Throughput Analysis of an Extended Service Set in IEEE

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1 Throughut Aalysis of a xteded ervice et i 82. Mustafa rge, Baris udar, Pravi Varaiya {erge,dudar,varaiya}@eecs.berkeley.edu et. of C at Uiversity of Califoria Berkeley Abstract this aer, we itroduced a ovel method to determie the throughut of a exteded service set i 82. etwork. The method leverages idoor radio roagatio models ad R redictio. We itroduce a ew aalytical Markov Model of C access mechaism. Markov Model itroduced here has caability to suort o-saturated traffic ad differet data rates. 82.a is selected as the hysical layer ad more tha oe access oit has bee cosidered i the aalysis.. NTROUCTON Wireless Local Area Networkig has bee roliferated after the stadardizatio; with the raid decrease i the rice of the 82. radios, 82. chis have bee itegrated to most of the gadgets of moder life. Wireless etwork erformace is becomig more ad more imortat for eterrisers deloyig busiess-critical wireless etworks. As the etworks grow i size ad become a itegral art of our daily life, throughut itesive alicatios like voice over WLAN are also gaiig oularity. such alicatios, where etwork throughut erformace is critical, detailed etwork laig, moitorig ad maagemet become essetial. Network laig icludes detailed site surveys, determiig the umber of access oits, locatios, access oit cofiguratios. Curretly, choosig how may access oits to deloy, where to lace them are ad hoc rocesses ad ca be very time cosumig. this aer, we reset a software simulatio latform which automates all of these issues. Our simulator cosists of a 3- R redictio egie which models the R eviromet as well as the iteractios betwee the devices ad a throughut estimatio egie which estimates the idividual throughut of the mobiles ad APs usig the R redictio data ad aalytical Markov model of 82. [], [2]. The simulator ca be used i the detailed laig of a wireless LAN or it ca be used as art of a real-time etwork maagemet system which moitors the etwork i real-time ad takes theraeutic actios deedig o the state of the wireless etwork NTWORK ARCHTCTUR 82. etwork itroduces two differet chael access mechaisms: istributed Coordiatio uctio (C) ad Poit Coordiatio uctio (PC) [4]. C is a based rotocol which imlemets Collisio Avoidace Carrier ese Multile Access Mechaism CA/CMA. PC is o the other had has a oit coordiatio fuctio which schedules trasmissio. C is widely used access mechaism ad it is based o cotetio. tatios cotet for the chael ad whe they fid chael busy they for a iterval. igure 2 shows a time realizatio for 6 statios ad medium. order to overcome hidde statios, RT/CT exchage has bee itroduced. tatio who has acket to trasmit first trasmits RT acket ad waits for the CT from the addressee. After gettig CT, data acket is set ad receivig comletes the trasmissio. etectig the chael before trasmissio at least amout of time after successful acket trasmissio ad amout of time after collisio are madatory [4], [], [6].. NOOR R PROPAGATON Pheomea related to R roagatio, like multi-ath roagatio, reflectio, diffractio ad shadowig have a sigificat ifluece o the received ower. o, the roagatio models should cosider these heomea to obtai accurate results. The redictio model used i the simulator is a variat of the COT 23 Multi Wall Model with some additios for otimizig the ray-tracig imlemetatio. This 3- model calculates the ath loss accordig to both the distace betwee the trasmitter ad receiver ad the eetratio losses through walls ad ceiligs. The equatio is as follows; L = L + L e + k wi L wi + kf L c () i= [ kf ] +2 k f + b where L is free sace loss of the ath i db, L e is costat excess atteuatio of the ath i db, L wi is loss of wall tye i i db, L c is loss betwee adjacet floors i db, k wi is umber of walls of wall tye i eetrated by the ath, k f is the umber of ceiligs eetrated by the ath, is umber of wall tyes, b is multi-floor arameter. V. R PRCTON R redictio models, beig caable of redictig the ath loss betwee the trasmitter ad receiver ateas, are basic tools i coverage redictio ad throughut estimatio i wireless LANs. Our simulator uses the 3-d R roagatio model to comute the R coverage iside a buildig, the model also takes ito accout the R iterferece caused by uwated or iterferig devices reset i the eviromet. additio to advaced modellig techiques it is essetial that the erformace of the roagatio models is verified by

2 AT A (7 slots) (9 slots) (9 slots) RT CT tatio defers ATA tatio sets uo receivig RT tatio defers, but kees couter (=2) tatio sets uo receivig RT tatio defers tatio defers ew ( slots) remaiig (2 slots) RT RT RT CT tatio defers tatio defers tatio defers tatio defers ATA 2 (a) AP Coverage (dividual Throughut/ ata Rate) (b) igal Power Ma ig.. Proagatio Model imulatio TA TA 2 TA 3 TA 4 TA TA 6 Medium uccess ig. 2. uccess Collisio C Procedure uccess comariso with measuremets. everal extesive measuremet camaigs have therefore bee carried out usig the ite urvey tool which was develoed to validate the accuracy of the R roagatio model used i the simulator ad to calibrate the model if eeded. Kowig the data rate ad access oit of each statio we ca determie the system throughut by usig a aalytical model of 82. itroduced first i [2] ad exteded at []. V. THROUGHPUT ANALY The aalytical model derived here is based o semi-discrete Markov chai model. imilar to the models i [2], [7], [8] C is rereseted by a two dimesioal Markov chai. throughut aalysis we cosider the saturated ad o-saturated case where the statio always has acket to trasmit ad the statio trasmits with robability λ. The derivatio has two hases first obtaiig the τ which is the robability that the statio trasmits a acket i a give slot time ad the lacig the τ i throughut calculatio. Observatio of the time leads to idetify the oeratio i terms of slots (ee igure 2). There is either a emty slot durig which the couter is decremeted, or a trasmissio durig which the couter stays the same. Therefore, the evets that drive the Markov model are emty slot or trasmissio. regard to this, Markov chai show i ig. 3 has two dimesios which are s(t) ad b(t) reresetig deth ad state umber resectively. Adotig the key aroximatio time i [2], reresets the coditioal collisio robability ad is ideedet ad costat i each acket collisio regardless of the umber of retrasmissios suffered. also stads for robability of detectig the chael busy. Havig b i,k, i (, m), k (, W i ) as the statioary distributio we ca solve this Markov chai by balace equatios. um of the robabilities of each state is equal to, = m i= W i k= b i,k (2) order to fid the τ, we eed the statioary robability of b,. Packet is trasmitted i states b i, where i (, m). We ca exress the trasmissio robability τ as τ = m b i, (3) i= Whe the statio is ot i the saturatio state, statio waits i the idle state for a acket that is set from uer layers to trasmit. That corresods to delay i the idle state. Oe ca ifer that the dashed box rereset the idle state with λ traffic robability. τ is τ = ( 2)(W +)+W ( (2) m ) 2( 2)( ) + ( )( λ 2 ) where cotetio widow doubles with W i = 2 i W ad where i the equatio is ut to make the equatio cosistet with the saturatio oeratig case (λ = ). ice addig additioal states itroduces at least oe slot time delay to the system. Whe there is o that will result i a situatio where the statio waits oe slot time for trasmissio. Although this will ot have sigificat value whe λ is high, it is imortat to ote the characteristic of modellig a fiite state machie by a Markov model. τ is a fuctio of τ(, m, W, λ) where oly is ukow. τ should deed o the umber of active users sice it is highly (4)

3 3-2,W -2-2, (-)/W (-)/W -, -, -,2,W -2 -,W /W - i, /W i /W i - i, - i, - i,2 i,w i -2 - i,w i /W i+ /W m - m, - m, - m,2 m,w m -2 - m,w m /W m /W m ig. 3. Markov Model for the 82. C Model i Normal Oeratig Coditio Throughut (Mbs) 2 2 Without RT/CT λ=. λ=. λ=.2 λ= ig. 4. ata Rate=4Mbs w/o RT/CT correlated with. Collisio robability deeds o the active umber of statios. Therefore ad τ i steady state are tied by equatio 4 ad = ( τ) or τ() = ( ) ( ) () Now, τ is a fuctio of kow variables τ(, m, W, λ). ice (, ), τ (, ) ad both equatios (4) ad () are cotiuous, the solutio of τ is uique. ollowig [2], the throughut is the fractio of time the chael is used to successfully trasmit ayload bits. efie the robability P tr that there is at least oe trasmissio i the cosidered slot time ad the robability P s that a trasmissio occurrig o the chael is successful as P tr = ( τ) P s = τ( τ). Let s exress the total throughut as the ratio = (6) P s [P ] ( P tr )σ + P s T s + (P tr P s )T c. (7) where [P ] is the average acket ayload size, P s is the robability for successful trasmissio. The average legth of emty slot time is with robability P tr ad with robability (P tr P s ) there is a collisio. T s is the average time the chael is sesed busy due to a successful trasmissio, ad T c is the average time the chael is sesed busy by each statio durig a collisio. σ is the duratio of a emty slot time [2]. or two differet access mechaism the time values are rereseted i equatio 8. T AT A is the time that takes to sed a acket with size [P ] ad T RT,T CT,T are the times that take to sed the corresodig frames. TAT A stads for average time that takes to sed [P ] which is the average legth of the logest acket ayload ivolved i a collisio. Whe all ackets have the same size, [P ] = P = [P ] [2]. δ is the roagatio delay. Ulike the basic access mechaism Tc rts oly cotais T RT sice oly ossibility to exeriece a collisio occurs i the RT frame trasmissio.

4 λ. λ 2 2 Max. λ. Mea λ. Mi. λ. Max. λ Mea λ Mi. λ 6 Total Throughut 6 Throughut Mbs (a) Total Throughut (b) dividual Throughut ig.. Performace whe there are AP Total Throughut Mbs Total Throughut dividual Throughut #Access Poits (a) Total Throughut whe there are TAs dividual Throughut Mbs Throughut Mbs Throughut Mbs 2 data ata Rate Mbs 3 data 2 2 liear ata Rate Mbs 3 data 3 Throughut Mbs ata Rate Mbs (b) Utilizatio ig. 6. Performace ad Utilizatio T basic s = T AT A + + δ + T + δ + = TAT A + δ + = T RT + + δ + T CT + + δ + T AT A + + δ + T + δ + c = T RT + δ +. T basic c Ts rts T rts (8) 82.a hysical layer (PHY) uses OM for the modulatio scheme. 82.a PHY rovides eight PHY modes with differet modulatio schemes ad codig rates as see i igure 7. NR values are rorietary by vedor. The above aalysis lead us to obtai the duratio of each acket. Trasmissio duratio of a frame with [P ] octets data ayload with the 82.a PHY 7 is as follows [6]; T AT A (m) = 2µs + [ 28+(6+6)/8+[P ] B(m) ] 4µs T RT (m) = 2µs + [ 2+(6+6)/8 B(m) ] 4µs T CT (m) = T (m) = 2µs + [ 4+(6+6)/8 B(m) ] 4µs. () igure 4 shows the system erformace of sigle access oit i differet traffic itesities. The key cotributio of the formula is to itroduce idividual throughut if the data rate is differet for each user. The 82. gives the same chace to each user eve if the data rate is differet. ata rate oly chages the duratio values thereby average

5 T s = Ps i= i Ts i T c = i= j= j k= ( k j l= t i ) T j c τ i+ ( τ) i (9) rame Cotrol Rate 4 - Bits uratio/ Reserved - Bits PLCP Preamble 2 - ymbols MAC Header Address PLCP - Header Legth 2 - Bits Address 2 Parity - Bits Coded - OM BPK Rate = /2 igal () OM ymbol PPU Address 3 Tail 6 - Bits eq. Cot. ervice 6 - Bits Address 4 PU Coded - OM Rate idicated by igal ymbol rame Body -232 Tail 6 - Bits ata Variable umber of OM ymbols 6 microsecods 4 6, 9, 2, 8, 24, 36, 48, 4 Mb ig. 7. C 4 - Octets Pad Bits Modulatio Code Rate ata Rate B NR BPK, ½ BPK / QPK, ½ QPK, / QAM, ½ QAM, / QAM, ½ QAM. / a OM Packet duratio value chages. uccessful duratio is the average of the duratio of each user ad collisio duratio is determied by the logest duratio of the statio ivolvig i the collisio. f Ts i ad Tc i are the duratio for data rate i ad if i is the umber of odes with data rate i, the exected duratio values are calculated i equatio 9; where is the total umber of data rates suorted ad = i= i. Throughut of TA x i is as follows; i = P s [P ] ( P tr )σ + T s + T () c V. PRORMANC ANALY We used fixed floor la to determie the throughut. Access oit ower levels are re-selected betwee 2mW ad mw. [P] is costat ad 24 bytes. tatios are distributed ly ad statios that falls out of ay AP coverage are cosidered iactive. All access oits are set to the same chael to see the egative effect of iterferece. Variables are umber of access oits, umber of statios ad traffic itesity. igure (a) deicts the system whe there are fixed AP as see i igure (a). The umber of statios scattered are varied ad aalysis is reeated for two differet traffic itesity which are. ad. The figure deicts that the total etwork throughut is also almost cocave as i igure 4 where a sigle access oit erformace is illustrated. igure (b) illustrates the idividual throughut of the statios whe the iactive statios are deducted. This grah is useful to observe the miimum idividual throughut of the etwork. igure 6 shows the throughut erformace of the system whe the umber of access oits are, 8 ad 2. As the access oits icrease i umber, the total throughut of the system ad idividual throughut also icrease. This is because of the icrease i the sigal stregth i each oit ad decrease i the umber of statios associated to a access oits. We exect decrease i the erformace whe there is a icrease i the umber of statios. Although the data rate of each statios are determied by the distributio ad fixed locatio of the access oits, the throughut erformace ca be abstracted out by lookig at the idividual utilizatio of each statio which is defied as idividual throughut/data rate. The average utilizatio versus the umber of odes for two differet traffic itesity has bee showed i igure 6(b) ad figure cofirms the decrease i utilizatio. V. CONCLUON A ovel idoor radio roagatio model has bee cosidered with a ovel aalytical throughut model to determie the system throughut of a 82. etwork. Markov Model itroduced i [2] has bee modified for osaturated traffic ad differet data rates. Cosiderig differet data rates for each statio is aother modificatio i the throughut aalysis sice duratio values of successful trasmissio ad collisio ow becomes deedet to the data rates of each statio. door Radio roagatio simulatio determies the coverage area of each access oit ad sigal to oise ratio of each statio. igal to oise ratio sets the data rate of the statio ad umber of associated statios to a access oit is determied by the umber of statios whose locatio falls ito the coverage of the access oit. Performace aalysis has bee coducted for varied umber of access oits ad statios. RRNC [] M. rge, P. Varaiya, Admissio Cotrol ad Throughut Aalysis i 82. aear o ACM-Kluwer MONT ecial ssue o WLAN Otimizatio at the MAC ad Network Levels. [2] G. Biachi, Performace Aalysis of the 82. istributed Coordiatio uctio td , Vol., 22 Pages: URL: Joural o elected Areas i Commuicatios, Vol 8, No. 3, March 2. [3]. Qiao,. Choi, K. G. hi, Goodut Aalysis ad Lik Adatatio for 82.a Wireless LANs Trasactios o Mobile Comutig, VOL, NO.4, October-ecember 22. [4] 82., Wireless LAN Medium Access Cotrol (MAC) ad Physical Layer (PHY) ecificatios, tadard,, Aug [] Part : Wireless LAN, Medium Access Cotrol (MAC) ad Physical Layer (PHY) ecificatios: High-eed Physical Layer xtesio i the 2.4GHz Bad, sulemet to 82. tadard, et [6] 82.a, Part : Wireless LAN Medium Access Cotrol (MAC) ad Physical Layer (PHY) ecificatios: High-eed Physical Layer xtesio i the 2.4GHz Bad, sulemet to 82. tadard, et [7] H. Wu, Y. Peg, K. Log,. Cheg, J. Ma, Performace of Reliable Trasort Protocol over 82. Wireless LAN: Aalysis ad hacemet [8] Y. Xiao, A imle ad ffective Priority cheme for 82., Commuicatio Letters, VOL. 7, No. 2, ebruary 23. [9] M. rge, 82. Tutorial htt:// erge /docs/ieee.df