Research Article A Comparison Performance Analysis of QoS WLANs: Approaches with Enhanced Features

Transcription

1 Hndaw Publshng Corporaton Advances n Multmeda Volume 007, Artcle ID 387, 3 pages do:055/007/387 Research Artcle A Comparson Performance Analyss of QoS WLANs: Approaches wth Enhanced Features Ioanns Papapanagotou, Georgos S Paschos, and Mchael Devetskots Department of Electrcal and Computer Engneerng, North Carolna State Unversty, PO , Ralegh, NC 7695, USA Natonal Research Insttute of Fnland VTT, 050 Espoo, Fnland Receved 30 May 007; Accepted 3 July 007 Recommended by Stavros Kotsopoulos The man contrbuton of ths work s to compare and enhance known methods for performance analyss of the IEEE 80e MAC layer, such as the use of Markov chans, queung theory, and probablstc analyss It s the frst paper that bases ts outputs upon comparson of metrcs such as complexty, flexblty, and accuracy, leadng to the novel use of a metamodelng comparson For the analyss, complexty theory and the L-square dstance method for accuracy are used In addton, the proposed analyses carry by themselves scentfc nterest, because they are extended enhancements wth the latest EDCA parameters A form of the PMF of the MAC delay and frst-order moments are found usng the PGF complex frequency doman functon The analyses ncorporate a Gaussan erroneous channel n order to reflect the real condtons of the MAC layer Copyrght 007 Ioanns Papapanagotou et al Ths s an open access artcle dstrbuted under the Creatve Commons Attrbuton Lcense, whch permts unrestrcted use, dstrbuton, and reproducton n any medum, provded the orgnal work s properly cted INTRODUCTION The wde deployment of WLANs has set an ncreased pace for extensve scentfc studes of the IEEE 80 standard [] In addton, heterogeneous multmeda applcatons requre advanced edtng over the standard, so as to accomplsh specfc QoS characterstcs [] Accomplshng such QoS features wll make capable transmsson of vdeo and voce over new 3G-WLANs [3] The core 80e standard proposes a new hybrd coordnaton functon (HCF, whch has the HCF controlled channel access (HCCA and the enhanced dstrbuted coordnaton access (EDCA mechansms, capable of offerng access accordng to specfc QoS features A typcal lterature search demonstrates a number of performance analyses for the legacy IEEE 80 and 80e [4 7] or smlar enhancements [8], whch ncorporate dscrete tme Markov chans (DTMC Other models, such as [9 ], use alternatve methods of analyss A trend has developed, snce [4] frst presented hs case study, to mprove and provde more accurate performance values Due to the subject maturty, the space left for new models that could prompt scentfc nterest s small Our novel approach s to propose amendments over these known analytcal methods, fnd ther accurate values, and open a new feld of performance comparson It s straghtforward that, snce new protocols tend to be analyzed by ether DTMCs, queung theory, or general probablstc methods, the results of the proposed methods can be used to fnd the best method of analyzng forthcomng or known standards We have used three known models [5, 0, ], whch depct the three man methods of analyss, and they are extended accordng to QoS features proposed n the dote standard and error-prone channel The frst model uses DTMC analyss, whch takes nto account the state of the prevous slot The second one s based on elementary condtonal probablty arguments, and fnally, n the last model, queung theory and Lttle s theorem are used to analyze the standard Accurate values of delay and a way for calculatng the PMF of the MAC delay are also gven The proposed analyss alteratons carry by themselves scentfc nterest, and couldbestudedseparately Except from some already nvestgated features of the dote, addtonal ones have been added These performance enhancements are summarzed n the followng ( In our models, the effect of dfferent retransmsson lmts among the access categores s mplemented ( Freezng of backoff counters s taken nto account

2 Advances n Multmeda ( A more accurate equaton of saturaton throughput s provded n correlaton wth a way of ncorporatng the AIFS dfferentaton phenomenon among the access categores (v It was also noted that hgher ACs monopolzed relatvely quckly the channel, especally when the type of multmeda traffc was bursty After revson of D40 of the IEEE 80e standard [], the standard defned that after a successful transmsson, the AC should get back to backoff, and contest agan for the channel n the next tme slot Ths means that the state 0 of the DTMC cannot be chosen after a successful transmsson a feature that older models have omtted or partly mentoned [], but not analyzed (v The proposed models nclude Gaussan erroneous channel for EDCA Although some works exst, for example, [3, 4], they tend to analyze such problems by mplementng the bt error rate (BER probablty n the busy probablty, whch means that an error can make the channel busy Snce the MAC layer n the backoff level does not see errors and nner codes n the sublayers provde a specfc codng gan, the erroneous channel mplementaton should be made n the performance analyss (v We analyze n the same envronment the effect of Block-ACK and the effcency of the new IEEE 80n ntroducng much hgher transmsson rates (v Most of the aforementoned analyses tend to gve results for the basc transfer rate, n whch analytcal features such as the dual effect of the RTS/CTS n throughput are not shown In our models, these are corrected whle addng new features and gvng the exact soluton wth RTS/CTS, basc access mode n Mbps, and multples of 4 Mbps transfer rate (v Z-transform s also used for the PGF of the MAC delay, and frst-order moments are found through ts frst and second dervatves The proposed analyss alteratons carry themselves scentfc nterest, and could be studed separately Addtonally, a metamodelng analyss s added, by processng the mathematcal performance and smulaton outcomes Thus results aregvenntermsof ( complexty, based on bg-o notaton; ( accuracy, based on L-square dstance; ( depcton of the states of the MAC protocol, nonsaturaton easness of mplementaton, and flexblty The smulaton results are based on the HCCA model ncluded n the last verson of OPNET modeler The proposed models requre advanced knowledge of [, 4, 0], snce formulas and other proved explanatons are taken as prerequstes The paper s organzed as follows In Secton, we provde numercal analyss of the transmsson probablty (τ and mean backoff duraton (E[BD] ofeachofthe three models In Secton 3, takng nto account the values of throughput and delay the transmsson rates are extracted, wth varous condtons of the channel and features enabled or dsabled A thrd subsecton s also gven for the anal- Table : 80e EDCA standard parameters AC0 AC AC AC3 Type of servce VoIP Vdeo Best effort Backround CWmn[] CWmax[] AIFS[] SIFS+ SIFS+ SIFS+3 SIFS+7 yss of the Block-ACK feature In Secton 4, valdaton,results, and comparson analyss and evaluaton are provded In Secton 5 a conclusve dscusson s made upon advantage and dsadvantage of each one NUMERICAL ANALYSIS OF THE MODELS In [], qualty of servce succeeded va usng four access categores (ACs wth dfferent transmsson parameters each The standard uses dfferent values of AIFS[], CWmn, CWmax and backoff persstent factor (πf, ={0,,, 3} Fnally, transmsson opportunty (TxOP s the maxmum amount of bytes that a staton s allowed to transmt consecutvely before t releases the channel In ths paper, all ACs are consdered to send packets wth equal number of bytes below TxOP lmt and therefore TxOP s not studed We defne W,0 = CW,mn +,wherew,j s the contenton wndow sze and j s the backoff stage m s defned as the retry lmt, after whch the contenton wndow remans the same for a number of retransmssons When the backoff exponental algorthm reaches L (long retry lmt tmes of retransmsson and there s a collson, the packet s dropped In the legacy 80 [], persstent factor (πf has the value of, whch means that after every collson, the backoff contenton wndow doubles ts value In [], persstent factor can have dfferent values accordng to each access category ( jw,0 πf, j = 0,,, m, W,j = ( m πf W,0, j = m +,, L, where s the closest nteger functon In Table, a summary of the EDCA s presented Before defnng the mathematcal analyss, the followng assumptons have been made regardng all models The number of statons N s fnte and equal for all ACs and contends only n a sngle-hop network There s a constant packet generator and the network s saturated, whch means that there s always a packet ready to transmt n each termnal The channel s erroneous, wth unform dstrbuted errors, and there are no hdden termnal, capture effects, and lnk-adaptaton mechansms Fnally, as n all exstng models, the transmt probablty s consdered to be ndependent per staton Markov chan model (model A three-dmensonal DTMC s proposed, whch presents the effect of contendng termnals on the channel access probablty of each access class (AC, and s descrbed by the statonary probabltes b,w,j,k The parameter = {0,,, 3} (

3 Ioanns Papapanagotou et al 3 /W,0,,0,,,0, p,,,0,w,0,,0,w,0 p,0,0,0,0 p, p,0 p, p,0 p, p,0 p, p, p, p, p p,0 p,0,0,0,0,,0,0,,0,0,w,0 p,0 /W, p, p,0 /W,j /W,j /W,j /W /W,j,j /W,j p, p, p, p, p,,,j,0,,j,,,j,,,j, W,j,,j, W,j p, p, p,0 p, p p, p,0 p,0, p,0 p,0 p,0 p,0,0,j,0,0,j,,0,j,,,j, W,j /W,j+ p,0 p, p,0 /W,L /W,L /W,L /W,L /W,L /W,L,,L,0 p, p, p,,,l,,,l,,,l, W,L p,,,l, W,L,0,L,0 p, p, p, p, p,0 p,0 p,0 p,0 p,0 p,0,0,l,,0,l,,0,l, W,L Fgure : Analytcal Markov chan for each access category AC[] descrbes the four access categores, whch dfferentate the access method accordng to the dote standard The frst dmenson, w, represents the condton of the prevous slot, where s for the busy channel and 0 for the dle channel Smlar to [5], a dvson s needed snce specal cases exst accordng to the state of the prevous slot If t was dle, all access categores of all statons may access the channel f ther backoff counter s decremented to zero On the other hand, f the prevous slot was busy, another dvson must take place A busy slot can occur f there s a collson or a transmsson of another staton In the frst case, the statons that dd not partcpate n the collson have frozen ther backoff counter and wll not be able to transmt Instead, the statons that collded can transmt n the next slot f they choose a new backoff value equal to 0 In the second case, when there s a successful transmsson, none of the statons can transmt n the next tme slot Ths happens specfcally for the standard IEEE 80e and not for the legacy IEEE 80 The latest defnes that after a successful transmsson, the contenton wndow starts from and not from 0 All these are consdered n the provded analyss and shown n the DTMC of Fgure, whch refers to each access category separately Note that the state {,,0,0} s mssng The other two symbols are j for the backoff stage descrbed above and k whch accounts for the backoff delay and takes values k [0,,, W,j ] for w = 0, k [0,,, W,j ] for j>0andw =, and k [,, W,j ] for j = 0andw = In [5], a smlar DTMC s used for the legacy dot Ths model s extended consderably so as to nclude all the new characterstcs of dote and a fnte retry lmt Our analyss also devates from [5] snce the frst state of the chan does not exst The probablty p,0 (or p, s that another termnal s access category s transmttng after an dle perod (or after a busy perod, wthout errors The opposte case, that the channel remans dle after an dle perod, s represented by q 0 (or after a busy perod q After these explanatons, all the transtons of the DTMC have been verfed and the followng equatons are accrued: b,,j,0 = ψ,j b,0,0,0 ( for j =,,, L, b,,j,k = +p (,0 W,j k ψ p,j b,0,0,0 (3, for k =,,, W,j andj = 0,, L, b,0,j,k = ( W,j k ψ,j b,0,0,0 (4

4 4 Advances n Multmeda for k = 0,,, W,j andj =,, L,where W 0, j = 0, p,0, j =, W ψ,,j = p,0 Π,j, j =, 3,, m, W, p,0 Π,m P,j, j = m +,, L W, Π,j and P,j are defned as j [ p, Π,j = + p,0 ( W,x ], W x=,x W,x j [ p, P,j = + p,0 ( W,m ] x=m + W,m W,m Applyng the normalzaton condton for each access category s DTMC, as each exponental backoff algorthm runs ndependently, we have W,0 k=0 W,0 b,,0,k k= L [ W,j W,j b,0,0,k + + j= k=0 b,0,j,k + k=0 b,,j,k ] = (5 (6 (7 After solvng ths equaton, b,0,0,0 s found as b,0,0,0 = ( p, K + Λ, (8 K = W,0 ( p, + p,0 ( W, ( p, +p,0 (W,0 + 4, L [( Λ = ψ,j W,j W,j ( (9 ] p, + p,0 + j= The probabltes of accessng the channel n a tme slot, whether the prevous slot was dle or busy, are gven by the followng equatons: τ,w = m j=0b,0,j,0 + L j=m b,0,j,0 P dle,, w = dle, m j=b,,j,0 + L j=m b,,j,0 P dle,, w = busy, (0 where P dle s derved by the soluton of P dle = q 0 P dle +q ( P dle, and descrbes the probablty that the channel s dle n the prevous tme slot (take notce that ths s dfferent from the current dle slot symbolzed below as P dle Successful transmsson probablty The probabltes that the channel remans dle after an dle (or busy tme slot can be found n a straghtforward manner by supposng that no other staton transmts n that tme slot: 3 ( N q w = τ,w ( =0 Channel AC[] AC[] Busy channel Backoff = AIFS[ ] Backoff = 0 E[Ψ] AIFS[ ] Busy channel Fgure : The AIFS dfferentaton prevents a collson that otherwse would have happened The probablty of another AC transmttng s relatvely complex Except from the other staton s AC transmton, an ntercollson handler and vrtual collson handler must also be taken nto account In the proposed analyss, such a collson handler s also mplemented, addng as well as a correlaton measure whch gves a close approxmaton of the ntercollson problem The phenomenon of ntercollson happens when two ACs have dfferent AIFS, and the one wth the hgher AIFS and hgher E[Ψ] has a smaller backoff value Thus t may happen that these ACs wll collde and the dfferentaton offered from the use of AIFS wll be lost see Fgure : r ( [, = max AIFS[ ] [ ] ] AIFS,0,, E[Ψ] ( where E[Ψ] s the mean consecutve number of dle slots The notaton mn s used to mantan the accuracy of the model: ( Pdle E[Ψ] = mn, (3 P dle Ths specfc correlaton measure smplfes the analyss, because t does not ncrease the complexty of the mathematcal analyss when tryng to solve the DTMC Therefore, the probabltes of a transmsson falure (takng nto account the collson probablty and error probabltes after an dle or busy slot are p,0 = z< TX ( τz,dle Nz r(z, ( N 3 ( Nz τ,dle τz,dle, z> p, = ( τ,busy N 3 z> (4 ( τz,busy Nz (5 The successful transmsson probablty n a tme slot of an AC s ( Nz r(z, P s, = P dle N τ,dle τz,dle z< ( N ( Nz τ,dle τz,dle z> + ( P dle N τ,busy ( τ,busy N z> ( τz,busy Nz (6

5 Ioanns Papapanagotou et al 5 Mean backoff duraton E[BD] s defned as the mean backoff delay, whch s the sum of the backoff transtons E[X] when the channel s dle, and the delay due to freezng E[F], all of whch referrng to each AC: E[BD] = E[X] σ + E[F] (7 The backoff transton delay s E[X] defned as the number of slot tmes k that are needed for the AC to reach state 0 and transmt, consderng that the counter s at the state b,,j,k or b,0,j,k The number of tmes the counter s stopped (freezes s not taken nto account, as they are calculated separately n (0 E [ L W,j ] j=0 k=0 kb,0,j,k X = (8 P dle After some algebra, the backoff transton delay s found as E [ X ] = b,0,0,0 M, P dle L ( M = ψ,j W,j ( W,j ( 4W,j 3, j= (9 and the delay due to freezng of the backoff counter s calculated as follows Note that the denomnator of E[F] s the exact opposte of the denomnator of E[X] : E[F] = E[ N f ] P dle [ 3 P s, T s, + PcT c, ], (0 =0 where E[N f ] s the number of freezes, and t s analyzed as the fracton of the mean value of the counter E[X] dvded wth the mean consecutve number of dle slots, defned n (3 In order to fnd the MAC delay, the mean delay must be subtracted from the droppng delay defned as ( E[Drop] = b,0,0,0 Tc + T protect ψ,l [ ] +p,0 (W,L p, +(W,j p,0 p, ( Elementary condtonal probablty analyss (ECPA The proposed probablstc analyss s smpler than the prevous soluton of DTMC, because t s based on condtonal probabltes of each access category ndependently [0] Two events are defned here The frst s called TX and means that a staton s AC s transmttng a frame nto a tme slot, and the second s s = j s that the staton s AC s n backoff stage j, wherej [0, L ], whenever L s dfferent n basc and RTS/CTS method accordng to the short and long retry lmt From Bayes theorem, we have P ( TX P ( s = j TX P ( TX s = j = P( s = j ( Successful transmsson probablty From [0, equatons ( (7], wth amendments so as to nclude the four ACs ( ={0,,, 3}, we have that the transmsson probablty can be wrtten as τ = (( ( p / p L + L j=0 p j (+E[BD],j (3 In order to nclude the freezng of the backoff counters, a dstncton must be made The nterrupton of the backoff perod of the tagged staton can occur by three dfferent events and s analyzed as follows The frst s the collson of two or more statons, the second s the transmsson of a sngle staton other than the tagged one, and the thrd s the transmsson of a sngle staton p s the probablty that the tagged staton s nterrupted the transmsson of any other staton (one or more beng p = z ( τz Nm,z (4 and N m,z = N z δ m,z (δ m,z s the Kronecker functon [5] The probablty that the tag staton s nterrupted by the transmsson of a sngle staton (one exactly s gven by p = ( N τ ( τ N ( Nz τz (5 z> Mean backoff duraton In order to fnd the mean backoff duraton, the duraton of each exponental backoff must be found, whch should nclude the fnte lmt of CW H[j ] and the freezng of backoff counter each tme the slot s detected busy For example, f there were k freezngs, then the delay would be E[SD],j = CW H[j ] k=0 (kp k ( p, whch gves fnally E[SD],j = CW H[j ] ( p (6 Takng nto account all the possble seres of the exponental backoff, the mean backoff duraton s gven from CW, BD k,j, 0 j m, E[BD],j = CW k=0,j E[BD],m, m j L 3 Queung network (QN model analyss (7 Ths analyss s based on the Cho et al [] queung model In our model, the approach towards the network s dfferent than any one proposed before, because t models the behavor of each AC, whch contans N statons nstead of a sngle staton, ndependently (see Fgure 3 Except from that, each backoff stage s modeled by a G/G/ queung system

6 6 Advances n Multmeda p 0 p 0 p 0 p 0 AC[0] p 0 p 0 p 0 p 0 p 0 Queue 0, 0 Queue 0, Queue 0, m 0 Queue 0, L 0 λ 0,0 λ 0, λ 0, λ 0,m0+ p 3 p 3 p 3 p 3 AC[3] p 3 p 3 p 3 p 3 p 3 Queue 3, 0 Queue 3, Queue 3, m 3 Queue 0, L 3 λ 3,0 λ 3, λ 3, λ 3,m3+ Fgure 3: Queung network model and analyzng the backoff duraton wth Z-transform An nfnte number of parallel servers are used so that each queue can serve all statons smultaneously wthout queung delay In addton, the queung delay s found by takng nto account the freezng of backoff counters Smlar to the prevous two models, the frst queue has less length than the other ones Ths soluton s based on the assumpton that the transmsson probablty can be expressed as the total attempt rate λ, dvded by the number of statons of each AC ndependently: τ = λ (8 N Let us defne λ,j as the arrval rate and μ,j as the average servce rate, at each queue of each AC, where μ,k s found from the backoff duraton of each queue, whch s calculated from the Z-transform of each queue gven below From Lttle s theorem, the number of statons n each queue and n each AC can be found by N,j = λ,j μ,j (9 The transton probablty from one queue to the next onesrelatedthearrvalrateshowever,tshouldbenoted that a small dfference s found from queue 0 to queue, as t has been explaned that the value 0 of the frst backoff wndow s not chosen: λ,j+ = p λ,j, j = 0,, L, (30 where the total attempt rate λ s gven by L p L+ λ = λ,j = λ,0 (3 p j=0 and the average servce rate of each queue s found from μ,j = (3 +E[BD],j The reason for addng wth E[BD],j s that to get out of the queue one more slot s requred, correspondng to transmsson 3 Successful transmsson probablty Havng calculated λ,j and μ,j, we can use agan Lttle s theorem: L L N = N,j = λ,0 p j ( +E[BD],j (33 j=0 j=0 In (33, the sum s too complcated to be solved and t needs computer mathematcal tools Fnally τ s computed from (8: τ = λ N = (( p / ( p L + L j=0 p j (+E[BD],j (34 From the above mathematcal results, we can see that (3 and(34 are the same So both types of solutons gve smlar results Thus to fnd the probablty of successful transmsson n both models, we use ( Nm,z P s, = N τ τz (35 3 Mean backoff duraton z The mean backoff duraton s smlar to the one analyzed n the ECPA analyss 3 THROUGHPUT AND DELAY 3 Saturaton throughput 3 Block-ACK dsabled The saturaton throughput for every AC and for packets wth mean length E[L] sgvenby S = p e,p s, E[L], (36 T slot, where 3 [( ] ( T slot, = P dle σ + pe, Ps, T s, + Pc + pe, P s, Tc, =0 (37

7 Ioanns Papapanagotou et al 7 ( p e, P S, p e, P S, Performance level P S, P c P dle Backoff level P dle Fgure 4: Probablty spaces n the analyss of 80 standards for error behavor As shown n Fgure 4, the probablty of error affects the successful transmsson probablty only Thus whenever both the events of successful transmsson probablty and error happen, they are regarded as collsons Snce the errors are unformly dstrbuted, the error events are ndependent and dentcally dstrbuted (d thus the frame error probablty s gven by p e, = ( p data e, ( p ACK e, ( p RTS e ( p CTS e (38 pe, data and pe, ACK show the unformly dstrbuted errors n the data packet and n the acknowledgment, and the same apples for the probabltes pe, RTS and pe, CTS whch are used only n RTS and CTS access method If Basc access method s used, then pe, RTS = pe, CTS = 0 Then the collson probablty s 3 Pc = P dle P s, (39 =0 We must also menton that whenever the retry lmt s reached, the packet s dropped However such a probablty s ncluded n Pc, and the retransmssons requred after a collson or a drop are based on the upper layer and do not affect the performance of the studed MAC layer 3 Block-ACK enabled Another characterstc of the IEEE 80e standard s the Block-ACK feature, whch s not oblgatory However Block- ACK can mtgate the overhead problem, especally n hgher data rates whch are supported by the forthcomng 80n Data rates of nearly 43 Mbps tend to have 0% of MAC effcency [4] The Block-ACK feature allows a number of data unts to be transmtted and afterwards the sender sends a Block- ACK request (BAR and receves a Block-ACK (BA frame Throughput s ncreased snce less ACK frames are used for a transmsson Analyss of the Block-ACK scheme (BTA s not wthn the scope of the paper and more nformaton can be found n the standard [] The problem wth errors n the BTA scheme s smlar to the RTS/CTS and requres to change all of the above equatons whch nclude errors n RTS and CTS frames wth errors n BAR and BA frames, and to make all the respectve errors of ACK equal to zero However snce the errors are unformly dstrbuted, the probablty of error n one of these packets s equal Fnally S = ( pe, P s, F E[L] P dle σ + 3 =0 ( pe, P s, T s, + ( Pc + p e, P s, (40 The tme for successful transmsson T s, s thus much bgger snce t ncludes F frames and SIFS tme, plus the exchange of the BAR and BA Moreover H s the physcal layer header and δ s the transmsson delay: Ts, basc =T E, = F (H + E[L] + SIFS + δ + AIFS[]+H + T BAR + SIFS + δ + H + T BA + δ, T c, =F (H + E[L] + SIFS + δ + EIFS[]+H + T BAR + δ, (4 where EIFS[] = SIFS + H + T BA + AIFS[] 3 MAC delay 3 Mean value of the MAC delay In 80e [], two dfferent access mechansms are provded The frst one s the use of acknowledgments by ACKs (called here basc and the other by transmttng request-to-send and s, c, and Tc, RTS/CTS for a collson can be found n [6] The mean delay can be defned for each AC by the followng equaton: and clear-to-send packets The transmsson tmes Ts, Basc T RTS/CTS, and the tmes T Basc E[D] = E [ ( N cs ] E[BD] + T c + T protect + E[BD] + T s, (4 The frst part of the equaton s the delay due to consecutve unsuccessful transmssons, the second part s the mean backoff delay, whenever ths transmsson wll be completed, and the thrd part s the transmsson duraton All are referred to each AC Followng (4, E[N cs ] can be defned as the mean number of collsons that are followed by a successful transmsson: E [ N cs ] = P dle P s, P s, (43

8 8 Advances n Multmeda 3 PMF of the MAC delay Havng supposed that the standard refers to an nteger number of tme slots, then the Z-transform can be used to calculate the delay Z-transform s well used n the analyss of queung systems, because ts dervatves can provde measures such as mean values, varances, and some other possble moments of the PMF of the MAC delay In order to nclude the freezng of the backoff counters, a dstncton has been made n (4and(5 The probablty that the tag staton s nterrupted by the transmsson of a sngle staton (one exactly s gven by ( p N = τ ( τ N ( Nz τz (44 z> The phenomenon that the slot s nterrupted from a collson or a successful transmsson s descrbed by P(collson slot s nterrupted= p c, = p p, p P(successful by one AC slot s nterrupted = p t, = p p (45 In our case, each state of backoff duraton s sad to have a delay SD (z In order to count down to the next state, the slot must reman dle, whch s symbolzed by the duraton of the empty n Z-transform multpled by the probablty of the slot to be dle, P dle Z σ Hence the Z-transform of that delay s P SD (z dle Z σ = (46 p (p t, Z Ts, + p c, Z Tc, Then the total delay of backoff duraton s gven from the geometrc sum, snce ts state s chosen unformly Note that the frst queue of each AC s smaller snce the frst state s not chosen: CW,j SD k (z, 0 j m, BD,j (z = CW k=0,j (47 BD,m (z, m j L In the prevous subsecton, we have shown a unfed method to fnd the mean MAC delay for all the models In the followng subsecton, the above metrcs for MAC delay wll correspond only to the model 3 Ths happens because the soluton of the DTMC after theoretcally nfnte retres gves mean values Thus the Z-transform of the MAC delay wll be gven as a functon of D (z: D (z = ( L [ (p j ] j p z T s, z Tc BD, f (z j=0 + ( L+ p z Tc BD, f (z f =0 f =0 (48 The frst part sgnfes the correct transmsson (( p z Ts, havng encountered a number of collsons n the prevous stages, whereas the second part s the delay assocated wth droppng of a packet after L + retres However, to fnd the mean value and the standard devaton (SD, the st and the nd moments of the above equatons must be found, respectvely, and we need E[D] = D (z z, z= Var [D] = D (z z + D { } (z D (z z= z z= z z= (49 The last part s to fnd MAC delay dstrbuton It s well know that every Z-transform of the PGF can be wrtten as D (z = d,k z k (50 k=0 It seems that from the defnton d,k s the nverse Z- transform of the D (z A method that gves the nverse Z-transform wth a predefned error bound s the Lattce- Posson algorthm [6],whchsvaldfor d,k Thus the PMF (probablty mass functon of the MAC delay s gven by k dg,k = kr k ( h Re ( ( DG re π j/k, (5 h= where DG (z s the generatng functon DG (z = dg,k z k = D (z (5 z k=0 The followng values can be used: r = γ/( k andγ = 4 COMPARISON ANALYSIS AND EVALUATION For valdatng the correctness of the mathematcal analyses, OPNET modeler (verson was used wth the EDCA smulaton model ncorporated For further valdaton, we also compare the Xao model [6] whch s slghtly alternated for reasons of far comparson In Table, the smulaton parameters are summarzed The accuracy values of the fgures are explaned n Secton 4 In Fgure 5, saturaton throughput comparson s presented for the three models, the Xao model, and the smulatons The throughput of AC0 s twce the throughput of AC, whch s derved from the half CWmn and CWmax values (see Table It seems that most models have results close to the smulaton values, wth the DTMC model beng the most accurate one In fact ths happens due to the ablty of the DTMC to capture possble parameters of the EDCA scheme of 80b/e, n each tme slot, rather than average values of the other models Smlar results can be found for the RTS/CTS access method n Fgure 6 However one major dfference between these methods, whch cannot be derved from basc rate analyses ( Mbps, s that, as the number of nodes (load ncreases, RTS/CTS can solve, except from the hdden node termnal, part of the hgh collson rate Thus a hybrd system

9 Ioanns Papapanagotou et al 9 Table : Smulatons parameters Smulator OPNET modeler Model EDCA model august (006 Standards 80b/e and 80a/e Packet sze Constant 03 bytes (no segm Interarrval tme Set accordng to saturaton condtons RTS threshold 5 bytes Smulaton 00 s Intal seed 8 Space Square (sngle hop Mode No AP functonalty (ad hoc Throughput (Mbps Basc access transmsson rate Mbps AC Smulatons Accuracy DTMC model ( ECPA & QN model ( Xao model ( AC Fgure 5: Model comparson n terms of saturaton throughput usng basc access method at Mbps transmsson rate that would change the transmsson process, accordng to the load, would provde hgher performance of the standard In Fgure 7, throughput s shown as a functon of the number of nodes and probablty of error, thus provdng a 3D graph The probablty of error s a dervaton of cross layer archtectures and probablstc nature of the channel It s worth seeng that n RTS/CTS method, the degradaton of throughput stays n very low values, and shows that RTS/CTS transmsson can be a soluton n erroneous envronments as well The comparson of the three models n these graphs s avoded snce the degradaton of the performance due to errors seems to be lnear to probablty of errors Accordng to Fgures 8 and 9, the performance analyss shows that our DTMC remans equally accurate as n throughput metrc Xao s model tends to dverge sgnfcantly from the smulaton results whereas the elementary probablstc and queung models seem to have a good accuracy Moreover from the ECPA and queung model, the frst Throughput (Mbps RTS/CTS transmsson rate Mbps AC0 AC Smulatons Accuracy DTMC model ( ECPA & QN model ( Xao model ( Fgure 6: Model comparson n terms of saturaton throughput usng RTS/CTS access method at Mbps transmsson rate Throughput (Mbps Probablty of errors Basc RTS/CTS Fgure 7: Saturaton throughput at Mbps, as a functon of probablty of error and number of statons for AC0 dervatve (sgnfed as FD n the fgures of the Z-transform PGF of the MAC delay, shows the mean value Such a mean value seems to be more accurate than the mean values provded by the other models, because t dfferentates the freezng probablty n collson or busy channel due to a transmsson Smlarly, takng the second dervatve of the PGF of the Z-transform, the varance s found as shown n Fgure 0 Varance of the MAC delay s a sgnfcant metrc, snce t sgnfes the jtter of the multmeda traffc transmtted over the standard usng Mbps bandwdth In Fgure, IEEE 80a/e s modeled wth a bandwdth of 4 Mbps (analytcal and smulaton set and as t s seen when enabled, the Block-ACK mechansm can offer hgher throughput n hgher load and can even provde

10 0 Advances n Multmeda MAC delay (s Basc access transmsson rate Mbps AC Table 3: Bg-O notaton for computatonal complexty of the compared models τ E [BD] Both τ and E [BD] DTMC Com Com Com ECPA Com3 Com3 Com3 Queung Com3 Com3 Com3 ments are not taken because the graph s not provded for depcton of Block-ACK Secton AC Smulatons Accuracy DTMC model (0007, 000 ECPA & QN model (00036, 005 FD of Z-transform (0004, 0007 Xao model (00075, Fgure 8: Analyss of MAC delay of the two hgher ACs under saturaton condton and basc access mode MAC delay (s RTS/CTS transmsson rate Mbps AC 00 AC Smulatons Accuracy DTMC model (0009, 0009 ECPA & QN model (0000, FD of Z-transform (00009, 0005 Xao model (00069, 0034 Fgure 9: Analyss of MAC delay of the two hgher ACs under saturaton condton and RTS/CTS access mode better results n hgher bandwdth occasons Ths s due to the reducton of unnecessary ACKs The reason for modelng IEEE 80a s that hgher bandwdths are gong to be used n 80n wth Physcal (PHY and MAC layers that do not change sgnfcantly (In Fgure,accuracymeasure- 4 Complexty analyss Complexty s an mportant characterstc as regards mathematcal analyss and algorthms Comparng the three approaches n terms of complexty allows for an nsght n to the usablty and scalablty of each one The DTMC model s obvously the most complex one Ths s due to the ndependence of each state, whch models a state of the BEB, and the correlaton wth the state of the prevous slot However the state of the prevous slot s hardly ncorporated n models based on queung theory or geometrc dstrbuton snce t does not allow the flexblty to change backoff duraton accordng to the smulaton needs A sgnfcant drawback of the proposed DTMC s that nonsaturaton throughput analyss becomes a complex problem, whereas n the other analyses, the arrval rate could be changed very easly wth smple algebra On the other hand, the modelng of ndependent states makes easer to provde amendments n the analyss, such as the one gven wth the nexstence of the frst state Thus t s easy to observe that the analyss of ths frst model requres bg DTMC and more mathematcal formulastobecalculated Moreover, the addton of extra features and the ncorporaton of realstc modelng n ths approach nject even more complexty n the fnal calculatons Apart from ths heurstc approach, a computatonal complexty comparson can be performedntermsofbg-o notaton Instead of computer nstructons, we use a smple formula calculaton as the basc unt of complexty Each algorthm s order of complexty can be estmated as a functon of the number of calculaton ponts N, the number of steps used n the fxed pont teraton method M, the retry lmts L, and the number of ACs calculated InTable 3, the results show that all three algorthms have lnear complexty relatve to M and N, and that the DTMC model s approxmately four tmes more complex than the other two approaches: [ ( ( Com = O NM 4L + ], Com = O Com3 = O [ [ N ( NM M ( ( ( 4L + + ( L +3 ] L ], (53 Ordnary values for the parameters are: N = 0, M = 0, L = 7, and = 4

11 Ioanns Papapanagotou et al Table 4: Metamodel comparson DTMC ECPA Queue Accuracy Hgh Medum Medum Flexblty Hgh Medum Medum Complexty Hgh Low Low Nonsat Low Medum Low Depcton Hgh Low Medum 4 Accuracy analyss In order to prove the accuracy of each model, we have used the L dstance, whch s defned as the dstance d ( m sm,n (mn q, m anal,n = FN (, (54 msm,n (mn q m anal,n FN N =0 where m anal,n s the analytcal metrc (throughput or delay of each model, m sm,n (mn q% s the smulaton of each metrc (we menton t as a functon of (mn q% whch s the closest % quartle n our case mean values of smulaton have been used, both as functons of N, whch s the number of nodes of each AC FN s sad to be the maxmum number of nodes of each AC, defned for case FN = 0 Thus for the comparson analyss, we have the dstances, as wrtten n Fgures 5, 6, 9, and 0 It s readly seen that the DTMC model s more accurate than the other two models, snce t can capture the freezng of the backoff counter, and the effect of the prevous slot to the current one In addton, the frst dervatve of the MAC delay dverges the freezng probablty to busy perod due to a transmsson or collson, and gves the best possble accuracy 5 DISCUSSION AND CONCLUSION The purpose of ths work s threefold The frst goal s to present a comparson analyss of the most known analyses n order to fnd the best method to numercally analyze the standard, whle settng the pace for future methods of analyss Furthermore the modelng technques, based on complexty and accuracy theory, have not been studed before n wreless networks and they could be a feld of great nterest, snce the computer resources are fnte The second goal was to extend the already known analyses, ntroducng features that change consderably the performance analyss The combnaton of such features optmzes the MAC protocol outcomes, and makes each mathematcal analyss avant-garde by tself The thrd goal was to correct the IEEE 80e from general msunderstandngs, such as the phenomenon of not provdng nstant access after a successful transmsson and the freezng of backoff counter From the evaluaton part of the proposed work, the performance (of general BEB algorthms numerous standards mplement BEB and smulaton conclusons are as follows Varance of MAC delay (s Both access mechansms at Mbps AC0 basc AC0 RTS/CTS AC basc AC RTS/CTS Fgure 0: Jtter (second dervatve of Z-trasform s shown for the AC0 and AC, and for varable number of statons n each AC The transmsson rate s at Mbps 80b/e Probabltes AC0 AC Probablty mass functon for N = MAC delay (ms Log 0 Fgure : Probablty mass functon (PMF for basc access mode and for both ACs The transmsson rate s at Mbps 80b/e and the graphs are for 5 numbers of states at each AC[] ( Performance conclusons ( In order to have better performance n exponental backoff algorthms, methods that provde farness of transmsson (such as RTS/CTS, apart from adng n the hdden termnal problem, can reduce the collson rate and mprove the performance n erroneous envronment Thus t could be used n WF mplementatons over rural areas

12 Advances n Multmeda Throughput (Mbps Basc access-4 Mbps Block-ACK AC AC Opnet smulatons Markov chan model wth ACK Markov chan model wth Block-ACK Probablstc & queue model wth ACK Probablstc & queue model wth Block-ACK Fgure : Model comparson of saturaton throughput wth Block-ACK beng enabled (F = 64 n 4 Mbps wth IEEE 80a ( RTS/CTS and smlar access methods should be used only n hgher loads, because n lower ones they tend to dmnsh the throughput performance ( Analoges on ntal wndows (eg, CWmn n BEB algorthms can gve the smlar analoges on throughput performance (v Methods that group packets (eg, Block-ACK or TxOP can augment the throughput performance ( Smulaton conclusons As regards the accuracy, the DTMC model offers better results, owng to the fact that more EDCA characterstcs can be ncluded Ths leads to another advantage of the DTMC model whch s ts flexblty The modelng of each ndependent state allows for extreme detal n modelng each specfc characterstc of the MAC protocol, such as the absence of the frst state and the correlaton of each state wth the prevous slot Moreover the DTMC can also be used as a depcton of the states of the MAC protocol On the other hand, the other two models demonstrate dfferent advantages They lead to approxmate results bearng less complexty compared to the DTMC model, both havng the same accuracy and small dfferences n complexty Moreover they allow for nonsaturaton condtons of traffc, whereas n the DTMC model case, ths can prove to be a very complex ssue The Z-transform s used as a method to calculate the accurate delay dstrbuton, whle havng dfferent types of queues, depctng the heterogenety of the multmeda applcatons Even f such a combnaton of features and correctons ncrease, the complexty of the proposed analyses, t s the prce that must be pad for the mproved accuracy and realsm, especally when new machnes can solve problems n acceptable tme lengths OPNET modeler, was used n two ways: frst to verfy the correctness of analyses and second as a tool to calculate the accuracy analyss In Table 4, the above are summarzed Fadng channels can be used n order to optmze MAC layer metrcs through cross-layer technques n hgh-moblty scenaros REFERENCES [] Part : Wreless LAN medum access control (MAC and physcal layer (PHY specfcaton, IEEE, August 999 [] Medum access control (MAC enhancements for qualty of servce (QoS, IEEE, July 005 [3] I Polts, M Tsagkaropoulos, S Kotsopoulos, T Daguklas, and P Stavroulaks, On the QoS assesessment of vdeo sessons n heterogeneous 3G-WLANS networks wth seamless and secure moblty support, Journal of Chna Communcatons, vol 4, no, 007, specal ssue on Communcatons and Informaton Securty [4] G Banch, Performance analyss of the IEEE 80 dstrbuted coordnaton functon, IEEE Journal on Selected Areas n Communcatons, vol 8, no 3, pp , 000 [5] C H Foh and J W Tantra, Comments on IEEE 80 saturaton throughput analyss wth freezng of backoff counters, IEEE Communcatons Letters, vol 9, no, pp 30 3, 005 [6] Y Xao, Performance analyss of IEEE 80e EDCF under saturaton condton, n Proceedngs of the IEEE Internatonal Conference on Communcatons (ICC 04, vol, pp 70 74, Pars, France, June 004 [7] P E Engelstad and O N Østerbø, Delay and throughput analyss of IEEE 80e EDCA wth starvaton predcton, n Proceedngs of the 30th Annversary IEEE Conference on Local Computer Networks (LCN 05, pp , Sydney, Australa, November 005 [8] G S Paschos, I Papapanagotou, S A Kotsopoulos, and G K Karagannds, A new MAC protocol wth pseudo-tdma behavor for supportng qualty of servce n 80 wreless LANs, EURASIP Journal on Wreless Communcatons and Networkng, vol 006, Artcle ID 65836, 9 pages, 006 [9]YCTayandKCChua, AcapactyanalyssfortheIEEE 80 MAC protocol, Wreless Networks, vol 7, no, pp 59 7, 00 [0] G Banch and I Tnnrello, Remarks on IEEE 80 DCF performance analyss, IEEE Communcatons Letters, vol 9, no 8, pp , 005 [] J Cho, J Yoo, and C-K Km, A novel performance analyss model for an IEEE 80 wreless LAN, IEEE Communcatons Letters, vol 0, no 5, pp , 006 [] J Hu and M Devetskots, A unfed model for the performance analyss of IEEE 80e EDCA, IEEE Transactons on Communcatons, vol 53, no 9, pp , 005 [3] Q N, T L, T Turlett, and Y Xao, Saturaton throughput analyss of error-prone 80 wreless networks, Wreless Communcatons and Moble Computng, vol5,no8,pp , 005 [4] T L, Q N, T Turlett, and Y Xao, Performance analyss of the IEEE 80e block ACK scheme n a nosy channel, n Proceedngs of the nd Internatonal Conference on Broadband Networks (BROADNETS 05, vol, pp , Boston, Mass, USA, October 005

13 Ioanns Papapanagotou et al 3 [5] A Banchs and L Vollero, A delay model for IEEE 80e EDCA, IEEE Communcatons Letters, vol 9, no 6, pp , 005 [6] J Abate and W Whtt, Numercal nverson of probablty generatng functons, Operatons Research Letters, vol, no 4, pp 45 5, 99