136 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY Ching-Ling Huang and Wanjiun Liao, Senior Member, IEEE

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1 136 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007 Throughput and Delay Performance of IEEE e Enhanced Dstrbuted Channel Access (EDCA) Under Saturaton Condton Chng-Lng Huang and Wanjun Lao, Senor Member, IEEE Abstract In ths paper, we analyze the saturaton performance of IEEE e Enhanced Dstrbuted Channel Access (EDCA), whch provdes contenton-based dfferentated channel access for frames of dfferent prortes n wreless LANs. Wth EDAC, Qualty of Servce (QoS) support s provded wth up to four access categores (ACs) n each staton. Each AC behaves as an ndependent backoff entty. The prorty among ACs s then determned by AC-specfc parameters, called the EDCA parameter set. The behavor of the backoff entty of each AC s modeled as a two-state Markov chan, whch s extended from Banch s model to capture the features of EDCA. The dfferences of our model from exstng work for e EDCA nclude: () vrtual collsons among dfferent ACs n an EDCA staton are modeled, thus more accurately capturng the behavor of EDCA; () the nfluence of usng dfferent arbtrary nter-frame spaces (AIFS) for dfferent ACs on saturaton performance are consdered; () delay and delay jtter are derved, n addton to saturaton throughput. The analytcal model s valdated va ns-2 smulatons. The results show that our analytcal model can accurately descrbe the behavor of IEEE e EDCA. Index Terms Delay, EDCA, IEEE e, saturaton performance, throughput. I. INTRODUCTION IEEE Wreless Local Area Network (WLAN) wth the Dstrbuted Coordnaton Functon (DCF) [1] s the domnant wreless medum to access the Internet. Wth DCF, moble statons contend for the access to the channel. All statons operate ndependently and share the channel bandwdth equally. IEEE e [2] s the supplementary standard of Medum Access Control (MAC) to provde QoS for dfferent knds of applcatons. In e, QoS s supported wth a new access method called the Hybrd Coordnaton Functon (HCF). In HCF, two medum access mechansms are defned: controlled channel access and contenton-based channel access. In ths paper, we focus only on the HCF Manuscrpt receved December 8, 2004; revsed November 10, 2005 and March 21, 2006; accepted May 4, The assocate edtor coordnatng the revew of ths paper and approvng t for publcaton was K. K. Leung. Ths work was supported n part by the Natonal Scence Councl (NSC), Tawan, under a Center Excellence Grant NSC E PAE, and n part by NSC under Grant Number NSC E Chng-Lng Huang was wth the Department of Electrcal Engneerng, Natonal Tawan Unversty, Tape, Tawan. He s now wth the Dept. of Cvl and Envronmental Engneerng, Unversty of Calforna Berkeley, Berkeley, CA USA (e-mal: huang@calcct.org). Wanjun Lao s wth the Department of Electrcal Engneerng and the Graduate Insttute of Communcaton Engneerng, Natonal Tawan Unversty, Tape, Tawan (e-mal: wjlao@ntu.edu.tw). Dgtal Object Identfer /TWC contenton-based channel access mechansm, referred to as Enhanced Dstrbuted Channel Access (EDCA). A. Legacy DCF /07$20.00 c 2007 IEEE IEEE DCF s based on Carrer-Sense Multple Access wth Collson Avodance (CSMA/CA), whch ntroduces the "Inter Frame Space" (IFS) and the backoff nterval to avod collsons. Each staton wshng to transmt montors the wreless channel. When the channel becomes dle, the staton wats for a perod of DCF IFS (DIFS) and a backoff process before a transmsson. If the channel s stll dle, the staton starts a transmsson; otherwse, the transmsson s deferred. Once the staton enters the backoff process, a backoff nterval s selected. The selected value s unformly dstrbuted n the nterval [0,CW 1], where CW (.e., Contenton Wndow) falls between the mnmum (CW mn ) and maxmum (CW max ) contenton wndows. The value of the backoff nterval s decremented by one at each tme slot on an dle medum. When the channel s busy, the backoff process s frozen, and resumed after the channel becomes dle agan. Eventually, the backoff nterval reaches zero, and the staton starts transmsson. A collson occurs when more than one staton transmts n the same slot. In ths case, the CWs of the collded statons are doubled untl CW max s reached. CW s reset to CW mn after each successful transmsson. In DCF, the "Request to Send (RTS) / Clear to Send (CTS)" access mechansm s optonal for packet transmssons. A staton wshng to transmt must frst obtan the channel access rght based on the operaton of the basc access mode descrbed above. The sender staton then transmts a specal short frame called RTS frame, and the recever, on recevng an RTS frame, responds wth a CTS frame after an SIFS perod. The sender starts transmttng a data packet after t has receved the CTS frame correctly; the recever, on recept of the data, sends an ACK n response after another SIFS to fnsh the transmsson. The frames RTS and CTS carry nformaton about the duraton of channel occupancy. Other statons recevng these frames set ther Network Allocaton Vector (NAV) accordng to the duraton recorded n the frames and stop sensng the channel untl the end of the duraton. After that, they sense the channel agan. If the channel s dle for a DIFS perod, they wll apply the backoff procedure and compete for the channel agan.

2 HUANG AND LIAO: THROUGHPUT AND DELAY PERFORMANCE OF IEEE E ENHANCED DISTRIBUTED CHANNEL ACCESS (EDCA) 137 B e EDCA The EDCA of e s an enhanced verson of DCF for prorty-based QoS support. Wth EDCA, a staton can mplement up to four access categores (ACs), correspondng to voce, vdeo, best effort, and background traffc, respectvely. Each AC s assocated wth one backoff entty and some AC-specfc parameters called the EDCA parameter set composed of Arbtrary Inter-Frame Space Number (AIF SN[AC]), mnmum contenton wndow (CW mn [AC]), and maxmum contenton wndow (CW max [AC]). AIF SN[AC] s used to determne the duraton of Arbtrary IFS (AIF S[AC]) accordng to AIF S[AC] =SIFS + AIF SN[AC] aslott me, where AIF SN[AC] >= 2,andaslotT me s the duraton of one slot. Snce the value of AIF SN[AC] s at least 2, the earlest access tme for an EDCA staton s after a DIFS. The backoff enttes are prortzed accordng to the values of ther EDCA parameter sets. The smaller the AIF S[AC] or CW mn [AC], the hgher the prorty n medum access, and thus, the hgher the throughput. The backoff nterval for an AC n EDCA s randomly selected from [1,CW], nstead of [0,CW 1] as n DCF. Another EDCA feature dfferent from DCF s that the backoff counter wll be decreased by one slot before the end of AIFS as shown n Fg. 1. Ths feature of EDCA may cause problems n applcatons wth coexstng legacy DCF and EDCA systems [19]. The operaton of e EDCA s descrbed as follows. Each data frame from the hgher layer arrves n the MAC layer wth a specfc prorty value. Then, each frame s mapped nto an AC based on the specfed prorty. The values of the EDCA parameter set for each AC are announced perodcally by the AP va beacon frames. Each AC behaves as a sngle enhanced DCF contendng entty, and the correspondng queue has ts own AIFS, backoff nterval, and contenton wndow (CW). After each unsuccessful transmsson attempt, the contenton wndow s doubled untl a retry lmt or the maxmum contenton wndow s reached. The collson s handled n a vrtual manner. That s, the hghest prorty frame among the colldng frames s chosen and transmtted, and the others perform a backoff wth an enlarged CW value. Note that there s no prorty among EDCA statons; dfferent EDCA statons have to compete for channel access wth equal opportunty. C. Related Work Most exstng work on evaluatng the performance of IEEE e QoS n the lterature (e.g., [3-11]) are based on smulatons (e.g., [3-6]). The analytcal studes for IEEE e are manly extended from Banch s model [12] (e.g., [7-11]). Banch s model s based on a two-state Markov chan to calculate the saturaton throughput of DCF n an deal physcal envronment. In [7-9], only the saturaton throughputs of e are analyzed. In [10], the saturaton throughput and saturaton delay are derved. However, that model does not consder the effect of vrtual collsons among ACs nsde an EDCA staton. Thus, t cannot accurately calculate the MAClayer delays of dfferent ACs for each staton. In [11], the Fg. 1. EDCA. Comparson of Backoff Counter Decrement behavor for DCF and behavor of dfferentated CW and AIFS s consdered, but the backoff procedure for dfferent ACs wth dfferent AIFSs s not addressed. D. Problem Specfcaton In ths paper, we analyze the saturaton performance of IEEE e EDCA throughput, access wth delay, and delay jtter. The saturaton throughput s defned as the maxmum throughput that the system can acheve n stable condtons. The access delay s the nterval from when a head-of-lne data frame at the sender starts contendng for the channel to when the data reaches the MAC layer of the recever. The jtter s referred to as the standard devaton of the access delay descrbed above. The Markov chan for the backoff entty of each AC n ths paper s also extended from Banch s model [3] to accommodate the QoS features of e EDCA. The proposed analytcal model dffers from exstng work n that: () we consder vrtual collsons among dfferent ACs nsde each EDCA staton n addton to external collsons among statons. Thus, our model can capture the behavor of e EDCA more accurately. () We consder the mpact of hghprorty ACs AIFSs on low prorty ones. Thus, the probablty that the backoff counter for each AC can be decreased by one n each tme slot may not be dentcal or equal to one. () We model the effect of the frame retry lmt,.e. the maxmum number of retransmssons each frame can experence before beng dropped. After ths lmt s reached, the retryng data frame s dscarded. (v) In addton to modelng the saturaton throughput as n exstng work, we also model the delay and delay jtter performance. Note that we do not consder channel errors n our model. Such consderatons can be easly extended from exstng work such as [13, 14]. The rest of the paper s organzed as follows. In Secton II, the saturaton throughput of e EDCA s analyzed. In Secton III, the delay and the jtter are analyzed. In Secton IV, the analytcal model s verfed wth network smulator ns-2. Fnally, the paper s concluded s Secton IV. II. THROUGHPUT ANALYSIS OF E EDCA In ths secton, we analyze the saturaton throughput of IEEE e EDCA. Notatons used n the analyss are

3 138 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007 summarzed n Table I. To reach the throughput lmt, each AC s assumed always backlogged,.e., there s at least one data frame n each AC s queue ready to be sent. We also assume that the system operates n an deal physcal envronment,.e., no frame errors, the hdden termnal effect, and the capture effect n our model. For convenence, we denote ACs from the hghest prorty to the lowest prorty by subscrpts 0, 1, 2, and 3 n the analyss. In [12], the DCF model s smplfed by assumng the backoff decrement probablty s one, whch does not always hold for DCF snce the decrement probablty depends on whether there are other statons wth backoff counters equal to zero. However, n EDCA, the backoff counter wll always be decremented by one slot before the end of AIFS. Therefore, the basc Markov chan model presented n [12] s stll vald for each AC and s further modfed for the analyss as follows. The two-state Markov Chan for the EDCA backoff entty of an AC s shown n Fg. 2. The state (s(t),b(t)) s defned as follows. s(t) s the backoff stage of a request packet at tme t, defned as the number of collsons the request packet has suffered; b(t) s the backoff counter at tme t. The packet s sent whenever the backoff counter becomes zero regardless of the backoff stage. In DCF, the backoff counter s chosen n the range (0,W 1), but n e EDCA, t s chosen n (1,W ). The effect of the frame retry lmt s consdered,.e., after M + f transmsson falures, the frame wll be dscarded. Here f s defned as the dfference between M and the frame retry lmt. Fnally, we also consder the mpact of dfferent AIFSs of dfferent ACs on the probablty that the backoff counter of each AC can be decreased by one (denoted by PT). The state transton probabltes for each AC n the proposed Markov model are expressed as follows. 8 >< >: P (, k, k +1)=PT,k (0,W 1), (0,M + f) P (, k, k) =1 PT,k (1,W ), (0,M + f) P (0,k, 0) = (1 PC)/W 0,k (1,W 0), (0,M + f 1) P (, k 1, 0) = PC/W,k (1,W ), (1,M + f) P (0,k M + f, 0) = 1/W 0,k (1,W 0) (1) where M s the maxmum number of tmes the contenton wndow may be doubled, M + f s the frame retry lmt of the AC, W 0 s the mnmum contenton wndow sze, W s the wndow sze at backoff stage (.e. W = W 0 2 for (0,M 1) and W = W M for (M,M + f 1)), PT s the probablty that the backoff counter s decreased by one n a gven tme slot, and s the collson probablty at each transmsson attempt. The frst equaton n (1) accounts for the fact that, at the begnnng of each slot tme, the backoff counter s decreased by one wth probablty PT. The second equaton says that the backoff counter s not successfully decreased wth probablty 1 PT due to the effect of dfferent AIFSs of dfferent ACs. Recall that, n EDCA, dfferent ACs may wat for ntervals of dfferent lengths (.e., AIF S[AC]), before the channel can be accessed agan or the backoff procedure s resumed. A lower prorty AC may need to wat longer, because the wreless channel may be used agan by a hgher prorty AC wth a relatvely shorter AIFS. Ths leads to that ths low-prorty AC s very lkely to be frozen agan before t can successfully fnsh watng for ts AIFS. The thrd equaton corresponds to Notaton M W 0, W k, M + f PI PO PIDLE dff PT τ σ N PTR PS PFC S E[L ] aslott me t s t c t H t E[P ] t E[P ] t SIFS t AIF S t ACK δ B,k X K Z AD D Y Q T F λ α TABLE I NOTATIONS USED IN THE ANALYSIS Defnton Maxmum number of tmes for doublng the contenton wndow sze after a transmsson falure for access class Mnmum contenton wndow sze for access class Contenton wndow sze at backoff stage k for access class Frame retry lmt of class for an EDCA staton,.e. retry counter, for access class Collson probablty of class for an EDCA staton Probablty that a class colldes wth hgher prorty access classes nsde the EDCA staton Probablty that class colldes wth other EDCA statons whle accessng the channel Probablty that class senses the channel s dle durng backoff state n the Markov Chan model Number of tme slots between AIFSmn and AIFS for access class Probablty that backoff counter can be decreased by one for access class ; ths probablty accounts for the effect of dfferent AIFSs among access classes Probablty of transmsson attempt for access class observed nsde an EDCA staton Probablty of transmsson attempt for access class observed outsde an EDCA staton Total number of EDCA statons n the system Probablty of at least one EDCA staton transmts n the consdered tme slot Probablty of a transmsson of class s successful n the consdered tme slot Probablty of a transmsson attempt fals due to collsons n the consdered tme slot Average saturaton throughput of access class n the system Average packet length of access class Length of one slot tme Average tme of a successful transmsson for access class Average tme of a collson nvolved n the system Transmsson tme of PHY and MAC headers Transmsson tme of the average payload sze for class Average tme nterval of the longest packet sze nvolved n a collson n the system Tme nterval of SIFS Tme nterval of AIFS for access class Transmsson tme of an ACK massage Propagaton delay Random varable representng the backoff counter n stage k of access class before transmsson attempt Random varable representng the total backoff counter of class before the successful transmsson or before reachng the frame retry lmt Average deferrng tme spent n every backoff decreasng attempt for access class whle current channel state s busy Average transton tme of backoff counter decreasng successfully for access class Access delay of a packet frame for class Total delay of a packet frame for class, ncludng the queueng delay, the channel access delay and the transmsson delay Random varable representng the number of collsons wth other EDCA statons whle accessng the channel before the successful transmsson for class Watng tme spent n the queue of access class before tryng to access the wreless medum Servce tme for access class n a queueng system Number of data frames n the queue of access class Arrval rate of traffc n access class Varance of nter-arrval tme of traffc n access class

4 HUANG AND LIAO: THROUGHPUT AND DELAY PERFORMANCE OF IEEE E ENHANCED DISTRIBUTED CHANNEL ACCESS (EDCA) 139 Fg. 2. Markov chan model for a Sngle AC nsde the EDCA staton. when a new data frame starts at backoff stage 0, and thus the backoff counter s ntally unformly chosen n (1,W 0 ).The fourth equaton descrbes when an unsuccessful transmsson occurs at backoff stage 1, the backoff stage ncreases, and the new backoff value s unformly chosen n (1,W ). Note that W wll not be ncreased but fxed at W M after M transmsson retres. The last equaton says that once the backoff stage reaches the retry lmt M + f, the frame s dscarded after transmsson falure and the next data frame n the queue s served. Thus, the state wll start another backoff procedure wth probablty one. The statonary dstrbuton of the states n ths model s defned as b,k = lm t P (s(t) =, b(t) =k). From the transton probabltes n (1) and the fact that the sum of all states n the Markov model equals one, the lmtng probablty of state b 0,0 s obtaned n (2). Snce a transmsson occurs whenever the backoff counter becomes zero, the transmsson probablty for an AC can be expressed by τ = M+f =0 b,0 = M+f b 0,0 =0, as n (3). Let τ denote the transmsson probablty of AC[] n an EDCA staton, =0, 1, 2, 3. See equaton followng (3) on top of next page, where s the collson probablty of AC[], PT s the probablty that the backoff counter for AC[] can be decreased by one, M s the maxmum number of tmes AC[] can double ts contenton wndow, M + f s AC[] s frame retry lmt, and W 0, s the mnmum contenton wndow sze of AC[]. Collsons may occur among dfferent ACs n the same EDCA staton (.e., vrtual collsons), and collsons may also take place among dfferent EDCA statons (.e., external collsons). Let PI denote the probablty of vrtual collsons for AC[], andpo be the probablty of external collsons n the system. Hence, the collson probablty of AC[] (.e., ) can be expressed by = PI +(1 PI )PO. (4) The probablty of vrtual collsons PI can be expressed as follows, consderng that each AC wll collde only wth hgher prorty ACs n the same staton. PI 0 =0 PI 1 = τ 0 PI 2 =1 (1 τ 0 )(1 τ 1 ) PI 3 =1 (1 τ 0 )(1 τ 1 )(1 τ 2 ) Let σ, =0, 1, 2, 3, denote the transmsson probablty of AC[] for an EDCA staton. Thus, σ 0 = τ 0 σ 1 = τ 1 (1 PI 1 )=τ 1 (1 τ 0 ) σ 2 = τ 1 (1 PI 2 )=τ 2 (1 τ 0 )(1 τ 1 ) σ 3 = τ 1 (1 PI 3 )=τ 3 (1 τ 0 )(1 τ 1 )(1 τ 2 ) and the total transmsson probablty for an EDCA staton s σ total = 3 =0 σ. Wth σ total, the probablty of external collsons PO can be expressed by (5) (6) PO =1 (1 σ total ) N 1, (7) where N s the total number of EDCA statons n the system. After watng for the wreless medum to become dle for AIF S, AC[] wll start decreasng ts counter value. Let PT denote the probablty that the backoff counter of AC[] can be successfully decreased by one n a gven tme slot,.e., when there are no transmssons ntated by other statons or other hgher prorty ACs nsde the same staton n the perod between AIF S mn (.e., DIFS) and AIF S. Note that, snce AC[] wll freeze ts counter value untl the channel has been dle for AIF S, PT wll be zero before AC[] starts to count down. Snce we attempt to understand the behavor of the saturated channel condton, we assume that each AC[] n all wreless statons can perceve the same collson probablty as descrbed n [12]. Let dff denote the dfferences n the number of tme slots between AIF S mn and AIF S,.e., AIF S AIF Smn AIF S DIFS dff = aslott me = aslott me. The relatonshp between PT, AIF S,anddff s llustrated n Fg. 3. Wth dff, PT can be expressed by 8 < : PT0=0, before AIFS0; PT 0=1, after AIFS 0.

5 140 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007 b 0,0 = 2PT (1+2PT) (1 PC M+f+1 )+W 0 (2PC) M (1 PC f+1 ) 1 PC + W0 (1 (2PC)M ) 1 2PC (2) τ = 2PT (1 PC M+f+1 ) (1 + 2PC) (1 PC M+f+1 )+W 0 (2PC) M (1 PC f+1 1 PC 1 PC 1 2PC )+ 1 2PC (3) τ = (1 + 2 ) (1 PC M+f+1 2PT (1 PC M+f+1 ) )+W 0, (2 ) M (1 PC f+1 1 PC 1 2 )+ 1 PC 1 2 { PT 1=0, beforeaifs 1; PT 1=((1 τ 0)(1 σ 0) N 1 ) dff 1 dff 0,afterAIFS 1. PT 2=0, before AIFS 2; PT Q 2=((1 τ 0)(1 σ 0) N 1 ) dff 1 dff 0 1 ( =0 (1 τ)(1 σ)n 1 ) dff 2 dff 1, after AIFS 2. PT 3=0, before AIFS 3; PT 3=((1 τ 0)(1 σ 0) N 1 ) dff 1 dff 0 ( Q 1 =0 (1 τ)(1 σ)n 1 ) dff 2 dff 1 ( Q 2 =0 (1 τ)(1 σ)n 1 ) dff 3 dff 2, after AIFS 3. Based on PI, PT,andPO, both τ and σ, =0, 1, 2, 3, can be derved accordngly wth numercal technques. We are now ready to derve the saturaton throughput for each AC n the system. Let PTR denote the probablty that at least one staton transmts n the consdered tme slot, PS be the probablty that a transmsson attempt of AC[] s successful gven that there s at least one staton transmttng n the consdered tme slot, and PFC denote the probablty that a transmsson attempt fals due to a collson gven that there s at least one staton transmttng n the consdered tme slot. By defnton, PTR =1 (1 σ total ) N ; PS = N σ (1 σ total) N 1 PTR,=0, 1, 2, 3; PFC = 1 (1 σ total) N N σ total (1 σ total ) N 1 PTR. Let S denote the average throughput of AC[] n the system. Thus, PS S = PTR E[L ] = P 3 (1 PTR) aslott me+ j=0 PTR PS j t sj +PTR PFC t c E[L P ] 1 σ total 3 σ N σ aslott me+ j, j=0 σ t sj + PFC PS t c (10) where E[L ] s the mean packet sze of AC[], and PFC PS = 1 (1 σ total ) N N σ total (1 σ total ) N 1 N σ (1 σ total ) N 1. The frst term of the denomnator n (10) corresponds to an dle slot, the second term accounts for a successful transmsson, and the thrd term s for a collson. The expressons t c and t s for AC[] can be derved based on two access modes. A. Basc Access Mode { ts = t H + t E[P] + t SIFS + δ + t ACK + t AIF S + δ t c = t H + t E[P ] + t AIF S + δ (11) where t H s the transmsson tme perods of the frame header, t SIFS and t AIF S are the tme perods of an SIFS and an (8) (9) AIFS, respectvely, t ACK s the transmsson tme of an ACK frame, t E[P] s the transmsson tme of the average payload for AC[], t E[P ] s the transmsson tme of the largest payload nvolved n a collson, and δ s the propagaton delay. B. RTS/CTS Access Mode t s = t RT S + t SIFS + δ + t CTS + t SIFS + δ +t H + t E[P] + t SIFS + δ + t ACK + t AIF S + δ t c = t RT S + t AIF S + δ (12) Note that t c s the same for every AC n the RTS/CTS mode snce only RTS frames are nvolved n collsons. Substtutng t s and t c nto (10), we obtan the average throughput for each AC accordngly. III. ACCESS DELAY AND JITTER ANALYSIS OF E EDCA In ths secton, we analyze the access delay and the delay jtter for channel access n e EDCA. To smplfy the analyss, we assume no data frame s dscarded due to exceedng the frame retry lmt as n [15]. Let B,k, k (0,M + f ), denote the random varable representng the backoff counter at stage k for AC[] before a transmsson attempt, and s unformly dstrbuted n (1,W,k ). The expectaton of B,k E[B,k ] = W,k j j=1 W,k can be expressed by = W,k+1 2.LetX be the random varable representng the total backoff counter of a successful transmsson for AC[]. SnceB,k,k (0,M + f ),are mutually ndependent random varables, X can be expressed by X = M +f k=0 B,k ( ) k. The expectaton of X then can be expressed by E[X ] = M +f k=0 E[B,k ] ( ) k. Substtutng E[B,k ] nto the expectaton and the varance of X, we obtan E[X ]= M 1 k=0 k = W0, 2 [ 1 (2PC)M (2PC)M (1 PC f +1 ) 1 W,k +1 2 PC k + M +f W,M +1 k=m 2 ]+ 1 PCM+f+1 2(1 ). (13) Snce X s the number of decrements n the backoff counter for AC[] before a successful transmsson, from Fg. 2 we can observe that the behavor of gong through several backoff stages (due to transmsson falures) untl frst success may be approxmated by a geometrc random varable. To smplfy

6 HUANG AND LIAO: THROUGHPUT AND DELAY PERFORMANCE OF IEEE E ENHANCED DISTRIBUTED CHANNEL ACCESS (EDCA) 141 Fg. 3. Illustraton of PT, AIF S,anddff :Anexample. the calculaton, we assume that X follows the geometrc dstrbuton to derve the varance. Thus, Var[X ]=E[X ](E[X ] 1). (14) Ths assumpton wll be verfed n the smulaton secton. Let PIDLE represent the probablty that AC[] senses the channel dle,.e., the probablty that no other EDCA staton or other AC n the same EDCA staton s currently usng the channel. Thus, PIDLE =(1 σ total ) N 1 j (1 τ j). Let K be the tme spent n every backoff attempt for AC[] gven that the current channel state s busy. Thus, K = P dff 1 n=0 n aslott me (1 PIDLE ) (PIDLE ) n + P 3 j=0 PSj ts j +PFC tc =[ PIDLE (1 PIDLEdff 1 ) 1 PIDLE aslott me + P 3 j=0 PSj ts j +PFC tc, (dff 1) PIDLE dff )] (15) where t s s the average tme of a successful transmsson for AC[], andt c s the average tme of a collson. Note that a lower prorty AC needs to wat longer than those ACs of hgher prortes, thus the channel may become busy after the low-prorty AC has wated longer than a DIFS but shorter than ts AIFS. The frst term n (15) s the tme duraton when AC[] tres to fnsh watng for ts AIFS but stll fals due to the channel used by other hgh-prorty ACs. The second (respectvely, the thrd) term corresponds to the "frozen tme" causedbythechannelbusyperodusedbyotheracsdueto a successful transmsson (respectvely, a collson). Let Z denote the average transton tme of a decrease n the backoff counter for AC[]. Thus, Z can be expressed wth K as follows. Z =(1 PTR) aslott me+ptr [(AIF S AIF S P mn)+ 3 +PFC tc+p j=0 PSj ts j n=1 n K PT (1 PT)n ] =(1 PTR) aslott me+ptr [(AIF S AIF S P mn)+ 3 j=0 PSj ts j +PFC tc+ K (1 PT ) PT ]. (16) The frst part n (16) corresponds to the stuaton that the channel s dle before the transton, and thus the state transton tme takes only one aslott me. The second part descrbes the stuaton that the channel was prevously occuped and just beng released. Thus every AC ether resumes the backoff countdown or starts a new backoff procedure after watng for ts AIFS. An AC may fal to fnsh ts AIFS several tmes before a success,.e. counted down to one, as shown n Fg. Fg. 4. Illustraton of average state transton tme. 4. Thus the last term n the second part (.e., n=1 n K PT (1 PT ) n ) accounts for the total tme for an AC to successfully fnsh watng for ts AIFS. The access delay AD for AC[] then can be expressed by AD = X Z + Y (1 PI ) PO t c. (17) The frst term n (17) corresponds to the total tme spent n the backoff procedure. The second term represents the total tme due to external collsons. Y of the second term represents the number of collsons before a successful transmsson for AC[]. Accordng to the Markov model n Fg. 2, we obtan E[Y ]= M +f 1 k=0 k (1 )( ) k ; E[Y 2]= M +f 1 k=0 k 2 (1 )( ) k ; Var[Y ]=E[Y 2] E2 [Y ]. Recall that there are two knds of collsons for each AC. One s vrtual collsons wth hgher prorty ACs n the same EDCA staton, wth probablty PI. The other s external collsons wth other EDCA statons for channel accessng, wth probablty (1 PI ) PO. Assume that the scheduler entty of the EDCA staton resolves vrtual collsons wthn neglgble tme. Thus approxmately only (1 PI) PO of those collsons are external collsons. Takng expectaton and standard devaton of AD, we obtan the average delay and the jtter as E[AD ] and Var[AD ], respectvely,.e., E[AD ] = E[X ] Z +E[Y ] (1 PI ) PO t c ; (18)

7 142 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007 Fg. 5. Illustraton of treatng each AC as a queueng system. Var[AD ] = Var[X ] Z 2 + Var[Y ] ( (1 PI ) PO t c ) 2. (19) We can also derve the mean watng tme n the queue for each data receved from the upper layer to each AC, as shown n Fg. 5. Based on (18), we can express the end-to-end delay of a packet transmsson for AC[] by E[D ] = E[Q ]+E[X ] Z + E[Y ] (1 PI) PO t C + t s,whereq s the watng tme spent n the queue of AC[] before the packet tres to access the wreless medum, and t s corresponds to the average tme of a successful data transmsson for AC[]. Toderve E[Q ], we consder two arrval traffc patterns. A. Posson Arrval Traffc Each AC n an EDCA staton can be modeled as an M/G/1 queueng system f the traffc nto the watng queue follows Posson arrvals. Thus, the backoff procedure along wth transmsson mechansm of each AC s the server of the M/G/1 system. The mean and the varance of the servce tme T n the queueng system then can be expressed as below. E[T ] = E[X ] Z + E[Y ] (1 PI) PO t c + t s ; Var[T ] = Var[X ] Z 2 + Var[Y ] ( (1 PI) PO t c ) 2. (20) Wth the P-K formula for an M/G/1 system n [16] and [17], the average watng tme n the queue E[Q ] can be expressed by (21), where λ s the Posson arrval rate of traffc to AC[]. Here we assume that λ s large enough so that AC[] s always backlogged. E[Q ]= λ E[T 2] 2(1 λ E[T ]) = λ (Var[T ]+E 2 [T ]). (21) 2(1 λ E[T ]) The expected number of data frames E[F ] n the queue of AC[] can be derved by E[F ]=λ E[Q ]= λ2 (Var[T ]+E 2 [T ]). 2(1 λ E[T ]) Wth average data frame sze E[L ], the average queue sze of AC[] s expressed by E[L ] E[F ]. B. Non-Posson Arrval Traffc For non-posson arrvals, each AC can be modeled as a G/G/1 system, from whch the upper and lower bounds of average watng tme spent n the queue can stll be derved. Let λ be arrval rate and α be the varance of nter-arrval tme for the traffc enterng AC[]. Hereweassumethatλ s large enough such that AC[] s always backlogged. Wth the upper and lower bounds of a G/G/1 system, the range of the average watng tme n the queue of AC[] can be derved wth these two characterstc parameters of arrval traffcs: (λ,α ). λ Var[T ]+E[T ](λ E[T ] 2) 2(1 λ E[T ]) E[Q ] λ(α+v ar[t]) 2(1 λ E[T ]) (22) Note that λ E[T ] s the server utlzaton of a G/G/1 system. When λ E[T ] approaches one,.e. when the traffc load s heavy or the wreless medum s very busy, the watng tme n the queue wll grow dramatcally. From (22), the range of the mean end-to-end delay E[D ] can also be derved. Then the expected range of the number of data frames E[F ] n the queue of AC[] can be expressed by λ 2 Var[T]+E[T](λ2 E[T] 2λ) 2(1 λ E[T ]) E[F ] λ2 (α+var[t]) 2(1 λ E[T ]). Agan, wth the average data frame sze E[L ], the average queue sze of AC[] can be expressed by E[L ] E[F ]. For constant bt rate traffc, such as voce and meda streamng, the characterstc parameters of those arrval traffc should smply be (λ,α =0). Thus, (22) can further be reexpressed by A B E[Q ] A; A = λ Var[T] 2(1 λ E[T ]) ; B = E[T] (2 λ E[T]) 2(1 λ E[T ]) = E[T ] (1 + λ E[T] 2(1 λ ). E[T ]) (23) Note that λ E[T ] s the utlzaton of the server. In order to make the system stable, the value of λ E[T ] must be confned between 0 and 1. Here 0 corresponds to an dle server, and 1 means that the server s fully utlzed. Apparently, when λ E[T ] s close to 1, E[T ] (1 + λ E[T] 2(1 λ ) E[T ]) = E[T ], whch means B s small as compared to the total delay spent n the queue. Therefore, when the traffc load s very heavy, E[Q ] = A = λ Var[T] 2(1 λ E[T ]) for constant bt rate traffc wth arrval rate λ. Ths result can be very useful, snce each AC s always busy wth sendng frames n our prevous assumpton,.e. the utlzaton of each AC s close to 1. IV. PERFORMANCE EVALUATION In ths secton, the analytcal model derved n the prevous secton s valdated wth the ns-2 EDCA mplementaton created by G. Chesson and A. Sngla [18]. The data frames of all ACs are fxed at 256 bytes, and the frame retry lmt s fxed at 7. For each AC, CBR UDP traffc s generated at a rate of 1Mbps. Each staton keeps sendng packets to the AP to acheve the saturaton throughput. There s no traffc gong between any two neghborng statons, and no traffc from an AP to other statons except ACK frames. The smulaton parameters are lsted n Table II. We smulate two access modes: basc mode and RTS/CTS mode. In each mode, we measure the followng tems: () Aggregate throughput for all ACs: the overall throughput of each AC n the system. ()

8 HUANG AND LIAO: THROUGHPUT AND DELAY PERFORMANCE OF IEEE E ENHANCED DISTRIBUTED CHANNEL ACCESS (EDCA) 143 TABLE II PARAMETER SETTINGS USED IN THE SIMULATION General Parameters Value Data Transmsson Rate 24Mbps Control Message Transmsson Rate 6Mbps Bytes per OFDM symbol 27 An dle slot tme 9 μsec SIFS tme 16 μsec DIFS=SIFS+2 slot 34 μsec Propagaton delay 1 μsec Maxmum staton number 25 RTS frame length 20 octets CTS frame length 14 octets Data payload length 256 octets ACK frame length 14 octets MAC sublayer overhead 28 octets PHY layer overhead 20 μsec OFDM symbol nterval 4 μsec CBR sendng nterval of each AC 1 msec AC 0,1,2,3 retry lmt 7 Frst Set of EDCA parameters Value AC 0 (CW mn,cw max) (15,31) AF IS 0 SIFS + 2 slots AC 1 (CW mn,cw max) (31,63) AF IS 1 SIFS + 3 slots AC 2 (CW mn,cw max) (31,127) AF IS 2 SIFS + 4 slots AC 3 (CW mn,cw max) (63,255) AF IS 3 SIFS + 4 slots Second Set of EDCA parameters Value AC 0 (CW mn,cw max) (31,63) AF IS 0 SIFS + 2 slots AC 1 (CW mn,cw max) (63,127) AF IS 1 SIFS + 2 slots AC 2 (CW mn,cw max) (127,255) AF IS 2 SIFS + 3 slots AC 3 (CW mn,cw max) (127,255) AF IS 3 SIFS + 7 slots MAC-to-MAC delay of each AC: the delay from the MAC layer of the sender to the MAC layer of the recever. () MAC-to-MAC jtter of each AC: the standard devaton of MAC-to-MAC delay of each AC. (v) End-to-end delay of each AC: the delay from the UDP layer of the sender to the UDP of the recever, ncludng both queueng delay and the MAC-to-MAC delay. Fgs. 6 to 9 plot the analytcal curves (sold lnes) and the smulaton curves (dashed lnes) based on the two sets of dfferent EDCA parameter combnatons descrbed n Table II. In each fgure, the sub-fgure(a) represents the results obtaned from the frst set of parameter settngs, and the sub-fgure(b) represents the results from the second set of parameter settngs. We can see that all the analytcal curves match the smulaton ones very well. Thus, the total backoff counter of a successful transmsson for an AC, whch s assumed to be a geometrc dstrbuton (eq (14)), can be verfed. Note that due to space lmtatons, we only nclude the results of the RTS/CTS mode. The results of the basc access mode are consstent wth those ncluded n ths paper. V. CONCLUSION In ths paper, we have developed the performance of EDCA n terms of the saturaton throughput, the delay, and the jtter for IEEE e WLANs. The contrbutons of ths paper are summarzed as follows. () We consder vrtual collsons Fg. 6. Aggregate throughput of each AC from frst parameter settngs (left) and second parameter settngs (rght). among dfferent ACs nsde each EDCA staton n addton to external collsons among statons. Thus, our model can capture the behavor of e EDCA more accurately than exstng work. () We consder the mpact of hgh-prorty ACs AIFSs on low prorty ones. Thus, the probablty that the backoff counter of each AC can be decreased by one n each tme slot may not be dentcal or equal to one. () We model the effect of the frame retry lmt,.e., the maxmum number of retransmssons each frame can experence before beng dropped. After ths lmt s reached, the retryng data frame s dscarded. (v) In addton to modelng the saturaton throughput as n exstng work, we also model the delay and delay jtter performance. Smulatons based on ns-2 are conducted to verfy the analytcal model. The results show that the analytcal curves match the smulaton results very well, provng that our analytcal model s very accurate n descrbng the behavor of IEEE e EDCA.

9 144 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 6, NO. 1, JANUARY 2007 Fg. 7. MAC-to-MAC delay of each AC from frst parameter settngs (left) and second parameter settngs (rght). REFERENCES [1] IEEE , Wreless LAN medum access control (MAC) and physcal layer (PHY) specfcatons, IEEE Standard, Aug [2] IEEE WG, IEEE e/D5.0, Draft supplement to standard for telecommuncatons and nformaton exchange between systems- LAN/MAN specfc requrements-part 11: Wreless medum access control (MAC) and physcal layer (PHY) specfcatons: Medum access control (MAC) enhancements for qualty of servce (QoS), Aug [3] A. Grlo and M. Nunes, Performance evaluaton of IEEE e, n Proc. IEEE PIMRC, Sep. 2002, vol. 1, pp [4] D. He and C. Q. Shen, Smulaton study of IEEE e EDCF, n Proc. IEEE VTC-Sprng, Apr. 2003, vol. 1, pp [5] S. Cho, J. Pavon, S. N. Shankar, and S. Mangold, IEEE e EDCF performance evaluaton, n Proc. IEEE ICC, May 2003, vol. 2, pp [6] J. Pavon and S. N. Shankar, Impact of frame sze, number of statons, and moblty on the throughput performance of IEEE e, IEEE WCNC, Mar. 2004, vol. 2, pp [7] H. Zhu and I. Chlamtac, An analytcal model for IEEE e EDCF dfferental servces, n Proc. ICCCN, Oct. 2003, pp Fg. 8. MAC-to-MAC jtter of each AC from frst parameter settngs (left) and second parameter settngs (rght). [8] J. W. Robnson and T. S. Randhawa, Saturaton throughput analyss of IEEE e enhanced dstrbuted coordnaton functon, IEEE J. Select. Areas Commun., vol. 22, no. 5, pp , June [9] P. Ferre, A. Doufex, A. Nx, and D. Bull, Throughput analyss of IEEE and IEEE e MAC, n Proc. IEEE WCNC, Mar. 2004, vol. 2, pp [10] X. Yang, Enhanced DCF of IEEE e to support QoS, n Proc. IEEE WCNC, [11] S. Mangold, S. Cho, G. R. Hertz, O. Klen, and B. Walke, Analyss of IEEE e for QoS support n wreless LANs, IEEE Wreless Commun. Mag., vol. 10, pp , Dec [12] G. Banch, Performance analyss of the IEEE dstrbuted coordnaton functon, IEEE J. Select. Areas Commun., vol. 18, pp , Mar [13] J. Gosteau, M. Kamoun, S. Smoens, and P. Pellat, Analytcal developments on QoS enhancements provded by IEEE EDCA, n Proc. IEEE ICC, June 2004, vol. 7, pp [14] P. Chatzmsos, A. C. Boucouvalas, and V. Vtsas, Performance analyss of IEEE DCF n presence of rransmsson errors, n Proc. IEEE ICC, June 2004, vol. 7, pp [15], IEEE packet delay-a fnte retry lmt analyss, n Proc. IEEE Globecom, Dec. 2003, vol. 2, pp

10 HUANG AND LIAO: THROUGHPUT AND DELAY PERFORMANCE OF IEEE E ENHANCED DISTRIBUTED CHANNEL ACCESS (EDCA) 145 [16] D. Bertsekas and R. Gallager, Data Networks. Upper Saddle Rver, NJ: Prentce Hall PTR, [17] D. Gross and C. M. Harrs, Fundamentals of Queueng Theory. New York: John Wley and Sons, Inc, [18] ns-2. [Onlne.] Avalable: planete/qn/research.html [19] G. Banch, I. Tnnrello, and L. Scala, Understandng e contenton-based prortzaton mechansms and ther coexstence wth legacy statons, IEEE Network, vol. 19, no. 4, pp , July/Aug Chng-Lng Huang receved hs BS ( 99) and MS ( 04) degrees from Electrcal Engneerng, Natonal Tawan Unversty. From 2005, Chng-Lng s workng at CCIT(Calforna Center for Innovatve Transporaton) on Berkeley campus. Hs current projects ncludes BHL(Berkeley Hghway Lab) vdeo traffc montorng, the WMax backhaul network, HICOMP(Hghway Congeston Montorng Program) software archtecture desgn, and Travel Tme estmaton on CMS(Changeable Message Sgns). Chng-Lng s gong to pursut hs PhD degree at Cvl System, U.C. Berkeley from Fall 06. Hs research areas cover wreless communcaton, vehcular network, VII(Vehcle-Infrastrcutrue Integraton), and realted ITS (Intellent Transportaton System) ssues. Fg. 9. End-to-End delay of each AC from frst parameter settngs (left) and second parameter settngs (rght). Wanjun Lao receved her BS and MS degrees from Natonal Chao Tung Unversty, Tawan, n 1990 and 1992, respectvely, and the Ph.D. degree n Electrcal Engneerng from the Unversty of Southern Calforna, Los Angeles, Calforna, USA, n She joned the Department of Electrcal Engneerng, Natonal Tawan Unversty (NTU), Tape, Tawan, as an Assstant Professor n Snce August 2005, she has been a full Professor. Her research nterests nclude wreless networks, multmeda networks, and broadband access networks. Dr. Lao s actvely nvolved n the nternatonal research communty. She s currently an Assocate Edtor of IIEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS and IEEE TRANSACTIONS ON MULTIMEDIA. Shewas a tutoral co-char of IEEE INFOCOM 2004, and the TPC vce char of IEEE Globecom 2005 (Autonomous Network Symposum). Dr. Lao has receved many research awards. Two papers she co-authored wth her students receved the Best Student Paper Award of the Frst IEEE Internatonal Conferences on Multmeda and Expo (ICME) n 2000, and the Best Paper Award of the Frst Internatonal Conference on Communcaton, Crcuts and Systems n She was a recpent of K. T. L Young Research Award honored by ACM Tape chapter 2003for her research achevement. Dr. Lao was elected as one of Ten Dstngushed Young Women n Tawan n 2000 and was lsted n the Marqus Who s Who n Scence and Engneerng, and the Contemporary Who s Who n 2003.