An Analytical Model for IEEE Point-to-Point Link

Transcription

1 An Analytcal Model for IEEE 82. Pont-to-Pont Lnk Yong Yan, Xaowen hu Department of omputer cence, Hong Kong Baptst Unversty Emal: {yyan, Abstract - Wreless mesh networks have attracted extensve research nterests n recent years. Wth the maturty and pervasve deployment of IEEE 82.a/b/g technology, 82. DF protocol s consdered as a promsng canddate for constructng the backbone of wreless mesh networks. In a multchannel mult-nterface wreless mesh network, pont-to-pont 82. wreless lnk can provde the hghest throughput; hence t s crtcal to understand the 82. throughput performance n a pont-to-pont confguraton. Ths paper presents a smple yet precse Markov model for the analyss of pont-to-pont 82. lnk performance n terms of saturaton throughput. Dfferent from prevously proposed analytcal models, our model does not assume a constant and ndependent collson probablty. Our analytcal model s valdated by computer smulatons for both 82.b and 82.g confguratons. I. Introducton Wreless mesh networks (WMNs) are ganng sgnfcant progress n both academa research and commercal deployment n recent years [6, 7]. It has been shown that the aggregated system throughput can be sgnfcantly mproved by explotng mult-channel and mult-nterface technque [8, 9,, ]. A typcal wreless mesh network s shown n Fg., whose backbone conssts of a set of wreless mesh routers. Wreless statons (.e., end users) can access the Internet by assocatng wth a nearby wreless mesh router. Wth a sutable channel assgnment scheme and the help of drectonal antenna, t s possble that two nearby wreless mesh routers are connected by dedcated pont-to-pont wreless channel. Ths can greatly ncrease the capacty of wreless mesh backbone because each channel s shared by only two wreless mesh routers. IEEE 82. s almost pervasvely deployed by wreless LANs nowadays. The supported data rate of 82. has also been ncreased from Mbps (82.b) and 54Mbps (82.a/g) to 3Mbps or even 6Mbps (82.n) [, 2, 3]. It s therefore very promsng to use IEEE 82. protocol n wreless mesh networks. Due to the lmted number of wreless channels, t s very crtcal to mprove the utlzaton of the scarce wreless spectrum. Our paper ams to analyze the saturaton throughput of IEEE 82. pont-to-pont lnk, and also to fnd a sutable system parameter whch can lead to the mum saturaton throughput. The performance of IEEE 82. has been actvely studed n the last years. Most of them focus on the scalablty of 82. DF,.e., how to handle a large number of wreless statons. al et al. [4] derves an analytcal model for 82. DF usng a p-persstent backoff scheme to approxmate the orgnal bnary exponental backoff scheme. Banch [5] proposes a Markov chan model to derve the saturaton throughput by assug a constant and ndependent collson probablty of a packet transmtted by each staton. Ths assumpton s accurate only when the number of statons n the wreless LAN s farly large, however. Our paper ams to develop a precse analytcal model to calculate the saturaton throughput of an 82. pont-to-pont lnk. The man dfference between our model and exstng models s that, our model does not make the assumpton that the collson probablty s constant and ndependent. Instead, our model makes a smple assumpton that W = 2W. Ths assumpton s reasonable for a pont-to-pont wreless lnk, as we wll show by computer smulatons that the saturaton throughput s almost a constant value for all ntegers of m where W = 2 m W. Our model acheves better accuracy as compared wth the well known Banch s model [5]. Internet Gateway Wreless Mesh Router Wreless tatons Fgure : A mult-channel mult-nterface wreless mesh network The rest of the paper s organzed as follows. ecton II brefly revews the 82. Dstrbuted oordnaton Functon (DF) protocol. ecton III presents a Markov model used to calculate the saturaton throughput for a pont-to-pont 82. DF lnk. In ecton IV, we valdate our model by comparng wth smulaton results, for both 82.b and 82.g confguratons. Fnally, ecton V concludes the paper. II. Dstrbuted oordnaton Functon (DF) The IEEE 82. standard s workng on both the physcal (PHY) and medum access control (MA) layers of the network. Other than consderng about the physcal detals, we wll concentrate on the MA layer protocol tself /8/$ IEEE 2536

2 The basc access method n the 82. MA protocol s DF (Dstrbuted oordnaton Functon) known as carrer sense multple access wth collson avodance (MA/A) []. DF employs a dstrbuted MA/A algorthm and an optonal vrtual carrer sense usng RT and T control frames. When usng the DF, before ntatng a transmsson, a staton senses the channel to detere whether another staton s transmttng. If the medum s found to be dle for an nterval that exceeds the Dstrbuted InterFrame pace (DIF), the staton proceeds wth ts transmsson. However f the medum s busy, the transmsson s deferred untl the ongong transmsson terates. A random nterval, henceforth referred to as the backoff nterval, s then selected; and used to ntalze the backoff tmer. The backoff tmer s decreased as long as the channel s sensed dle, stopped when a transmsson s detected on the channel, and reactvated when the channel s sensed dle agan for more than a DIF. The staton transmts when the backoff tmer reaches zero. MA/A s a strategy that ntends to avod collsons, but t can not elate collsons. When more than one node are countng down ther backoff tmers, there s a probablty that some of them have ther tmers reach zero at the same tme slot, and start transmttng at the begnnng of next tme slot smultaneously, whch causes a collson. The collson probablty ncreases wth the number of actve senders n the network. DF requres each sender to wat for a random backoff perod after the channel s dle for DIF, t adopts a slotted bnary exponental backoff scheme. The backoff tme s calculated as BackoffTme = Random() alottme where Random() ndcates a unformly dstrbuted random nteger between [, W ] and W represents the value of contenton wndow, whch starts from W, doubled each tme a retransmsson occurs, untl reachng the mum value W. III. Analytcal Model of DF We consder a smple ad hoc wreless network that conssts of two nodes, that s, a pont-to-pont network. The preassumptons of our model are: () only two nodes are n the network; (2) each node always has packets to send to the other one; (3) the probablty densty functon of both nodes backoff tmers are unformly dstrbuted n the same range, whch means that both nodes are competng for the channel equally. In our model, we set the W as twce of W, whch ndcates a 2-level exponental backoff scheme. Although the IEEE 82.g standard defnes a mult-level exponental backoff scheme where W = 2 m W, we wll show that there s neglgble dfference between 2-level and mult-level schemes for a pont-to-pont wreless lnk. A. The Markov ystem Model We use a Markov chan to model the network wth two nodes. Each node has a backoff tmer. Our model focuses on the dfference between two backoff tmers. Let each state n levels: the states from to the Markov chan be the current absolute dfference, n unt of tme slots, between the two backoff tmers. For nstance, state represents that currently the backoff tmer of one sender s tme slots longer than another sender s backoff tmer. Apparently, collson wll happen at state, because the two senders have the same backoff tmers and they wll transmt ther packets smultaneously. On the other hand, every nonzero state mples a successful transmsson. Fg. 2 shows the Markov chan model, n whch all states are dvded nto two W belong to the Low-Level, whle the states from W to W belong to the Hgh-Level. Let P { } denote the transton probablty from state to state. Then the transton probabltes are: P{ } = / W, =, = () P{ } = 2( W )/ W,, [, W ] (2) 2 P{ } = / W, [, W ], = (3) P{ } = 2/ W, [, W ], [,( W /2) ] (4) P{ } = / W, [,( W /2) ], [ +, W ] (5) P{ } = / W, [ W /2, W ], [ W, ] (6) P{ } = / W, [ W, W ], [ W +, ] (7) At the Low-Level, snce state represents collsons, Eqs. () and (2) account for the process followng a collson. In partcular, P { } s the probablty that system encounters two consecutve collsons. Eq. (3) represents the process that a successful transmsson s followed by a collson. Eq. (4) accounts for the process of backward transton, whch means a new random backoff tmer makes a new dfference that s smaller than the prevous dfference. In contrast, Eqs. (5) and (6) accounts for the forward transton. Once the state s at W or hgher, the system s at the Hgh-Level. A non-zero state always mples a successful transmsson ahead, whch wll be followed by a selecton of random number between and W. Therefore, all states n the Hgh-Level can only have backward transtons to ther prevous W states, whch s represented by Eq. (7). To llustrate the Markov model, the transton probablty matrx for W = 6 and W =32 s shown n Fg. 3. In ths matrx, I represents the value of /W, X represents the 2 value of 2/W, and Z represents the value of /W. There are W equatons and W unknown parameters n ths matrx. If we denote each entry n ths matrx as m [, ], and the soluton to ths matrx s q [], these equatons can be wrtten by: W q[ ] = q[] m[, ], [, W ]. (8) 2537

3 W W W / 2 W W W W + k + W + k W + k W Fgure 2: The Markov model (to save space, W and W are expressed as W and W, respectvely) Accordng to the property of Markov chan, ths matrx can be solved by numercal method. The soluton q[] denotes the probablty that the dfference between the two backoff tmers s tme slots. B. Dstrbuton of ystem Idle tme We denote X and Y as the random varable of both random backoff tmers. At the Low-Level, both nodes have ther unform dstrbuton of random backoff tmers: f x (X ) = f y (Y ) = / W, where X and Y range from to W. By solvng the Markov matrx, we can get the probablty dstrbuton of the dfference of backoff tmers n two levels; and we denote the soluton q [] as f ( X ' Y ' ). Wth the above soluton, we are now ready to calculate the system throughput. In terms of throughput analyss, what really matters s the system dle tme cost by the random backoff perod, and ths dle tme always equals the shorter backoff tmer at each transmsson round. In other words, we are about to use the soluton f ( X ' Y ' ) to fnd the probablty p, whch s the probablty that system s dle for tme slots n one transmsson round, and t can be calculated as followng: p = q[]/ W + ( q[]) / W = / W, = (9) W p = q[]/ W + q[ ]( W )/ W + q[ ](/ W + 2( W )/ W ), 2 2 [, W ] () 2 2 p = q[](/ W + 2( W ) / W ), [ W, W ] (). alculaton of ystem Throughput In order to calculate the throughput, we frst lst our notatons for the mportant parameters n Table : Table : Notatons of parameters T tme cost by successfully transmtted payloads, excludng backoff tme T T tme cost by successfully transmtted packets, ncludng backoff tme tme cost by collsons, ncludng backoff tme N number of successfully transmtted packets Payload Payload n bts, ncludng UDP IP LL headers, excludng MA header. Fgure 3: Transton Probablty Matrx LnkRate t The lnk rate n bps Basc tme cost of a collson,excludng backoff tme 2538

4 t UPay MacP AK Basc tme cost of a successful transmtted packet, excludng backoff tme UDP payload, the real data, excludng any headers, mum s 4728 n ths research. Mac frame length n a PDU, ncludng Payload plus F and/or all other tals on the MA layer. Ack frame length on the MA layer N number of symbols needed to encode a MA layer data, bl only for 82.g Rate ymbol encodng rate, only for 82.g. In ths paper, we defne the throughput as n equaton (2), T N Payload / LnkRate Throughput = =, (2) T + T T + T where N Payload, T and T can be calculated by: N = TotalRound ( q ), (3) Payload = ( LL + IP + UDP) Header + UPay, (4) W = + T TotalRound q p ( lottme t ), (5) W = + T TotalRound ( q ) p ( lottme t ), (6) For the calculaton of t and t, the 82.b and 82.g protocol should be treated respectvely: For 82.b, t and t can be expressed as: t = T + MacP / LnkRate + DIF + PROP, (7) PLP t = t + IF + T + AK / AckRate + PROP, (8) PLP MacP = Header ( MA + LL + IP + UDP ) + UPay + F, (9) TPLP = PLPpreamble/ PreambleRate + PLPheader / HeaderRate, (2) For 82.g, every 26 bts are encoded nto one symbol when the Lnk rate s 54Mbps, t and t can be expressed as: t = PLP / PlcpRate + N Rate + DIF + PROP (2) sbl t = t + IF + PLP / PlcpRate + AK / AckRate + PROP (22) MA = Header( MA + LL + IP + UDP) + UPay + F + ervce + Tal, (23) N bl = MA / ymbolze, (24) where Rate s 4µs/symbol and ymbolze s 26 bts n the 82.g standard, and N bl accounts for the number of symbols needed to encode a MA layer data unt. The system throughput can then be calculated by equatons (2)-(24). IV. Model Valdaton To valdate our analytcal model, we conduct smulaton studes on 82. pont-to-pont lnk. Two wreless statons are confgured n ad hoc mode and both of them generate saturated UDP traffc. We report the results of 82.b and 82.g WLANs n whch the RT/T scheme s dsabled. Table 2 lsts the of the PHY and MA parameters used n 82.b and 82.g standard. A. Throughput Analyss of 82.b In ths paper, our parameters n smulaton and analytcal model are all set accordng to the 82. standard. Fg. 4 plots the throughput of 82.b pont-to-pont lnk wth dfferent payload szes. We can observe that our analytcal model results are exactly the same as smulaton results. We also compare our model to Banch s model [5] n terms of throughput, under the set of PHY and MA parameters n Table 2. It s obvous that Banch s model devate from the smulaton results a lttle bt. Ths s because Banch s model assumes a constant and ndependent collson probablty, whch s only accurate when there are a large number of statons n the network. Meanwhle, n Fg. 4 we also present the throughput when W s set to 24. The throughput of W = 24 s slghtly lower than the throughput of W = 64, though the dfference s neglgble. In another word, our model can approxmate the system of W = 24 much better than Banch s model, though we assume W = 2W. B. Throughput Analyss of 82.g Fg. 5 shows the throughput results of 82.g. mlar to 82.b, our model s precse, whle Banch s model devates from the smulaton results a lot. A specal phenomenon n ths fgure s that the curve has a sawtooth shape, manly due to the feature of symbol encodng n 82.g. When sendng a packet, 82.g encodes every 26 bts nto one symbol; f the payload s not a multple of 26 bts, 82.g adds paddng bts. The paddng bts are consdered as overhead and not counted n our calculaton of throughput. Another observaton s that, the throughput of W = 24 s slghtly lower than the throughput of W = 32. Ths s because there are only two statons competng for the wreless channel. Table 2 IEEE 82.b and 82.g parameters [] [2] 82.b 82.g lottme 2 µs 2µs (n ad hoc mode) 2539

5 IFTme µs µs DIF 28 µs 28 µs aw 32 6 aw PLP Preamble 72 bts N.A. PreambleRate Mbps N.A. PLP Header 48 bts 2 bts HeaderRate 2 Mbps N.A. ervce + Tal N.A. 6 bts + 6 bts MA_Header 92 bts 92 bts LnkRate Mbps 54 Mbps Normalzed Throughput Banch's Model(W=32) Our Model(W=32) mulaton(w=32) Banch's Model(W=24) mulaton(w=24) AckRate 2 Mbps 24 Mbps ymbol Rate N.A. 4 µs/symbol.42 ymbolze N.A. 26 bts Normalzed Throughput Banch's Model(W=64) Our Model(W=64) mulaton(w=64) Banch's Model(W=24) mulaton(w=24) 2 3 UDP Payload (Bytes) Fgure 4: Normalzed Throughput of 82.b V. onclusons In ths paper, we proposed a precse Markov model to analyze lnk performance n IEEE 82. Pont-to-Pont networks. Ths model focuses on the analyss of system dle tme caused by the random backoff perod. We demonstrate that our model s precse for the case of W =2 W, and t also approxmates W = 2 m W for other values of m much better than Banch s model. Acknowledgement Ths work s supported by Hong Kong RG under grants HKBU 246, Hong Kong RG entral Allocaton grant HKBU /5, and Hong Kong Baptst Unversty under grant FRG/6-7/II UDP Payload (Bytes) Fgure 5: Normalzed Throughput of 82.g REFERENE 472 [] ANI/IEEE tandard 82., 999 Edton, Part : Wreless LAN Medum Access ontrol (MA) and Physcal Layer (PHY) pecfcatons. [2] IEEE 82. part : Wreless LAN medum access control (MA) and physcal layer (PHY) specfcatons, Amendment 4: Further hgher data rate extenson n the 2.4GHz Band, June 23. [3] Yang Xao, IEEE 82.n: enhancements for hgher throughput n wreless LANs, IEEE Wreless ommuncatons, December 25. [4] F.alì, M. ont, E. Gregor, IEEE 82. wreless LAN: capacty analyss and protocol enhancement, n Proc. of IEEE Infocom 98, pages 42-49, March 29 - Aprl 2, 998. [5] Guseppe Banch, Performance analyss of the IEEE 82. dstrbuted coordnaton functon, IEEE Journal on elected Areas n ommuncatons, Vol. 8, NO. 3, pages , March 2. [6] R. Karrer, A. abharwal, and E. Knghtly, Enablng large-scale wreless broadband: the case for TAPs, n Proc. of HotNets, ambrdge, MA, 23. [7] I. F. Akyldz, X. Wang, and W. Wang, Wreless mesh networks: a survey, omputer Networks Journal (Elsever), vol. 47, no. 4, pp , March 25. [8] A. Ranwala and T. cker hueh, Archtecture and algorthms for an IEEE 82.-based mult-channel wreless mesh network, n Proc. of IEEE Infocom 5, 25. [9] P. Kyasanur and N. Vadya, apacty of mult-channel wreless networks: Impact of number of channels and nterfaces, n Proc. of Eleventh AM Mobom 5, 25. [] P. Kyasanur, J. o,. heredd, and N. Vadya, Mult-hannel mesh networks: challenges and protocols, n IEEE Wreless ommuncatons, Aprl 26. [] J. h, T. alonds, and E. Knghtly, tarvaton mtgaton through Multhannel coordnaton n MA multhop wreless networks, n Proc. of AM MobHoc 6,