Distributed Optimal TXOP Control for Throughput Requirements in IEEE e Wireless LAN

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1 Dstrbuted Optmal TXOP Control for Throughput Requrements n IEEE 80.e Wreless LAN Ju Yong Lee, Ho Young Hwang, Jtae Shn, and Shahrokh Valaee KAIST Insttute for Informaton Technology Convergence, KAIST, Daejeon, Korea Dept. of Computer Engneerng, Kwangwoon Unversty, Seoul, Korea School of Informaton and Communcaton Engneerng, Sungkyunkwan Unversty, Suwon, Korea Dept. of ECE, Unversty of Toronto, Toronto, Canada Abstract Ths paper desgns a dstrbuted Transmsson Opportunty TXOP adaptaton algorthm for IEEE80.e Enhanced Dstrbuted Channel Access EDCA. Each node measures ts throughput n a wndow and compares t wth a target value. If the measured throughput s hgher than the target value, the node reduces ts TXOP, otherwse f the measured value s less than the target throughput, the node ncreases ts TXOP. We show that the target throughput can be acheved n a globally stable manner. Index Terms IEEE 80.e, EDCA, WLAN, TXOP, Dstrbuted parameter control, Lyapunov stablty I. INTRODUCTION The IEEE 80.e Enhanced Dstrbuted Channel Access EDCA protocol [] defnes multple queues, denoted by access categores ACs, per each node and sets the correspondng control parameters such as the Arbtraon Interframe Space AIFS, the Contenton Wndow CW and the Transmsson Opportunty TXOP, per each queue n order to provde Qualty-of-Servce QoS dfferentaton. TXOP as our research target allows a staton to transmt multple frames consecutvely when gettng the channel wthout exceedng the specfc TXOP lmt duraton. Among the three man medum access control MAC parameters n wreless LAN, TXOP s the most mpactng one [, 3] because TXOP can provde multple contenton-free transmssons even n hgh contenton perods, whle CW and AIFS cannot lmt the collson rates. As a result, much attenton has been gven for desgnng TXOP adaptaton algorthms [3 6]. Unfortunately, most of the reported work n the lterature s ntutve wthout rgorous analyss. Hence, t s not yet clear how TXOP should be adapted n a dstrbuted fashon to provde a target QoS, dentfed for nstance by the throughput requrement for each queue n an IEEE 80.e network. In ths paper, we propose an algorthm to set TXOP for gven throughput requrement. The proposed soluton s a dstrbuted mechansm for TXOP adaptaton wth mnmal control overhead. In the proposed algorthm, each node ndependently measures ts throughput and compares t wth a target value. TXOP s then adapted usng the result of ths comparson; that s, TXOP s ncreased f the measured throughput s less than the target value, and t s decreased f the measured throughput s more than the target throughput. We show that the throughput converges to the target throughput n a globally and geometrcally stable manner. Our stablty analyss provdes a bass for optmal control of ndvdual TXOP values of the correspondng AC queues wth dfferent throughput requrements n IEEE 80.e-based wreless networks. II. TXOP SOLUTION FOR THROUGHPUT REQUIREMENTS We assume that there are n queues and denote the set of queues as N =,,..., n}. We also assume that all the traffc classes use the same AIFS whch s equal to dstrbuted nter-frame space DIFS n order to extract TXOP effect only. Hence, the QoS n each queue can only be dfferentated by CW mn and TXOP. Let τ be the probablty that the -th queue transmts durng a generc tmeslot. Let p b denote the probablty that the channel s busy. Then, p b = τ. Let p s, denote the probablty that a successful transmsson occurs n a tmeslot for the -th queue, and p s the probablty that a successful transmsson occurs n a tmeslot. Then, we can obtan the followng [7]: p s, = τ τ j for N, p s = j, p s,. 3 Let S be the throughput of the -th queue. Let δ, x, T s and T c denote the duraton of an empty tmeslot, TXOP of the -th queue, the average tme that the channel s sensed busy because of a successful transmsson, and the average tme that the channel has a collson, respectvely. Based on the prevous analyss [7, 8], we can derve the saturaton throughput of the -th queue as E[payload sze n a tmeslot for the -th queue] S = E[length of a tmeslot] p s, x R = 4 p b δ + p s T s + p b p s T c where R s the channel capacty of the -th queue. We assume that RTS/CTS exchange s adopted. Let T RT S and T CT S denote the tme to transmt an RTS frame and a CTS frame,

2 respectvely. Let T H, T ACK, and SIF S denote the tme to transmt the header ncludng MAC header, physcal layer header, and/or traler, an ACK, and short nter-frame spacng, respectvely. Then, T s and T c can be expressed as T s = p s, x + o s 5 p s T c = T RT S + SIF S + T ACK + DIF S 6 where o s s defned as o s = T RT S + 3 SIF S + T CT S + T H + T ACK + DIF S. 7 The throughput of the -th queue, S n 4 s a functon of τ = τ, τ,..., τ n and x = x, x,..., x n. The vector τ s determned by CW mn of all queues and s not affected by the varaton of the vector x [7]. In ths paper, we assume that CW mn are fxed for each queue although each queue can have dfferent CW mn values. Then, S s a functon of x. Let s be the normalzed saturaton throughput, whch s defned as s = S R. 8 Usng 8, s can be expressed as where τ s x = β x β j + 9 β = > 0, 0 τ = δ + β o s T c + + β T c > 0. To calculate τ n 0, we use Wu s model [] whch s a modfcaton of Banch s model [8] wth the frame retry lmt. Our objectve s to fnd the TXOP values, x, n a dstrbuted manner such that s x = for N, where s the target normalzed throughput of the -th queue. Note that bulds a set of n lnear equatons n varables x as follows: β x β j = for N. 3 j, Proposton : If the followng condton holds: <, 4 then the soluton for the problem, x = x, x,...x n, exsts unquely as x = β s j for N. 5 The condton 4 creates a stable system. Ths s ndeed the feasblty condton. That s, the target throughputs should be achevable and hence should create a feasble system. We wll dscuss shortly that f the system s not feasble then, the nodes extend ther TXOP to the maxmum value and stll cannot acheve the target throughput. Ths s of course an anomaly where no any other dstrbuted scheduler can satsfy the target throughputs. III. TXOP ADAPTATION AND STABILITY ANALYSIS If there s a centralzed coordnator, the TXOP values can be selected as n 5. However, the users may not know other users parameters ncludng throughput requrements. We propose a TXOP adaptaton algorthm wth whch the soluton 5 can be reached n a dstrbuted manner. We defne two sets, At and Bt for tme t 0: At = s t, N }, 6 Bt = s t <, N }. 7 Assume that each queue ndependently measures ts throughput and selects ts TXOP usng the followng control system for t 0: d dt x x t f At, t = 8 x t f Bt. Therefore, we can conclude that f a node has the measured throughput larger than the target throughput, t decreases ts TXOP, and f t has a throughput smaller than the target value, t ncreases ts TXOP. Snce the varaton of TXOP s drectly related to the throughput, we speculate that 8 adjusts the throughput so that t gets closer to the target throughput. We prove ths clam by showng that f At, then ds t dt < 0 and f Bt, then ds t dt > 0. From 9, the partal dervatves for sx are gven for, j N, as If At, s = ds dt = s d dt s s /x f = j, s s j / f j. = s s x x + + j Bt s s j j At,j s s j 9 = s s j + s j j A j B j Bt = s β j t + β < 0. 0 j t + On the other hand, f Bt, ds dt = s j At β j t + β j t + > 0.

3 Now, we nvestgate whether we can reach the pont s = s, s,..., s n wth the dynamcs 8. The global stablty of the algorthm can be studed by the applcaton of the Lyapunov functon. Let us ntroduce the followng Lyapunov functon: V s = s. n Note that V s = 0, and V s > 0 f s s. On the other hand, from 0 and, dv dt = s ds n s s < 0. 3 dt Therefore, the soluton s = s globally asymptotcally stable [9], whch mples that Therefore, lm st = t s. 4 lm x s t t = lm t t β s jt = x for N, 5 and the soluton x = x s globally asymptotcally stable. A. Practcal Consderatons In practce, we should measure the throughput n each measurement nterval. Let s k be the estmated normalzed throughput of user n [kt, k + T, N, k = 0,,,.... Let x k be TXOP of user durng [kt, k+t. We defne two sets, Ak and Bk as follows: Ak = s k, N }, 6 Bk = s k <, N }. 7 We consder the followng dscrete-tme nonlnear dynamcal system for k = 0,,,... η k x k f Ak x k + = 8 + η k x k f Bk, whch s the dscrete-tme verson of 8. Then, we can reach x usng the dynamcs 8 f the followng condtons hold [0]: η k = and k= lm η k = 0. 9 k In a dstrbuted control envronment, t s dffcult to adapt a varable step sze η k. Thus, we assume that η k, k =,,... are fxed at η, whch s a small postve constant. Now, we nvestgate the convergence speed. Let y k = β x k, N, k = 0,,,.... Suppose that Ak. Then, y k + s k + = y jk + + y k η = j Ak y jk η + j Bk y jk + η + y k = y η. 30 j Bk + yjk j Ak yjk η yjk+ yjk+ Therefore, the Taylor seres for s k + at η = 0 can be expressed for Ak as s k + = s k j Bk y y η + Oη, 3 where lm η 0 Oη /η s a constant. On the other hand, f Bk, s k + = s k + j Ak y y η + Oη. 3 We adopt the Lyapunov functon n as follows: V k + = s k n Applyng 3 and 3 n 33, gves V k + = s k n s η s k s k Ak s j Bk y y η s k s k Bk s j Ak y y + Oη s k n s η s k s k s y + Oη s k O n s η T y + Oη = V k η y + Oη Suppose that TXOP s bounded as. 34 x k x,max, for N, k = 0,,, If η s suffcently small, we can gnore Oη n 34. Then, V k + ρv k 36

4 where Moreover, where α mn = ρ = η β. 37 j,max + α mn s s V s α max s s 38 nmax, α max = nmn s. 39 Snce ρ <, the system s globally geometrcally stable at s = s [9]. If ρ approaches 0, the convergence speed s hgh. On the other hand, f ρ s close to, the system converges to the soluton slowly. From 36 and 37, the convergence speed s affected by the parameter η. As η ncreases, ρ decreases and the optmal soluton can be reached faster. We defne the overall normalzed throughput as s = s. Then, from 9 and 9, for N, s = s j = s s j = s x x x x 40 Therefore, the maxmum throughput can be acheved when all users set TXOP to the maxmum value, that s, x = x,max, N. Now suppose that the sum of all throughput requrements s greater than the system capacty. Then, unsatsfed users wll ncrease TXOP to the maxmum value. If all users set TXOP value to the maxmum value, then the throughput requrements cannot be enhanced and guaranteed. Ths s an unfeasble case n whch the target throughputs are so hgh that they cannot be acheved even wth the TXOP set at the maxmum. IV. NUMERICAL RESULTS In ths secton, we present smulaton results to valdate our algorthm. We consder four flows establshed over four pars of source-destnaton nodes. We assume that each node has one actve queue and the buffer sze s nfnte. The channel capacty s M bps. The RTS/CTS sgnallng s appled. Frst, we evaluate TXOP settngs for throughput requrements n IEEE 80.e WLAN wth system parameters shown n Table I. The target throughput for flows s gven by the vector.4,.8,., 0.6 Mbps. Snce the channel capacty s R = M bps, =,, 3, 4, the requred normalzed saturaton throughput s s = 0., 0.6, 0., From 5, the analytcal value of TXOP s x =.7,.03,.35, 0.68msec. Next, we nvestgate the proposed dstrbuted algorthm n 8. The length of measurement nterval s set to T = 00 msec. We measure the throughput of each flow as S k n [kt, k + T. By usng S k and x k n [kt, k + T, we adapt the payload sze of TXOP for each flow, x k +, at each nterval of length T accordng to 8. Fg. a shows the saturaton throughput varaton of each flow wth η = 0.0. If T s suffcently large, the measurement error becomes small. In Fg. a, the saturaton throughput of flow at tme t s depcted usng the average throughput TABLE I SYSTEM PARAMETERS Common Parameters Values Payload M P 068 bytes ntal value MAC header M H 7 bts PHY header length T P 9 µs Data Rate R D Mbps Control Rate R C Mbps DATA length M P + M H /R D + T P RTS length 60 bts/r C + T P CTS length bts/r C + T P ACK length bts/r C + T P CW mn 3 CW max 04 Retry Lmt 7 Propagaton Delay µs SIFS 0 µs Slot Tme 0 µs DIFS 50 µs durng [0, t, S k = k j= S j/k. The ntal payload sze of each flow x β > 0. 0 s.504 msec = 068 bytes [] j +. Then, the ntal saturaton throughput of each flow S 0 s calculated as.494 M bps accordng to 4 7. Snce there exsts the measurement error ncludng the randomness of the backoff wndow of flow, measured throughput of flow at k = 0, S 0 n Fg. a, may be dfferent from.494 Mbps. We observe that the measured throughput of each flow, S k converges to the requred throughput of each flow, S as tme ncreases. Fg. b shows the payload sze of TXOP for each flow wth η = 0.0. The target TXOP s x =.7,.03,.35, 0.68msec. We observe that the sze of TXOP for each flow, x k fluctuates about the target sze of TXOP for each flow, x, as tme ncreases. Now we examne the convergence speed accordng to the control parameter η. As a convergence crteron, we use the Lyapunov functon V k defned n 33. In Fg. a, V k decreases as k ncreases, whch mples that the measured throughput approaches the target throughput. As notced n the fgure, V k decreases fast wth tme as η ncreases, that s, the convergence speed for each flow ncreases as η ncreases. However, V k does not approach zero although tme ncreases. Ths s because η s a fxed parameter ndependent of k. We defne the convergence tme as kt such that V k = 0.0. If the throughput of every flow, S k s 0.9S S k.s, then V k 0.0. Note that ρ defned n 37 s the upperbound of decreasng rato of V k. Accordngly, we defne the cutoff tme as kt such that ρ k = /. Fg. b shows the convergence tme and the cutoff tme for the saturaton throughput wth varyng η. We observe that as η ncreases, the convergence tme and cutoff tme for saturaton throughput are reduced. In the IEEE 80.e standard [], the default value of TXOP lmt for AC VO s set to 3.64 ms or.504 ms accordng to dfferent physcal layers. For AC VI, the default value of TXOP lmt s set to 6.06 ms or ms accordng to dfferent physcal layers.

5 Saturaton Throughput Mbps Flow Flow Flow 3 Flow 4 S 0 S * Lyapunov functon, Vk η = 0.0 η = 0.05 η = 0. η = 0. η = 0.4 η = 0.6 η = 0.8 Vk= Tme sec Tme =kt sec a Saturaton throughput for each flow. a Lyapunov functon for saturaton throughput wth varyng η Flow Flow Flow 3 Flow 4 x 0 40 Convergence tme for saturaton throughput Cutoff tme for saturaton throughput x * Payload of TXOP usec Tme sec Tme sec 5 b Payload sze of TXOP for each flow TXOP adaptaton parameter, η Fg.. Throughput and TXOP for each flow wth η = 0.0. V. CONCLUSION Ths paper derves a closed-form soluton of TXOP settngs and proposes a dstrbuted TXOP adaptaton algorthm to satsfy target throughputs for IEEE 80.e users n a dstrbuted manner. Each node measures ts throughput n a wndow and compares t wth the target throughput. If the measured throughput s hgher than the target value, the node reduces ts TXOP; otherwse f the measured value s lower than the target throughput, the node ncreases ts TXOP. We show that f the optmal soluton of settng a TXOP for throughput requrements exsts, then the target throughputs can be reached n a globally and geometrcally stable manner. REFERENCES [] IEEE Standard for Wreless LAN Medum Access Control MAC and Physcal Layer PHY specfcatons: Medum Access Control MAC Qualty of Servce QoS Enhancements, 005. [] F. Rojers, H. Berg, X. Fan, M. Fleuren, A Performance Study on Servce Integraton n IEEE 80.e Wreless LANs, Computer Communcatons, vol. 9, ssue 3 4, pp , Aug [3] A. Ksentn, A. Nafaa, A. Guerou, M. Nam, ETXOP: A Resource Allocaton Protocol for QoS-senstve Servces Provsonng n 80. Networks, Performance Evaluaton, vol. 64, ssue 5, pp , June 007. Fg.. b Convergence tme and cutoff tme for saturaton throughput Lyapunov functon and convergence tme for saturaton throughput. [4] Y. Ge, J. C. Hou, S. Cho, An Analytc Study of Tunng Systems Parameters n IEEE 80.e Enhanced Dstrbuted Channel Access, Computer Networks, vol. 5, ssue 8, pp , June 007. [5] J. Majkowsk, F. Palaco, Dynamc TXOP Confguraton for QoS Enhancement n IEEE 80.e Wreless LAN, n Proc. of SoftCOM 006, pp , Sep [6] A. Andreads, R. Zambon, QoS Enhancement wth Dynamc TXOP Allocaton n IEEE 80.e, n Proc. of PIMRC 007, pp. 5, Sep [7] Y. Xao, Performance Analyss of Prorty Schemes for IEEE 80. and IEEE 80.e Wreless LANs, IEEE Transactons on Wreless Communcatons, vol. 4, no. 4, pp , July 005. [8] G. Banch, Performance Analyss of the IEEE 80. Dstrbuted Coordnaton Functon, IEEE Journal on Selected Areas n Comuncatons, vol.8, pp , March 000. [9] V. M. Haddad, V. Chellabona, Nonlnear Dynamcal Systems and Control: a Lyapunov-based Approach, Prnceton Unversty Press, 008. [0] H. F. Chen, Stochastc Approxmaton and ts Applcatons, Kluwer Academc Publshers, 00. [] H. Wu, Y. Peng, K. Long, S. Cheng, and J. Ma, Performance of Relable Transport Protocol over IEEE 80. Wreless LAN: Analyss and Enhancement, n Proc. of IEEE INFOCOM 00, pp , June 00.