s also assumed that all packets have equal szes, and errors are only caused by collson. Consderng the number of actve nodes n the network, a game theory based method s presented to mprove the network performance. In ths method, the nodes can adjust ther mnmum contenton wondows by creatng a tradeoff between network throughput, delay and the tme perod needed for droppng a frame due to the retransmsson lmt exceedng. A lst of abbrevatons and acronyms used throughout the paper s gven n Table. Table. Lst of acronyms and abbrevatons AP Access Pont CSMA/CA Carrer Sense Multple Access/Collson Avodance CTS Clear-To-Send CW Contenton Wndow CWmax Maxmum Contenton Wndow CWmn Mnmum Contenton Wndow DCF Dstrbuted Coordnaton Functon DIFS Dstrbuted Inter-Frame Space DSSS Drect Sequence Spread Spectrum EDCA Enhanced Dstrbuted Channel Access MAC Meda Access Control NE Nash Equlbrum PCF Pont Coordnaton Functon PHY Physcal PSO Partcle Swarm Optmzaton QoS Qualty of Servce RTS Request-To-Send SIFS Short Inter-Frame Space SNR Sgnal-to-Nose rato TFT Tt-For-Tat V-CSMA Vrtual Carrer Sense Multple Access WLAN Wreless Local Area Networks In the rest of ths paper, carrer sense multple access methods are brefly revewed n secton 2. Secton 3 s devoted to game theory ntroducton. In secton 4 some related researches are addressed. The proposed method s presented n secton 5. To evaluate the performance of the propose method, the smulaton results are reported and dscussed n secton 6 and fnally the paper s concluded n secton Carrer Sense Multple Access (CSMA) Protocols The CSMA protocols maybe based on non-persstent and p- persstent methods. In non-persstent CSMA method, a staton senses the channel and upon fndng the channel dle, t sends ts data; otherwse t wats for a random perod and repeats the procedure agan. In p-persstent CSMA whch s proper for tme slotted channels, once a staton s ready to transmt, t senses the channel, upon fndng the free channel, the staton sends ts data wth the probablty of p or postpones ts transmsson untl the next tme slot wth the

2 94 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 5, No. 2, August 203 probablty of q=-p. Due to propagaton delay and watng for the dle channel, collson s stll possble. But t s avoded durng the frame transmsson va backoff algorthms based on Contenton Wndow (CW) or persstence probablty. In the backoff algorthm, before transmsson, each node wats for a random tme, lmted to ts CW sze. In persstence mechansm, each node mantans a persstence probablty and whenever t fnds the channel dle, t makes an access to the channel wth ths persstence probablty. Moreover, CSMA/CA s an enhanced verson of CSMA n rado envronments []. The 802. famles are consdered as the most applcable set of standards for WLANs whch may be confgured and mplemented centrally or n dstrbuted manner. In centralze mode a key element called AP (Access Pont) s responsble to establsh the connecton among statons. All of the statons served accordng to ths scheme should be n the AP coverage area. In ths way, channel access procedure s under the constant control of AP. In IEEE lterature, ths s known as PCF (Pont Coordnaton Functon) mode. In the dstrbuted 802. mode, whch s known as DCF (Dstrbuted Coordnaton Functon), there s no central element to control the shared channel access procedure. So each staton has to enter a contenton procedure and resolve possble collsons before each frame transmsson. In DCF, statons use CSMA/CA as ther multple access control protocol, n fact a backoff algorthm wth a contenton bnary sgnal, expressng transmsson success or falure s exploted. Each node montors the channel actvty. If the channel s dle for a tme nterval called DIFS, the node begns sendng data. Otherwse, t perssts on montorng untl the channel becomes dle for DIFS duraton. Next, a random backoff tme s selected by the node based on Equaton.. Backoff Tme = Random (CW) a slot tme () There are two access mechansms n DCF mode: Basc access mechansm; and RTS/CTS mechansm. In basc access mechansm, when the backoff tmer s tmed out, the transmtter staton begns to transmt. Whenever a recever receves a frame successfully, t wll send an acknowledgment frame (ACK) back to the transmtter after a tme nterval called SIFS [2]. However, n RTS/CTS mechansm, at frst the transmtter staton sends an RTS (request-to-send) frame to the recever. After the RTS s receved by the recever, t sends back a CTS (clear-to-send) frame to the transmtter. It s worth notng that CTS s sent out only f the channel s dle. The transmtter recognzes a collson, f t does not receve any CTS. The data frame transmsson begns after recevng the CTS. And fnally the recever wll send the ACK frame to the transmtter f t receves the data frame correctly. Because of smultaneous transmssons, collson s possble wth ths protocol. So after each unsuccessful transmsson, the CW s multpled by σ, whch s called persstence coeffcent, then the backoff process s repeated agan. The process contnues untl the sze of the contenton wndow reaches ts maxmum value, CW max =σ m CW mn, where m s the maxmum backoff stages. Once CW reaches CW max, t s preserved untl the frame s transmtted successfully or the retransmsson tmes gets to the re-try lmt r. When the latter takes place, the frame wll be dropped. An example of ths procedure s presented n Fgure. Fgure. An example of ncreasng CW: CW mn =7, CW max =255, σ=2, r=7 and m=5 []. If persstence mechansm s mplemented, channel access probablty equals to the persstence probablty (τ ). In case of usng backoff mechansm, by assumng m=0, the transmsson probablty s related to the mnmum contenton wndow CW accordng to Equaton 2 [3],[5]: 2 = CW m n + mn τ (2) If some nodes make access to the channel smultaneously, collson happens, so the collson probablty (p ) s defned as Equaton3, where N s the number of competng nodes: p = ( τ ) (3) j N, j j Generally, users are able to tune ther transmsson probablty by modfyng the backoff control parameter (persstence coeffcent σ), CW mn value and maxmum backoff stages (m value) [6]. In WLANs, mddle nodes are exposed to collson more, rather than the ones wth less contendng neghbors, so mddle nodes tend to choose longer backoff delay [5 and 7]. In the orgnal verson of DCF, each new transmsson begns wth the mnmum value of CW, dsregardng the contenton level of the network. Hence, n the presence of a large number of nodes, f no real contenton status s consdered, the CW value ncreases due to consecutve collsons. Therefore, to gan hgher throughput, lower collson and better farness other methods whch can adjust the CW or persstence probablty dynamcally through modfyng the contenton parameters lke CW mn, CW max, m, σ, and r are needed. 3. Game Theory Game theory s a feld of appled mathematcs that descrbes and analyzes crcumstances n where multple partcpants nteract or affect one another. In other words, n games, a person s success depends on the other s actons. The problems of nterest nvolve multple partcpants, each wth ndvdual objectves related to some shared resources. A game ncludes some players, a seres of actons and a seres of payoff functons. A payoff functon s the subtracton of utlty and cost functons. A utlty functon s a parameter n

3 95 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 5, No. 2, August 203 measurng the satsfacton level of a user. By maxmzng the network utlty (e.g. the sum of all users utltes) the socal welfare s maxmzed. One player s strategy can nclude each acton out of the player s acton spaces or a mxture of them. The mathematcal representaton of a game s as follows where N s the number of players, A s are the users actons space and u s are the payoff functons. (4) G =< N, { A }, { u }> In a game, the pont where all players have made ther decsons and a result s obtaned, s called Equlbrum. The most popular equlbrum s a Nash Equlbrum (NE) where none of the users gan any beneft by changng ts strategy on ts own part. Let x be a strategy profle of player and x be a strategy profle of all players except player ; when each player N player obtans payoff x ) selects the strategy ( u as follows[], [3]-[9]: x, then * * * *, x A, x x : u ( x, x ) u ( x, x ) (5) If players clearly choose an acton; t s called the pure strategy and when they have no total trust n opponent s acton, ths type of acton s called mxed strategy. In the latter a pure strategy s chosen stochastcally. Nash proved that by explotng mxed strateges, n a game wth a fnte number of players who can choose from fntely many pure strateges, there s at least one NE. Pareto effcency s obtaned when a dstrbuton strategy s developed n a manner where one party's stuaton cannot get better wthout makng another party's stuaton worse. In formal defnton, a Pareto optmal Nash equlbrum of a * * * game s any Nash equlbrum x = ( x, K, ) provded that there does not exst any equlbrum * * * * * y = ( y, K, ) wth u ( x ) < u ( y ) y n x n. Snce the early 990s, computer scence and engneerng have been added to ths lst. [0 to 4 and 20 to 22]. Games are dvded nto several types from varous aspects. For example, statc and dynamc, cooperatve and noncooperatve, complete nformaton and ncomplete nformaton, repettve and non-repettve games. In statc games, the users choose ther own strateges smultaneously and even f they adopt the strateges n dfferent tmes, they do not have any knd of nformaton about other user s strateges. In the dynamc games, the players make alternatve decsons and every player s nformed about the strateges as prevously selected by the other players. Moreover, as the players should gan enough nformaton regardng all other features lke strategy space, payoffs and so on; they are dvded nto two complete and ncomplete nformaton games. If the payoffs of all the other players for any combnaton of strateges are clear, the game has complete nformaton. Otherwse, even f t s not clear for one of the players, the nformaton wll be an ncomplete one. In cooperatve games, the players collaborate wth each other and the problem wll be turned nto an optmzaton problem whereby every player leads the system toward a socal equlbrum. In a cooperatve game, all the players try to mantan agreements through collaboraton, barganng and negotaton wth one another, so that they may obtan maxmum payoff rather than the correspondng noncooperatve game. Pareto effcency s the regular standard crtera for expressng the equlbrum proftablty n cooperatve games. Pareto means that a user may be unable to ncrease hs/her utlty wthout decreasng at least one user s utlty. The other type s the non-cooperatve game where every player adopts strateges wthout sharng nformaton wth others. In non-cooperatve games, f there exsts equlbrum, t s the Nash equlbrum. In general, the Pareto optmalty s an optmal operatng pont for a system; but the non-cooperatve game s equlbrums are neffcent under general condtons. The manner the nteractve players are convergent towards equlbrum s defned as the dynamcs of a game. There are many technques that lead a system towards Nash equlbrum, the most common are: best response, Gradent, and Jacoban method. The smplest technque for updatng strateges s the best response strategy. Ths means that at every stage, each node selects the best possble reacton aganst the behavors of other nodes n the prevous stage. Another technque for updatng a strategy compared to the optmal response s the Gradent game whch s consdered as the better response. Here, every node gradually adjusts ts strategy. Fnally, n the Jacob method, every node adjusts ts strategy preferably towards the better response. The ablty to model ndvdual ndependent decson makers, whose actons potentally would affect all other decson makers, makes the game theory partcularly attractve n analyzng the performance of ad hoc networks. In medum access games, the reverse engneerng models of avalable protocols, reverse engneerng of desrable pont, and forward engneerng and heurstc methods are usually used to determne the utlty functon. In forward engneerng, usually an optmzaton problem takes nto account and the utlty functon and payoff are formulated accordng to the player s actons. Convergence and consstency features, dervablty and convexty of these functons are necessary. As heurstc and mathematcal models can ntroduce varous functons as a utlty and payoff, forward engneerng process accepts a larger class of utlty functons [23]. 4. Related works In WLANs, meda access control s a dstrbuted approach to sharng a wreless channel among contendng nodes. In random access games, the wreless nodes are able to observe the payoff of other nodes through some contenton parameters. Usually, the strategy adopted by a player s ether transmsson probablty or contenton wndow. Its payoff ncludes ts beneft obtaned from access to the channel and packet s collson cost. Users can estmate and adjust ther own transmsson probablty and condtonal collson probablty by sensng the channel [3], [24], [25]. Based on many prevous works, t s determned that the players try to ncrease ther benefts from the network by adjustng parameters lke contenton wndow, transmsson power and data rate. From the players strategy perspectve, the CSMA games can be dvded nto access control, jontly power and access control games as llustrated by the flowchart n Fgure 2.

4 96 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 5, No. 2, August 203 Fgure 2. Taxonomy of CSMA Games [] As the optmal value of CW mn depends on the number of nodes, n [26], [27] the channel contenton process between the nodes s modeled as a dynamc game. Zhao et al have proposed cooperatve games for mprovng the performance n Mesh networks, WSNs and Ad Hoc networks [6], [26]- [35]. In these proposed games each node estmates the number of competng node n and then adjusts ts mnmal contenton wndow as follows: n rand( 6,7) n rand(,8 ) n 5 CW mn 7 6 n = (6) Where, rand(x,y) returns a random value between x, y and z s the largest nteger not more than ts argument. In [29] mesh routers estmate the game state based on an ncomplete cooperatve game and broadcast ths nformaton to the clents. Then all clents perform a cooperatve game based on estmated game state and obtan the optmal equlbrum strategy. The best strategy for nodes wth more compettors s the selecton of a grater CW mn n order to reduce the collson probablty. One advantage of games compared to other games s that there s no need to exchange nformaton lke SNR [7]. If the dstrbuton functon of the payload sze of the frames s known, the optmal CW mn s a functon of bt rate and number of competng nodes. In [28], t s suggested that each node estmates the number of ts opponents n-, then tunes ts CW mn based on ts bt rate. In [30], [35] a game-theoretc EDCA (G-EDCA) to mprove QoS n WLANs s proposed. Another smple protocol called (G-CSMA/CA) that calculates CW mn after each packet transmsson to mantan the real contenton level s proposed n [29]. Wth respect to partcle swarm optmzaton, [36] has proposed a game called (G-PSO) for WMNs. Along the utlty functon defnton, new utlty functons to capture ther gan from channel access s defned [37], [38]. Authors of [39] have proposed a non-cooperatve and contenton-based medum access game (CAG) wth ntal frameworks smlar to that of the [40] wth selfsh users. Then CAG s converted nto a constraned optmzaton problem and the strategy s updated by the gradent method to reach Nash equlbrum. The behavor of non-cooperatve users who tune ther access probablty by changng ther persstence coeffcent or the backoff exponental control parameter n proporton to the network collson status s studed n [5]. To mnmze the communcaton overhead n the cooperatve scheme, Yang et al. [4], [4] formulated the random access as a non-cooperatve game to maxmze the ndvdual payoff. The utlty expresses users satsfacton of successful transmsson and the cost functon captures the energy cost and transmsson falure due to collson. Unlke non-cooperatve protocols such as [5], [40], ths Noncooperatve Random Access scheme(nra) uses a general ncreasng and twce dfferentable functon nstead of the lnear collson cost n order to express dfferent levels of servces tolerances of transmsson falure due to collson. Authors of [42], [43] have establshed a MAC protocol wth selfsh users who are energy constraned and are able to change ther contenton wndow as a repeated noncooperatve game, GMAC. In GMAC all network nodes are selfsh, ratonal and do not cooperate n managng ther communcaton. A tolerant strategy called Generous TFT (GTFT) for the random access game s suggested n [42]. Snce [42] selects a generc utlty functon and does not consder packet delay, jtter or other factors, the resulted CW n some cases s too long. A Two Round non-cooperatve Game (TRG/CSMA) s defned n a work proposed by [44]. In the frst round of the game, throughput and delay are selected as the optmzaton goals [45]. Then two games are played separately, between N nodes to acheve the Nash equlbrum n each case. In the second round, the throughput and delay are consdered as the players and form a 2-player game to adjust the transmsson probablty. The authors [46] propose two non-cooperatve games one of whch s complete nformaton and the other s ncomplete n order to model the contenton based medum access. It s proven that there are an nfnte number of Nash equlbra for the ncomplete one but not all end up n farness. Therefore, t may be benefcal for the selfsh users to adhere to a set of constrants that result n farness n a non-cooperatve fashon. The complete nformaton results are extended to a more realstc ncomplete-nformaton scenaro. The Contenton Wndow Select Game (CWSG) s formulated as a non-cooperatve game n [47] based on ts receved SNR n wreless sensor networks. Snce n the cooperatve game proposed n [48], there s not enough feedback and lttle nformaton s exchanged across the network, [49] proposed a non-cooperatve random access game wth prcng (NRAP). The problem of maxmzng CSMA throughput s nvestgated and an analytcal relaton between MAC throughput and system parameters s derved [50]. In ths game, each node not only needs to consder ts own throughput as proft but also needs to consder a certan penalty as the prce for ts adverse mpact on other nodes. An nterference-aware MAC protocol, whch consders that nodes are concurrently transmttng n nearby clusters s

5 97 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 5, No. 2, August 203 formulated n [5], both n the statc and dynamc game settngs. In [52] an Incentve Compatble Medum Access Control(ICMAC) s presented. It provdes ncentves for the players n a wreless network for optmzng the overall utlty by usng a Bayesan game formulaton. In, channel contenton problem s mplemented as a non-cooperatve power control game called GMAC. GMAC uses a shared channel for data and control and a lnear prcng factor of power consumpton s used n the defnton of utlty functon. In [56], [57], a dstrbuted power-aware MAC algorthm called PAMG s modeled for Ad Hoc networks, usng statc non-cooperatve game dea. In ths game, each actve lnk s consdered as a player and ts strategy vectors are two-dmensonal ncludng transmsson and power probabltes. In [58], the ssue of jont random access and power control desgn n wreless Ad Hoc networks s addressed wth the use of game theory. A cross layer optmzaton problem of power allocaton by controllng the contenton wndow sze n sensor networks s formulated n [59] and the utlty functon s consdered as the recprocal of tme delay. To get more nformaton about random access games, refer to [ and 60] for more detals. 5. The proposed method In the proposed method, a network consstng of n smlar nodes s consdered. Nodes have the same rado range and each node hears the others. Also, t s assumed that all packets are of the equal sze and errors are only caused by collson. Many studes have shown that DCF performance s very senstve to the number of competng nodes whch try to transmt ther packets on the shared meda, smultaneously [6 and 62]. DCF analyss ndcates that the number of competng players s a functon of condtonal collson probablty p and transmsson probablty τ. Each node can measure p and τ through several counters ndependently: Transmtted-Fragment Counter that counts the total number of successfully transmtted data frames, ACK Falure Counter that counts the total number of unsuccessfully transmtted data frames and the Slot Counter that counts the total number of experenced tme slots. Assumng an deal channel (free of nose or nterference) the number of competng nodes can be obtaned from the followng equatons [62]: log ( ) ( p) (7) n = f p, τ = + log( τ ) TransmttedFragmentCount + AckFalureCount τ = (8) SlotCount AckFalureCount p = (9) TransmttedFragmentCount + AckFalureCount In [62] a clear statement of n aganst p and contenton parameters lke CW mn, m and σ has been derved. However, Vercauteren et al., [63] have shown that Equaton.7 s only correct n the saturated stuatons where each node always has a packet to transmt, so they do not work properly for bursty traffc. To resolve ths problem, [6] proposes two mechansms for estmatng the operaton tme, ARMA and Kalman flters. These two methods are accurate even n unsaturated stuatons but ther mplementaton n mesh nodes s very complcated. A model called VCSMA/CA s proposed n [29], whch works lke CSMA/CA but only manages vrtual frames. To schedule such frames s smlar to real frames and ther dfference les n the fact that n VCSMA/CA when a node decdes to transmt a vrtual frame, no other frame s transmtted [29]. In the proposed game, each node wth packets to transmt, estmates the number of competng nodes usng CSMA/CA and n case of havng no packet to transmt, t obtans the number of nodes through VCSMA/CA. In DCF, each selfsh node attempts to ncrease ts transmsson probablty or equvalent by decreasng ts contenton wndow to mprove ts throughput. Increasng the transmsson probablty by a node stmulates other nodes to retalaton, whch enhances the collson, so the delay and packets drop ratos are ncreased. Therefore, every longsghted ratonal user, payng attenton to the other users retalaton, knows that she/he should cooperate wth other users n order to mantan or ncrease her/hs throughput n a satsfactory level. Snce t s assumed that all nodes hear one another, they can estmate the number of contendng nodes and can form a cooperatve game as [29]. The contenton wndow control problem can be formulated as a cooperatve game or an optmzaton problem. In game theory, payoff functon s very mportant. Payoff functon ncludes utlty functons and cost functons. The utlty functon s used for defnng the user s satsfacton level from her/hs acton. Maxmzng the network utlty wll result n maxmzng socal welfare of the system. The payoff functon should be convex to result a unque optmum soluton. The objectve here s to obtan a tradeoff n maxmzng global throughput and reducng the delay and packet drop probablty. In the game, throughput s consdered as a beneft for users, the users are also nclned to reduce ther packet drop probablty. The average delay of successful transmtted packet s consdered as the cost observed by each user. In other words, ncreasng the contenton level leads to an ncrease n the tme requred to wn a transmsson opportunty whch ncreases the meda access delay tme for watng packets n the transmsson buffer. An ncrease n contenton also causes an ncrease n collson probablty whch requres a greater number of retransmssons to mnmze the packet loss rato. Fnally, these retransmssons ncrease the delay tme requred for a successful packet transmsson [64]. For ths purpose, frst, defntons of throughput, packet drop rato and delay, whch are obtaned by DCF analyss, are gven and next the payoff functon s determned. In accordance wth the presented analyss models for 802., the saturaton throughput (S) s defned as a fracton of tme durng whch the channel succeeds n transmttng packet as follows [62 and 65]: S = P P E[ P] s tr ( Ptr ) σ + Ps Ptr Ts + ( Ps ) Ptr Tc (0) Where, σ s the duraton of an empty physcal slot tme, P tr s the channel busy probablty due to transmsson or collson - and P s s the successful transmsson probablty whch are defned as follows [62], [65]:

6 98 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 5, No. 2, August 203 P = τ ) tr n P = s n ( () ( P n τ τ (2) tr ) T s,t c,n and ndcate the duraton of successful transmsson, duraton of collson, the number of nodes and transmsson probablty, respectvely. T s and T c are calculated as follows [65], [66]: T basc s T basc ( P) + SIFS + ACK + δ = H + E DIFS + 2 ( P) + + δ (3) c = H + E DIFS (4) where, E[P] s the useful data (payload), H s the header of MAC and PHY layers and δ s the propagaton delay. DIFS and SIFS are DCF Inter-Frame Spacng and Short Inter- Frame Spacng, respectvely, defned n the 802. standard. Based on Equaton.0, t s apparent that each node can make ts throughput grow by ncrementng ts transmsson probablty. In fact, ncreasng the transmsson probablty means choosng lower values for CW mn, whch s equvalent to access the channel more quckly, that results n hgher throughput. As t s assumed that all nodes are smlar and they always have packets to transmt. The transmsson probablty ncrease results n the collson probablty growth. Hence, there s an optmal transmsson probablty that depends on the number of nodes, payload sze and other parameters n order to acheve hgher throughput. The MAC delay can be consdered as the tme nterval between the begnnng of the backoff stage and the successful recepton of a frame. In other words, the average tme duraton between two successve transmttng packets s consdered as the delay. MAC delay s measured from the moment a packet s arrved at the head of the MAC queue untl the transmsson s acknowledged. If a packet s dropped, the delay for such a packet s not calculated n the average MAC delay. Therefore, assumng that E[X] s the average number of tme slots for a packet s successful transmsson, the average delay for a packet to be transmtted successfully s estmated by Equaton.6, where r s the retransmsson lmt and s the collson probablty[67]: [ D] = E[ X ] E[ slot] E (5) E [ D] CW + r = r+ = 0 2 p r+ ( p p ) E[ slot] (6) E[slot] s the average length of a vrtual slot tme defned as: ( Ptr ) + Ps Ptr Ts + ( Ps Ptr Tc E [ slot] = σ ) (7) In addton, P drop s the probablty that a packet has reached ts re-try lmt (r), that s the maxmum back off stage, and experences another collson or error. By ncreasng transmsson probablty, P drop s ncreased, because of an ncrease n collson probablty whch s due to the small sze of CW mn. The packet drop probablty s defned as the probablty that a packet s dropped when the retry lmt s reached. Ths phenomena are defned as : r+ p drop = p (8) The average tme requred for a packet to experence r+ collson or error s named the average duraton of droppng tme. The average tme to drop a packet s gven by Equaton. [67]: E[ T ] = drop E[ N drop] E[ slot] (9) r CW + E[ Tdrop ] = E[ slot] =0 2 where [ ] N drop (20) E s the average number of slot tmes requred for a packet to experence r+ collsons or errors n (0,, r) stages and CW s the contenton wndow sze at stage. Based on Equaton 20, t could be concluded that n order to decrease the drop rate, the E[T drop ] has to be prolonged through ntalzng CW mn wth a great value. As mentoned, the objectve of ths artcle s to reach a tradeoff n maxmzng the throughput, decreasng the MAC delay and reducng the packet drop probablty by usng game theory. For ths purpose, a cooperatve game ncludes an nfnte set of strateges (0< τ <) and a set of utlty functons {u }. It s obvous that throughput, delay and drop tme have dfferent unts n dfferent ranges, and they have to be normalzed. Therefore the payoff functon s defned as the followng optmzaton equaton: S E( T drop ) E( D ) u ( τ ) = w + w2 w 3 Max S Max E T Max E D ( ) ( ( ) drop (2) Subject to < τ < (22) 3 0 w = (23) = ( ( )) The weghts w ) can be adjusted based on traffc types ( and some users objectves such as ncreasng throughput, decreasng delay or reducng the number of dropped frames. Payoff functon for dfferent number of nodes (2, 5 and 0) s presented n Fgure 3. It s obvous that ths functon s concave n [0, ] regon. Normalzed Payoff Functon n=2 n=5 n= Transmsson Probablty Fgure 3. Payoff Functon for n=2, n5, n=0. Accordng to the payoff functon, three statements nfluence the transmsson probablty, one wth postve mpact and the others wth negatve mpacts. Consderng that the proposed game s a cooperatve game, the objectve here s to obtan a global optmum pont. Hence, f the above

7 99 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 5, No. 2, August 203 optmzaton problem s solved by the best response method, the optmal transmsson probablty whch s also the Pareto optmal wll be obtaned through: du dτ = 0 du = w dτ ds τ Max drop (24) 2 3 ( S ) Max( E( T )) Max E( D ) + w de( T τ ) drop w de( D ) τ ( ) (25) Consderng that the obtaned optmum transmsson probablty, the mnmum sze of the contenton wndow can be calculated. The obtaned results have shown that n the suggested game, each user mproves ts successful transmsson chance by ncreasng ts transmsson probablty, whle ths ncrease causes an ncrement n collson probablty, as well. Such collsons wll result n ncreasng the packets drop rato and tme delay. Thus, n case of less number of contendng nodes, the nodes should select a smaller CW mn and t to be as the best strategy. In the case of more contendng nodes, greater CW mn s more approprate n order to reduce the collson probablty and the drop probablty. Ths game can be mplemented n a decentralzed manner. 6. Smulaton results To assess the accuracy of the proposed game, a wdespread smulaton was performed wth dfferent number of nodes up to 60 nodes and by physcal layer nformaton ncluded n Table 2. It s also assumed that all the nodes have smlar traffc types. The tme duraton for smulaton was 000 seconds and the CBR nput traffc was consdered wth 0. packets/sec arrval rate. Therefore as the traffc rate gets heaver, the network enters n saturaton status from about fve nodes. Each smulaton s repeated several tmes wth dfferent seeds and a seres of values for each seed are gathered. Consequently, the obtaned results are all based on mean values of all smulatons. Table 2. Smulaton Parameters PHY Header 92 bt MAC Header 272 bt ACK frame sze Payload sze (E[p]) Physcal layer Tme slot Maxmum retransmsson lmt Physcal Data Rate 2 bt 4096bt IEEE802. DSSS 20 µs 7 Mbps To have a better understandng wth respect to the performance of the suggested method, ths method s compared wth the 802. DCF. These comparsons are made based on three crtera: global throughput, end to end delay and packet drop rato. 6. Throughput Comparson The network throughput represents the total number of bts (n bts/sec) forwarded from wreless LAN layers to hgher layers n all WLAN nodes of the network (Fgure 2). For the total number of nodes n the DSSS PHY model, CW mn s 3 n DCF. Therefore by ncreasng the network arrval traffc, collson probablty s ncreased and DCF throughput s decreased. In fact, collsons waste the channel bandwdth and a bg fracton of tme s used as contenton tme. In the proposed method, collson probablty s controlled by changng the mnmum sze of contenton wndow as shown n Fgure 4. The network throughput of the proposed scheme s farly fxed around 3.5Mbps. In addton, the numercal results of DCF and the proposed method are presented n Fgure 4, whch show the smlartes of the numercal and smulaton results. Fgure 4. Throughput comparson between the proposed game and 802. DCF To show the proposed method accuracy, throughput wth confdence nterval 0.95 s llustrated n Fgure 5. Fgure 5. Throughput of the proposed method wth 0.95 confdence nterval. 6.2 Delay Comparson The end to end delay of all the packets receved by the wreless LAN MACs of all WLAN nodes n the network and forwarded to the hgher layer s consdered as delay. Ths delay ncludes medum access delay at the source MAC and transmsson delay. MAC delay represents the total of queung and contenton delays of the data, management and ACK frames transmtted by all WLAN MACs n the network. For each frame, ths delay s calculated as the duraton from the tme when t s nserted nto the transmsson queue, whch s the arrval tme for hgher layer data packets and creaton tme for all other frame types, untl the tme when the frame s sent to the physcal layer for the frst tme. In a smlar manner, ths tme may nclude multple numbers of backoff perods. Fgure 6 shows the

8 00 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 5, No. 2, August 203 comparson of the proposed method and DCF delay. DCF s much greater than the proposed scheme as shown n Fgure 7. Fgure 6. Comparson of the end to end delay of DCF and the proposed method. At DCF, CW mn for all numbers of nodes n DSSS model s always the same and s equal 3. When the number of nodes s less ths sze of CW s great, so n ths stuaton, the delay of DCF s about 4 second more than that of the proposed algorthm. Snce the proposed method uses CW mn smaller than DCF, t has lower delays. Due to the lower number of nodes, traffc s not very heavy so queung delay and MAC delay s lower. By an ncrease n nodes number, the delays are ncreasng; however, the delay of the proposed method s lower than that of the DCF. Snce a great queue sze (e.g packets) s used n ths smulaton, there s not any drop because of queue overflow and all packets are processed. However, t causes an ncrease n queung delay whch resulted n an end to end delay growth. As the delay s great and ts confdence nterval s very small, t s not vsble clearly and t s not shown here. In the saturaton mode, however, the DCF collson rate s drastcally ncreased and lots of packets are dropped, but the delays of these packets are not consdered n the MAC delay calculaton. Although the delay of dropped packets s not consdered n the meda access delay, the delay of DCF s more than that of the proposed method n most states. Ths s because of the extra collsons occurrng n DCF. 6.3 Drop Comparson From Drop perspectve, a packet may be dropped due to two reasons: queue overflow or retransmsson lmt surpasses. It s clear that queue overflow droppng rate s hghly depended on the queue sze. As the MAC queue sze s assumed to be about as a great value, the total sze of hgher layer data packets, no data packet n WLAN MACs s dropped to the queue saturaton. Retransmsson exceeds droppng s defned as total hgher layer data traffc (n bts/sec) dropped by all the WLAN MACs n the network as a result of consstently falng retransmssons. It represents the number of the hgher layer packets that are lost because the MAC could not receve any ACKs for the (re)transmssons of those packets and the packets re-try counts reached the MAC s re-try lmt. In retransmsson exceed aspect of droppng; the drop rate of Fgure 7. Comparson of retransmsson exceed drop rato of DCF and the proposed method The consderable mprovement of the suggested method wth respect to packet drop rate n tme compared to 802. s ndcated n Fgure 7. The packet drop rate because of exceedng from retransmsson lmt n ths proposed method s very small and gnorable. Fgure 8 llustrates the packet drop rato wth a 0.95 confdence nterval. Fgure 8. The Proposed Method Delay wth Confdence Interval 0.95 The proposed method mproves the network performance wth respect to throughput and drop rato. The suggested method s consderably dfferent from However, amongst the advantages of the suggested game compared to that of the other exstng games, one can menton no requrement of exchangng any nformaton lke SNR, queue sze and addtonal sgnalng. Despte the fact that the perodcal exchange of the game status s dffcult for the nodes and results n more energy consumpton and bandwdth wastage, the nodes are always sensng the channel n order to obtan the probable packets, nodes can estmate the game status by the channel sensng. It should be understood that takng the dynamsm of the game s status, t s not always possble to estmate the status of the game on tme and accurately. To reduce the computatonal complexty n ths proposed method use a lookup table to speed up the best CWmn

9 0 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 5, No. 2, August 203 selecton based on the number of opponents s beng suggested. In other words, each node before any attempt to contenton, can make ts lookup table whch determnes the CWmn based on the number of contendng nodes. After that, t can estmate the number of contendng nodes and use ths lookup table to adjust ts CWmn, n each state, fast. 7 Concluson and Future Works In ths study, a cooperatve game s presented to determne the best mnmum contenton wndow sze under heavy traffc. AS game theory has turned nto a powerful tool for analyzng and mprovng the performance of contentonbased protocols several MAC games are presented, where the nodes actons are transmsson mode or watng. In most of the games, a set of behavors ncludng transmsson probablty, transmsson power and data rate are consdered. Specfyng proper utlty functons provde better medum access schemes whch can gan servce dfferentaton and a better contenton control. Consequently, t can obtan a hgher throughput. Therefore, payoff functons that nclude utlty and cost functons, s very mportant n random access games. In most studes, however, ths functon s defned heurstcally wthout suffcent explanaton, but, t s tryng to use a reasonable payoff functon. In the proposed method, frst every node estmates the number of nodes, based on ts local nformaton and then, t adjusts the mnmum sze of contenton wndow by maxmzng the global network s payoff functon. The smulatons ndcate some mprovements of the suggested method compared to DCF n terms of the throughput, decreasng end to end delay and drop rate. In the future tasks, one can menton adjustng cooperatve mult hop contenton wndow and some nfluencng parameters on throughput by consderng the node's moblty. It seems that applyng mult-dmensonal strategy vectors whch consder parameters lke transmsson opportunty, rate and power, modulaton type and spatal reuse are more ratonal optons whle the users have dfferent preferences. In ths game, the traffc arrval rate s not consdered whle t may be benefcal. In addton, n CSMA networks, the users normally do not have much nformaton about one another and they make decsons based on estmatng ncomplete nformaton. They may mprove the power of ther decson makngs through gatherng more benefcal nformaton; thus, some smple solutons for gatherng more nformaton may be benefcal as well. Combnng the game theory and the artfcal ntellgence and learnng methods may be helpful to estmate the game status. Acknowledgment Ths work s partally supported n fnance by the Iran Telecommuncaton Research Canter on under Grant ITRC No.8507/500. References [] M. Ghazvn, N. Movahedna, K. Jamshd, and N. Moghm, "Game Theory Applcatons n CSMA/CA Method," IEEE Communcatons Surveys and Tutorals, Accepted for Publcaton, 202. [2] B. H. Walke, S. Mangold, and L. Berlemann, IEEE 802 Wreless Systems: Protocols, Mult-hop Mesh/Relayng, Performance and Spectrum Coexstence: Wley, [3] L. Chen, S. H. Low, and J. C. Doyle, "Contenton control: A game-theoretc approach," n 46th IEEE Conference on Decson and Control, New Orleans, LA, 2007, pp [4] X. Guan, B. Yang, G. Feng, and C. Long, "Random access game n ad hoc networks wth cooperatve and noncooperatve users," Int. J. Syst. Control Commun, vol., no., pp. 3-30, [5] Y. Jn and G. Kesds, "Dstrbuted contenton wndow control for selfsh users n IEEE 802. wreless LANs," IEEE J. Sel. Areas Commun, vol. 25, no. 6, pp. 3-23, [6] L. Zhao, J. Zhang, K. Yang, and H. Zhang, "Usng ncompletely cooperatve game theory n moble ad hoc networks," n IEEE Internatonal Conference on Communcatons,ICC '07, 2007, pp [7] Y. Xao, X. Shan, and Y. Ren, "Game theory models for IEEE 802. DCF n wreless ad hoc networks," IEEE Commun. Mag., vol. 43, no. 3, pp. S22-S26, [8] N. Nsan, Algorthmc game theory: Cambrdge Unv Press, [9] T. Roughgarden, "Algorthmc game theory," Commun. ACM, vol. 53, no. 7, pp , 200. [0] D. N. Zhu Han, Wald Saad, Tamer Başar, Are Hjørungnes, Game Theory n Wreless and Communcaton Networks: Theory, Models, and Applcatons: Cambrdge Unversty Press, 20. [] Y. Zhang and M. Guzan, Game Theory for Wreless Communcatons and Networkng: Taylor and Francs, 20. [2] K. R. Apt and E. Grädel, Lectures n Game Theory for Computer Scentsts: Cambrdge Unv Pr, 20. [3] D. E. Charlas and A. D. Panagopoulos, "A Survey on Game Theory Applcatons n Wreless Networks," Computer Networks, 200. [4] M. Felegyhaz and J. P. Hubaux, "Game theory n wreless networks: A tutoral," Techncal Report: LCA-REPORT , EPFL [5] M. J. Osborne and A. Rubnsten, A Course n Game Theory: MIT press, 994. [6] E. Altman, R. E. Azouz, and T. Jménez, "Slotted ALOHA as a game wth partal nformaton," Computer Networks vol. 45, no. 6, pp , [7] A. B. MacKenze and L. A. DaSlva, Game Theory For Wreless Engneers: Morgan & Claypool, [8] A. B. MacKenze and S. B. Wcker, "Game theory and the desgn of self-confgurng, adaptve wreless networks," IEEE Commun. Mag., vol. 39, no., pp. 26-3, 200. [9] A. Dxt, K., and Nalebuff, Ð., Thnkng Strategcally: WW Norton & Company, New York, 99. [20] V. Georgev, "Usng Game Theory to Analyze Wreless Ad Hoc Networks," RWTH Aachen,Department of Computer Scence [2] S. Mehta and K. S. Kwak, "Applcaton of Game Theory to Wreless Networks," n Convergence and Hybrd Informaton Technologes, M. Crsan, Ed.:

10 02 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 5, No. 2, August 203 InTech, 200. [22] V. Srvastava, J. Neel, A. B. MacKenze, R. Menon, L. A. DaSlva, J. E. Hcks, J. H. Reed, and R. P. Glles, "Usng game theory to analyze wreless ad hoc networks," IEEE Commun. Surv. Tutorals, vol. 7, no. 4, pp , [23] J. W. Lee, M. Chang, and A. R. Calderbank, "Utlty-optmal medum access control: reverse and forward engneerng," n 25th IEEE Internatonal Conference on Computer Communcatons, 2006, pp [24] L. Chen, T. Cu, S. H. Low, and J. C. Doyle, "A game-theoretc model for medum access control," n WICON 07, Austn, Texas, USA, [25] T. Cu, L. Chen, and S. Low, "A game-theoretc framework for medum access control," IEEE J. Sel. Areas Commun., vol. 26, no. 7, pp. 6-27, [26] G. Zhang and H. Zhang, "Modellng IEEE 802. DCF n wreless LANs as a dynamc game wth ncompletely nformaton," n IET Internatonal Conference on Wreless, Moble and Multmeda Networks, Mumba, Inda, 2008, pp [27] G. Zhang, H. Zhang, and L. Zhao, "A novel MAC scheme for wreless LANs from the perspectve of game theory," n IET Conference on Wreless, Moble and Sensor Networks, (CCWMSN07)., Shangha, Chna, 2007, pp [28] L. Zhao, X. Zou, H. Zhang, W. Dng, and J. Zhang, "Game-theoretc cross-layer desgn n WLANs," n Internatonal Wreless Communcatons and Moble Computng Conference, IWCMC ' , pp [29] L. Zhao, J. Zhang, and H. Zhang, "Usng ncompletely cooperatve game theory n wreless mesh networks," IEEE Network, vol. 22, no., pp , [30] L. Zhao, H. Zhang, and J. Zhang, "Selfsh traffc wth ratonal nodes n WLANs," IEEE Commun. Lett., vol. 2, no. 9, pp , [3] L. Zhao, H. Zhang, and J. Zhang, "Usng ncompletely cooperatve game theory n wreless sensor networks," n Wreless Communcatons and Networkng Conference, WCNC 2008, 2008, pp [32] L. Zhao, L. Guo, J. Zhang, and H. Zhang, "Gametheoretc medum access control protocol for wreless sensor networks," IET Commun., vol. 3, no. 8, pp , [33] L. Zhao, L. Guo, G. Zhang, H. Zhang, and K. Yang, "An energy-effcent MAC protocol for WSNs: game-theoretc constrant optmzaton," n th Internatonal Conference on Communcaton Systems, ICCS., 2008, pp [34] L. Zhao, L. Guo, L. Cong, and H. Zhang, "An energy-effcent MAC protocol for WSNs: gametheoretc constrant optmzaton wth multple objectves," Wrel. Sensor Networks, vol., no., pp , [35] L. Zhao, L. Cong, H. Zhang, W. Dng, and J. Zhang, "Game-theoretc EDCA n IEEE 802.e WLANs," n IEEE 68th Vehcular Technology Conference,VTC Calgary, BC, 2008, pp. -5. [36] L. Zhao, H. Zhang, W. Dng, and J. Zhang, "Gametheoretc partcle swarm optmzaton for WMNs," n 9th Internatonal Symposum on Personal, Indoor and Moble Rado Communcatons(PIMRC), Cannes 2008, pp. -5. [37] D. K. Sanyal, M. Chattopadhyay, and S. Chattopadhyay, "Improved performance wth novel utlty functons n a game-theoretc model of medum access control n wreless networks," n IEEE Regon 0 Conference,TENCON Hyderabad 2008, pp. -6. [38] D. K. Sanyal, M. Chattopadhyay, and S. Chattopadhyay, "Performance mprovement of wreless MAC usng non-cooperatve games," Adv. Ele. Eng. Comput. Sc., vol. 39, no., pp , [39] X. He and L. Tan, "Contenton Access Game Method n Wreless Ad-Hoc Networks," n 4th Internatonal Conference on Wreless Communcatons, Networkng and Moble Computng, WCOM '08., 2008, pp. -4. [40] L. Chen, S. H. Low, and J. C. Doyle, "Random access game and medum access control desgn," IEEE/ACM Trans. Networkng, vol. 8, no. 4, pp , 200. [4] B. Yang, "Competton, cooperaton and cognton n wreless resource allocaton." vol. PhD dssertaton, Cty Unv.of Hong Kong, [42] L. Chen, "On Selfsh and Malcous Behavors n Wreless Networks-A Non-cooperatve Game Theoretc Approach," Ph.D. dssertaton, Ecole Natonale Supereure des Telecommuncatons, Pars, [43] L. Chen and J. Leneutre, "Selfshness, not always a nghtmare: Modelng selfsh mac behavors n wreless moble ad hoc networks," n 27th Internatonal Conference on Dstrbuted Computng Systems (ICDCS'07), 2007, p. 6. [44] J. Yang and H. Sh, "Two Rounds Game CSMA algorthm of WSNs," n 2nd Internatonal Conference on Networkng and Dgtal Socety (ICNDS), Wenzhou 200, pp [45] E. Zouva and T. Antonakopoulos, "CSMA/CA performance under hgh traffc condtons: throughput and delay analyss," Comput. Commun., vol. 25, no. 3, pp , [46] S. Raksht and R. K. Guha, "Far bandwdth sharng n dstrbuted systems: a game-theoretc approach," IEEE Trans. Comput, vol. 54, no., pp , [47] M. Yan, L. Xao, L. Du, and L. Huang, "On selfsh behavor n wreless sensor networks: a game theoretc case study," n Thrd Internatonal Conference on Measurng Technology and Mechatroncs Automaton (ICMTMA), Shangsha 20, pp [48] B. Yang, G. Feng, and X. Guan, "Random access n wreless ad hoc networks for throughput maxmzaton," n 9th Internatonal Conference on Control, Automaton, Robotcs and Vson, 2006, pp. -6. [49] B. Yang, G. Feng, and X. Guan, "Noncooperatve random access game va prcng n Ad Hoc networks," n 46th IEEE Conference on Decson and Control, New Orleans, 2007, pp

11 03 Internatonal Journal of Communcaton Networks and Informaton Securty (IJCNIS) Vol. 5, No. 2, August 203 [50] K. J. Park, J. Cho, J. C. Hou, Y. C. Hu, and H. Lm, "Optmal physcal carrer sense n wreless networks," Ad Hoc Networks, vol. 9, no., pp. 6-27, 20. [5] H. J. Lee, H. Kwon, A. Motskn, and L. Gubas, "Interference-aware MAC protocol for wreless networks by a game-theoretc approach," n INFOCOM '09, Ro de Janero 2009, pp [52] N. BenAmmar and J. S. Baras, "Incentve compatble medum access control n wreless networks," n workshop on Game theory for communcatons and networks, 2006, p. 5. [53] F. Wang, O. Youns, and M. Kunz, "Throughput- Orented MAC for Moble Networks wth Varable Packet Szes," n 3rd Annual IEEE Communcatons Socety on Sensor and Ad Hoc Communcatons and Networks, SECON '06, Reston, VA, 2007, pp [54] F. Wang, O. Youns, and M. Krunz, "GMAC: A game-theoretc MAC protocol for moble ad hoc networks," n 4th Internatonal Symposum on Modelng and Optmzaton n Moble, Ad Hoc and Wreless Networks, 2006, pp. -9. [55] F. Wang, O. Youns, and M. Krunz, "Throughputorented MAC for moble ad hoc networks: A gametheoretc approach," Ad Hoc Networks, vol. 7, no., pp. 98-7, [56] A. Ghasem and K. Faez, "A Nash power-aware MAC game for ad hoc wreless networks," n IEEE 9th Internatonal Symposum on Personal, Indoor and Moble Rado Communcatons(PIMRC) 2008, pp. -5. [57] A. Ghasem and K. Faez, "A non-cooperatve game approach for power-aware MAC n ad hoc wreless networks," Comput. Commun., vol. 33, no. 2, pp , 200. [58] C. Long, Q. Ch, X. Guan, and T. Chen, "Jont random access and power control game n ad hoc networks wth noncooperatve users," Ad Hoc Networks, vol. 9, no. 2, pp. 42-5, 20. [59] H. Km, H. Lee, and S. Lee, "A cross-layer optmzaton for energy-effcent MAC protocol wth delay and rate constrants," n Internatonal Conference on Acoustcs, Speech and Sgnal Processng (ICASSP), Prague 20, pp [60] K. Akkarajtsakul, E. Hossan, D. Nyato, and D. Km, "Game theoretc approaches for multple access n Wreless networks: a survey," IEEE Commun. Surv. Tutorals, vol. 3, no. 3, pp , 20. [6] G. Banch and I. Tnnrello, "Kalman flter estmaton of the number of competng termnals n an IEEE 802. network," n INFOCOM 03, [62] G. Banch, "Performance analyss of the IEEE 802. dstrbuted coordnaton functon," IEEE J. Sel. Areas Commun., vol. 8, no. 3, pp , [63] T. Vercauteren, A. L. Toledo, and X. Wang, "Batch and sequental bayesan estmators of the number of actve termnals n an IEEE 802. network," IEEE Trans. Sgnal Proc., vol. 55, no. 2, pp , [64] T. Debnath, "A Novel QoS-Aware MPEG-4 Vdeo Delvery Algorthm over the Lossy IEEE 802. WLANs to Improve the Vdeo Qualty," PhD Thess, School of Electronc and Communcatons Engneerng, Dubln Insttute of Technology, 202. [65] E. Zouva and T. Antonakopoulos, "CSMA/CA performance under hgh traffc condtons: throughput and delay analyss," Computer Communcatons, vol. 25, no. 3, pp , [66] G. Banch, "IEEE 802.-saturaton throughput analyss," Communcatons Letters, IEEE, vol. 2, no. 2, pp , 998. [67] Perkls Chatzmsos, A. C. Boucouvalas, and V. Vtsas, "Performance Analyss of IEEE 802. DCF n Presence of Transmsson Errors," n Internatonal Conference on Communcatons, 2004, pp