Analysis of QoS in WLAN

Transcription

1 Analyss of QoS n WLAN PAAL E. ENGELSTAD AND OLAV N. ØSTERBØ Paal E. Engelstad s Research Scentst n Telenor R&D An analytcal model s proposed to descrbe the prorty schemes of the EDCA mechansm of the IEEE e standard. EDCA provdes class-based dfferentated QoS to IEEE WLANs. The man contrbuton of ths paper as opposed to other works, s that the model predcts the throughput, delay and frame droppng probabltes of the dfferent traffc classes n the whole range from a lghtly loaded, non-saturated channel to a heavly congested, saturated medum. Furthermore, the model descrbes dfferentaton based on dfferent AIFS-values, n addton to the other adjustable parameters (.e. wndow szes, retransmsson lmts, TXOP lengths, etc.) also encompassed by prevous models. AIFS dfferentaton s descrbed by a smple equaton that enables access ponts to predct at whch traffc loads starvaton of a traffc class wll occur. Moreover, vrtual collson handlng s ncluded nto the model. We show how ths part of the model can also be used to model the performance of the Vrtual Collson Handler. The model s calculated numercally and valdated aganst smulaton results. We observed a good match between the analytcal model and smulatons. Olav N Østerbø s Senor Research Scentst n Telenor R&D I Introducton Durng recent years the IEEE WLAN standard [1] has been wdely deployed as the most preferred wreless access technology n offce envronments, n publc hot-spots and n the homes. Due to the nherent capacty lmtatons of wreless technologes, the WLAN easly becomes a bottleneck for communcaton. In these cases, the QoS features of the e standard wll be benefcal to prortze for example voce and vdeo traffc over more elastc data traffc. The IEEE medum access control (MAC) comprses the mandatory Dstrbuted Coordnaton Functon (DCF) as a contenton-based access scheme, and the optonal Pont Coordnaton Functon (PCF) as a centrally controlled pollng scheme. However, PCF s hardly mplemented n any products, and DCF represents the commonly used MAC mechansm of DCF adopts carrer sense multple access ( lsten-before-talk ) wth collson avodance (CSMA/CA) and uses bnary exponental backoff. A staton not only goes nto backoff upon collson. It also carres out a post-backoff after havng transmtted a packet, to allow other statons to access the channel before t transmts the next packet. The IEEE e standard [2] works as an extenson to the standard, and the Hybrd Coordnaton Functon (HCF) s used for medum access control. HCF comprses the contenton-based Enhanced Dstrbuted Channel Access (EDCA) as an extenson for DCF, and the centrally controlled Hybrd Coordnated Channel Access (HCCA) as a replacement for PCF. EDCA has receved most attenton recently, and t seems that ths s the WLAN QoS mechansm that wll be promoted by the majorty of vendors. EDCA s therefore the area of nterest of ths paper, and HCCA wll not be dscussed any further here. EDCA enhances DCF by allowng four dfferent access categores (ACs) at each staton and a transmsson queue assocated wth each AC. Each AC at a staton has a conceptual module responsble for channel access for each AC and n ths paper the module s referred to as a backoff nstance. Hence each of the four transmsson queues (and the assocated ACs) on a staton s represented by one backoff nstance. The channel access between dfferent backoff nstances on a staton s not completely ndependent due to the vrtual collson handlng between the queues on the staton. If two or more backoff nstances on the same staton try to access the channel n the same tmeslot, the staton attempts to transmt the frame of the hghest prorty AC, whle the lower prorty frames wll go through backoff. The traffc class dfferentaton of EDCA s based on assgnng dfferent access parameters to dfferent ACs. Frst and foremost, a hgh-prorty AC,, s assgned a mnmum contenton wndow, W 0,, that s lower than (or at worst equal to) that of a lower-prorty AC. At a hghly loaded (or saturated ) medum, the post-backoff of the hgh-prorty AC wll normally be smaller than the post-backoff of a low-prorty AC. Ths results n an average hgher share of the channel capacty, because the hgh-prorty AC wll on average have to refran from the channel for a shorter perod of tme than the low prorty AC. Another mportant parameter settng s the AIFS value, measured as a Short Interframe Space (SIFS) pluss an AIFSN number of tmeslots. A hgh-prorty AC s assgned an AIFSN that s lower than (or at 132 Telektronkk

2 worst equal to) the AIFSN of a lower-prorty AC. The most mportant effect of the AIFSN settng s that the hgh-prorty AC normally wll be able to start earler than a low prorty AC to decrement the backoff counter after havng been nterrupted by a transmsson on the channel. At a hghly loaded channel where the decrementng of the backoff counter wll be nterrupted by packet transmssons a large number of tmes, the backoff countdown of the hghprorty AC wll occur at a hgher average speed than that of the lower-prorty AC. As the wreless medum gets more and more congested, the average number of empty tmeslots between the frames transmtted by the hgher-prorty ACs mght be lower than the AIFSN value of the low-prorty AC. At ths pont, the AC wll not be able to decrement ts backoff counter, and all packets wll fnally be dropped nstead of beng transmtted. Ths s referred to as starvaton. Other dfferentaton parameters that may be adjusted n e (and whch are also explctly or mplctly ncluded n the model proposed below) are the retry lmt, L (of short and long packets), the maxmum contenton wndow W, L and the TXOP-lmt of each AC,. Most of the recent analytcal work on the performance e EDCA stems from the smple and farly accurate model proposed by Banch [3] to calculate saturaton throughput of DCF. Later, Zouva and Antonakopoulos [4] mproved the model to fnd saturaton delays, however, stll of the undfferentated DCF. They also mproved the model by stoppng the backoff counter durng busy slots, whch s more consstent wth the IEEE standard. Based on ths work, Xao [5] extended the model to the prortzed schemes provded by e by ntroducng multple ACs wth dstnct parameter settngs, such as the mnmum and maxmum contenton wndow. It s also straghtforward to extend the model for the use of dfferent TXOP szes of dfferent classes. Furthermore, ths prortzed model also ntroduced a fnte retry lmt. Ths addtonal dfferentaton parameter leads to more accurate results than prevous models. (A lst of references for other relevant efforts and model mprovements of DCF can also be found n [5].) A dfferentaton parameter lackng n Xao s model, however, s the mportant AIFS parameter. Xao assumed equal AIFSN of all traffc classes. (In fact, a stuaton wth only two dfferent ACs was analyzed n the work.) Furthermore, the model does not correctly capture starvaton. In many cases the QoS-enabled Access Pont (QAP) would need to predct when the starvaton of an AC wll occur, so that t wll be able to know when to change the current parameter settngs, e.g. to avod that any AC s completely starved. The man problem s that the QAP cannot know that an AC s starved smply by observng that t does not receve any traffc of that AC. The reason for not recevng the traffc mght just as well be that the other statons, QSTAs, are accdentally not transmttng any traffc of that AC. By havng starvaton correctly descbed by the model, the QAP has a means to predct at whch traffc loads starvaton of an AC wll occur. It can predct starvaton smply by measurng the traffc load on the channel. The QAP mght also be nterested n predctng at whch traffc levels the Vrtual Collson Handler (VCH) wll start to starve a traffc class. The model s also lmted, as a fully saturated channel s assumed. Due to the bursty characterstcs of many types of data traffc, t s unlkely that the channel wll be fully saturated all the tme. The rate adaptaton of TCP, for example, wll often ensure that the total channel load wll not be fully saturated. Hence, n many cases an access pont wll be more nterested n knowng how to set parameters for a lghtly saturated channel, and to adjust these parameters dynamcally n ths regon. An analytcal model that covers the full range from a non-saturated to a fully saturated channel would be more useful. Ths paper extends Xao s model to enhance t n a number of ways: The presented model predcts the performance not only n the saturated case, but on the whole range from an unsaturated medum to a fully saturated channel. (Some works, such as [6] and [7] have explored unsaturated condtons, however, only of the one-class They are also prmarly focussed on the non-saturaton part nstead of fndng a good descrptve soluton for the whole range.) In the non-saturaton stuaton, our model accounts for post-backoff of an AC, although the queue s empty, accordng to the IEEE standard. If the packet arrves n the queue after the post-backoff s completed, the lsten-before-talk (or CSMA) feature of s also ncorporated n the model. Our model descrbes the use of AIFSN as a dfferentatng parameter, n addton to the other dfferentaton parameters encompassed by Xao s efforts and other works. Telektronkk

3 A smple closed-form equaton that predcts wth satsfactory accuracy the starvaton pont (or freeze pont ) of each traffc class s provded. The only prerequste for a staton (e.g. an access pont) to determne that starvaton of an AC has occurred, s to know the AIFSN value of the AC and to montor the traffc load on the channel. Vrtual Collson Handlng s treated n the model. The model s valdated aganst smulaton. Both uplnk and downlnk traffc scenaros are used. The majorty of other works that do analytcal performance evaluatons, emprcal smulatons and/or valdatons between analytcal numercal results and smulatons, seem to focus only on the uplnk traffc problem. They present results wth a number of statons contendng for the channel, and wth farly equal shares of traffc allocated to each staton and to each AC. In ths paper, we do smlar uplnk analyss as n earler works. However, n addton we look at downlnk traffc scenaros, whch mght be mportant n many real-lfe scenaros. The remanng part of the paper s organzed as follows: The next secton summarzes the dfferentaton parameters of e and provdes the bass for understandng the analytcal model. Secton III presents the analytcal model wth vrtual collson handlng and AIFS dfferentaton. Expressons for delays and estmaton of delay-dependent traffc parameters are calculated n Secton IV. In Secton V, expressons for the throughput (wth or wthout vrtual collson handlng) are found. Then, a secton s allocated to the valdaton of the model aganst smulatons. Both uplnk and downlnk traffc scenaros are consdered. Our fndngs are fnally summarzed n our concludng remarks. II Important dfferentaton parameters of E A Prorty based on Contenton Wndows (CWs) and Exponental Backoff For each AC, ( = 0,..., 3), we let W,j denote the contenton wndow sze n the j-th backoff stage,.e. AC[3] AC[2] AC[1] AC[0] AIFSN CWmn CWmax Retry Lmt (long/short) 7/4 7/4 7/4 7/4 Table 1 Recommended (default) parameter settngs for e after the j-th unsuccessful transmsson; hence W,0 = CW,mn + 1, where the recommended values for CW,mn are lsted n Table 1. We also denote j = m as the j-th backoff stage where the contenton wndow has reached CW,max + 1; the wndow wll no longer be ncreased n the subsequent backoff stages. Hence, m = log 2 ((CW,max + 1) / CW,mn + 1). Fnally, we let L denote the retry lmt of the retry counter; f the transmsson s unsuccessful after the L -th backoff stage, the packet wll be dropped. The specfcaton allows for dfferent retry lmts, Dot11ShortRetryLmt and Dot11LongRetryLmt, for packets that are longer than and shorter than the Dot11RTSThreshold, respectvely. In ths paper, however, we wll assume that the szes of all packets of a class are ether below or above the Dot11RTSTreshold-parameter, so that L s equal for all packets belongng to the same class. { 2 W,j = j W,0 ; j =0, 1,.., m 1 2 m W,0 = CW,max ; j = m,..., L In the specal case where m L, Eq. (1) s reduced to W,j = 2 j W,0 for j = 0, 1,..., L. (1) B Prorty based on Inter-Frame Spaces (IFSs) When a backoff nstance senses that the channel s dle after a packet transmsson, t normally wats a guard tme called the Dstrbuted Inter-Frame Space (DIFS) durng whch t s not allowed to transmt packets or do backoff countdown. The duraton of DIFS s the sum of a SIFS and two tme slots. The two tme slots of DIFS allow the Hybrd Coordnator (HC) on the QAP (or Pont Coordnator wth only plan ) to access the channel wth hgher prorty. The HC s allowed to enter the channel after only watng one tme slot (n addton to SIFS) and t does not need to go through post-backoff before accessng the channel. Moreover, certan packets ncludng the Clear-To-Send (CTS) and Acknowledgement (ACK) packets can be sent after only watng SIFS. Ths gves maxmum prorty to ths traffc, and ensures that a data exchange (such as a data transmsson followed by an ACK) can be consdered nearly an atomc transacton. Instead of usng DIFS, each AC[] of e uses an Arbtraton Inter-Frame Space (AIFS[]) that conssts of a SIFS and an AIFSN[] number of addtonal tme slots. In ths paper we defne A as: A = AIFS[] mn(aifs[]) 0 = 0,..., N 1 (2) where N s the number of dfferent ACs (.e. normally four). The e standard mandates that AIFSN[] 2, where the mnmum lmt of 2 slots corresponds to the DIFS nterval. The use of AIFSN to dfferentate between ACs has two consequences. Assume two 134 Telektronkk

4 backoff nstances wth dfferent AIFSNs. Both have a packet to send, but the channel s busy, so they have to wat. The frst effect occurs when nether of the two backoff nstances s n backoff;.e. they are not n bnary backoff and the post-backoff s completed (or the post-backoff s not necessary because t s the frst packet ever to be sent). In ths case, when the channel s sensed dle, the backoff nstance wth the lowest AIFSN s the frst to be allowed to make a transmsson attempt. The other backoff nstance wll sense that the channel s busy durng ths tme slot. It wll have to wat untl the transmsson attempt of the frst backoff nstance s completed before t s allowed to transmt the packet. The second effect occurs when both backoff nstances are n backoff. To descrbe the effect, assume that the backoff counters of both backoff nstances are equal. Each tme a packet transmsson s completed, the backoff contnues the countdown of dle tme slots as soon as the AIFS nterval s completed. However, after the packet transmsson, the backoff nstance wth the lowest AIFSN wll start countng down dle tme slots before the other backoff nstance s allowed to enter the count down procedure. Thus, the backoff nstance wth the lowest AIFSN wll be able to count down the backoff wndow faster than the backoff nstance wth hgher AIFSN. B Prorty based on Transmsson Opportuntes (TXOPs) Prorty based on dfferentated Transmsson Opportuntes s not treated explctly n ths paper. For smplcty and to keep focus on the most mportant ssues, we have assumed that all traffc classes send packets of equal lengths (.e. of 1024 bytes), and that each packet fts perfectly nto one TXOP. Calculatng the model wth respect to dfferent packet lengths s easy, as shown by Xao [5]. It s also easy to extend our analyss to contenton-free burstng (CFB) wthn a TXOP by summng up the dfferent SIFS occurrng between subsequent packets of the burst. III Analytcal model A Prorty based on Transmsson Opportuntes (TXOPs) Fgure 1 llustrates the Markov chan for the transmsson process of a backoff nstance of prorty class. The state changes n the fgure occur only when the backoff nstance s able to contend for the channel. If one or more statons transmt n a tme slot, that slot s sensed busy by the backoff nstances. For the subsequent tme that the packet s under transmsson, the backoff nstance remans n the same state. The Markov process fnally resumes at the frst slot where the channel agan s open for contenton,.e. after the transmsson (or collson) s completed and after the real-tme duraton of an addtonal DIFS. Hence the (vrtual) tme scale s dscrete and ntegral, and a backoff slot that s open for contenton trggers each clock tck. Measured n real-tme the duraton of a slot that leads to transmsson s equal to the length of the transmsson ncludng the RTS and CTS (f beng used), the data packet and the ACK as well as all the assocated nter-frame spaces. The real-tme duraton of an empty slot s equal to the duraton of a regular backoff slot. In the Markov chan, the utlzaton factor, ρ, represents the probablty that there s a packet watng n the transmsson queue of the backoff nstance of AC at the tme a transmsson s completed (or a packet dropped). Now, the backoff selects a backoff nterval k at random and goes nto post-backoff. If the queue s empty, at a probablty 1 ρ, the post-backoff s started by enterng the state (, 0, k, e). If the queue on the other hand s non-empty, the post-backoff s started by enterng the state (, 0, k). Hence, ρ balances the fully non-saturated stuaton wth the fully saturated stuaton and therefore plays a role to model the behavour of the ntermedate sem-saturated stuaton. We see that when ρ > 1 the Markov chan behavour approaches that of the non-saturaton case smlar to the one presented by Xao [5]. On the other hand, when ρ > 0 the Markov chan models a stochastc process where the backoff nstance after transmsson always goes nto post-backoff wthout a packet to send. As mentoned above, the states (, 0, k, e) n the upper row are entered when the channel s not fully saturated and when the queue of a backoff nstance s empty at the tme a transmsson s completed (or a packet dropped). The states (, 0, 1, e),..., (, 0, W,0 1, e) represent a stuaton where the transmsson queue s empty, but the staton s countng down backoff slots. The probablty that a backoff nstance of AC s sensng the channel busy and s thus unable to count down the backoff slot from one tmeslot to the other s denoted by the probablty p *. (We use the astersk to ndcate that ths s a probablty related to the countdown process.) It undertakes a countdown at probablty 1 p * and moves to another state. If t has receved a packet whle n the prevous state at a probablty q *, t moves to a correspondng state n the second row wth a packet watng for transmsson. Otherwse, t remans n the frst row wth no packets watng for transmsson. Whle n the state (, 0, 0, e), on the contrary, the backoff nstance has completed post-backoff and s only watng for a packet to arrve n the queue. If t Telektronkk

5 p /W j ρ 1-ρ q p 1(-ρ )/W,0 f from state{, L ; 0}; otherwse: (1-ρ )(1-p )/W, 0 1-q (1-q* )(1- ), 0, 0, e, 0, 1, e (1-q* )(1- ) (1-q* )(1- ) (1-q* )(1- ) (1-q* )(1- ), 0, 2, e,0,w,0-2,e,0,w,0-1,e q(1-p ) q* (1- ) q* (1- ) q* (1-p * ) 1-p 1-p*, 0, 0 1-p*, 0, 1, 0, 2 1-,0,W,0-2 1-,0,W,0-1 p /W 1 ρ/w,0 f from state{, L ; 0}; otherwse: ρ (1-p )/W, 0 1-p,j-1,0 1- p /W j p /W j 1-p 1-1-p*,j, 0, j, 1, j, , j,w,j -2, j,w,j -1 p /W j+1 p /W L1 p /W L1 1-p, L, 0 1-, L, 1 1-, L, p*, L,W,L -2, L,W,L -1 p DROP Fgure 1 Markov Chan (both saturaton and non-saturaton) receves a packet durng a tmeslot at a probablty q, t does a lsten-before-talk channel sensng and moves to a new state n the second row, snce a packet s now ready to be sent. If the backoff nstance senses the channel busy, at a probablty p, t performs a new backoff. Otherwse, t moves to state (, 0, 0, e) to do a transmsson attempt. The transmsson succeeds at a probablty 1 p. Otherwse, t doubles the contenton wndow and goes nto another backoff. All other rows apart from the frst row n the fgure llustrate a stuaton wth at least one packet n the system. Indeed, only these states are entered n the extreme case of a fully saturated channel and a nonzero traffc load on each AC, so that the transmsson queue s always full. Hence, after successful transmsson or after a packet has been dropped, the backoff nstance proceeds drectly nto one of the postbackoff states (, 0, k) (for k = 0, 1,..., W,j 1). For each unsuccessful transmsson attempt, the backoff nstance moves to a state n a row below at a probablty p. However, f the packet has not been successfully transmtted after L + 1 attempts, the packet s dropped. Hence, the accumulated frame droppng probablty, P,drop, can be estmated as: 136 Telektronkk

6 P,drop = p L +1 (3) Let b,j,k denote the state dstrbutons. Snce the probablty of a transmsson attempt enterng stage j (where j = 0, 1,..., L ) s p j, chan regulartes yeld: b,j,0 = p j b,0,0 ; j = 0, 1,..., L (4) Furthermore, we observe that a backoff nstance transmts when t s n any of the states (, j, 0) where j = 0, 1,..., L. Hence, f we let τ denote the transmsson probablty (.e. the probablty that a backoff nstance n prorty class transmts durng a generc slot tme, ndependent on whether the transmsson results n a collson or not), we have: L 1 p L+1 τ = b,j,0 = b,0,0 1 p j=0 (5) In the followng subsecton we wll fnd ways to express b,j,0 and p n terms of τ. Hence, a complete descrpton of the system can be found by solvng the above set of equatons (one equaton per AC ). B Markov chan analyss Frst we wll look at the post-backoff stage of the Markov chan for j = 0. From chan regulartes, we observe that: L 1 b,0,0 = b,l,0 + (1 p )b,j,0 By workng recursvely through the chan from rght to left n the upper row, we get: Furthermore, we see that: (6) (7) (8) From the upper left part of the Markov dagram we see that b,0,w,0-1 = b,0,0 / ((1 p * )W,0 ). By workng recursvely and horzontally through the chan we also observe that: for j=0 b,0,k,e = (1 ρ )b,0,0 1 (1 q )W,0 k W,0 (1 p ) ; k =1, 2,..., W,0 1 b,0,0,e = (1 ρ )b,0,0 W,0 q b,0,k = Undertakng the same analyss for the rest of the chan, we get: b,j,k = q 1 (1 q )W,0 q W,k k W,0 (1 p )(b,0,0 + q p b,0,k,e ) b,0,k,e k =1, 2,..., W,0 1 W,j k W,j (1 p )pj b,0,0; (9) (10) j =1,..., L and k =1, 2,..., W,0 1 Fnally, the normalzaton requres that: W,0 1 k=0 Ths yelds: 1 b,0,0 = L b,0,k,e + L j=0 j=0 W,j 1 k= p b,j,k =1 W,j k k=0 W,j k p j W,j (11) + 1 ρ 1 (1 q ( )W,0 1 q W,0 q 1+ (W ),0 1)q p (12) 2(1 p ) The frst sum n the equaton above represents the saturaton-part, whle the second part s the domnant term under non-saturaton. Hence, the expresson provdes a unfed model encompassng all channel loads from a lghtly loaded non-saturated channel, to a hghly congested, saturated medum. Ths full-scale model wll be valdated below. The non-saturaton part of the expresson mght requre further explanaton. Frst, the factor (1 ρ ) (where ρ s the utlsaton factor of the backoff nstance) represents the probablty of havng an empty queue after successful transmsson. If ths happens, t enters the empty-queue post-backoff procedure, whch s represented by the states (, 0, 0, e),, (, 0, W,0 1, e). Second, the geometrc sum 1 (1 q * ) W,0 / (W,0 q * ) expresses the probablty of not recevng any packets n the transmsson queue whle performng the complete empty-queue post-backoff. In other words, t s the probablty of fnally endng n the state (, 0, 0, e), nstead of transtonng to any of the regular post-backoff states (, 0, 0),, (, 0, W,0 2) where a packet s watng to be transmtted. In the geometrc sum, q * s the probablty that such a transton wll take place between any of the countdowns. Hence, q * s the probablty of recevng a packet durng the tmescale of one slot that s counted down. (The astersk denote that the probablty s assocated wth the countdown process.) Thrd, whle watng for a packet n the state (, 0, 0, e), q (wthout the astersk) represents the traffc generaton probablty. Wth a lghtly loaded channel, the factor 1 / q wll be the domnant part of the equaton. At low loads the factor ensures the typcal non-saturaton behavour where successfully transmtted traffc equals the traffc enterng the transmsson queue. Fnally, the factor (1+(W,0 1) q p / 2(1 p )) appears as a consequence of the lsten-before-talk test n state (, 0, 0, e) (whch can be replaced wth 1 f the test s not mplemented). We also note that the saturaton part of the equaton can be wrtten out. Performng the summaton, we wrte the frst sum as eq. (13), see overleaf. Telektronkk

7 L j= p W,j k k=0 W,j k p j W =,j (1 2p )(1 2p)(1 pl +1 )+W,0(1 p )(1 (2p ) L +1 ) 2(1 p )(1 p)(1 2p) ; m >L [ (1 2p )(1 2p)(1 pl +1 )+W,0 (1 p )(1 (2p ) m )+(1 2p )(2p ) m (1 p L m +1 2(1 p )(1 p)(1 2p) ; m L ] (13) C Modellng Probabltes wthout Vrtual Collson Handlng We let p b denote the probablty that the channel s busy. Snce ths means that at least one backoff nstance transmts durng a slot tme, we have: N 1 p b =1 (1 τ ) n (14) Here, n denotes the number of backoff nstances contendng for channel access n each prorty class, and N denotes the total number of classes. The probablty of unsuccessful transmsson p from one specfc backoff nstance (as descrbed n the Markov chan), requres that at least one of the other backoff nstances does transmt n the same slot: p =1 =0 N 1 (1 τ c ) nc =1 1 p b (15) 1 τ c=0,c D Probabltes wth Vrtual Collson Handlng It s possble to make modfcatons to take vrtual collsons nto account n the analytcal model. Consder for example a stuaton wth n statons and four actve transmsson queues on each staton. A backoff nstance can transmt packets f other backoff nstances do not transmt, except the backoff nstances of the lower prorty ACs on the same QSTA. The reason for ths excepton s that the vrtual collson handlng mechansm ensures that upon vrtual collson the hgher prorty AC wll be attempted for transmsson whle the colldng lower prorty traffc goes nto backoff. Ths can be generalzed by the expresson: N 1 c=0 p =1 (1 τ c) nc (16) c=0 (1 τ c) If ths expresson s replaced wth our orgnal expresson n (15), vrtual collsons should be correctly ncorporated n the model. E Modellng probabltes of the Vrtual Collson Handler tself One may use exactly the same analytcal model to study the behavour of the Vrtual Collson Handler (VCH). Here the VCH represents the channel, whle there are only N (typcally four) queues contendng for access;.e. one queue per AC. Hence, one may model the throughput of the Vrtual Collson Handler by settng n = 1 for all. In ths case, Eq. (14) s smply replaced by: N 1 p b =1 (1 τ ) =0 (17) and Eq. (15) s replaced by: p =1 (1 p N 1 b) (18) c=0 (1 τ c) =1 (1 τ c ) Here we note that the hghest prorty class wll correctly have p N-1 = 0, whch means that t s never blocked and never experences a collson when t tres to access the channel for transmsson. Lke before, N denotes the total number of classes. Note that the expressons typcally descrbe the specal case wth only one staton contendng for the channel, whch s the case when the channel refers to the vrtual channel represented by the VCH. These expressons wll be useful for analyss of downlnk traffc scenaros later n ths paper. F The backoff countdown rate wth AIFS dfferentaton At ths pont, we are ready to fnd all transmsson probabltes τ ( = 0, 1, 2, 3) for the saturaton condton (.e. by settng ρ = 1), wthout AIFS dfferentaton (by settng p * = p ). However, frst we wll ncorporate AIFS dfferentaton n ths subsecton. Then, n the next subsecton we wll subsequently fnd expressons for ρ, q, n order to later be able to fnd transmsson probabltes also under nonsaturaton condtons. We see that the model presented so far does not encompass AIFS dfferentaton. In the followng, however, we wll nclude AIFS dfferentaton as an ntegral part of the count-down blockng probablty, p *. The probablty that a backoff nstance senses a generc slot as dle s denoted p * n the Markov chan. Wthout AIFS dfferentaton, t equals the probablty that all other statons do not transmt, p : In ths artcle, however, we argue that IFS-dfferentaton can be modelled wth pretty good accuracy by adjustng the countdown blockng probablty p *. For the hghest prorty AC, AC[3], we set p 3 * = p 3. For lower prorty ACs wth a hgher AIFS (for whch A 1) we reduce ther countdown rate correspondngly. The addtonal A slots, where lower prorty backoff nstances of class have to suspend the backp,a =0 = p =1 1 p b 1 τ c=+1 (19) 138 Telektronkk

8 n*p b busy slots n*(a *p b ) blocked slots n*(1-p b ) emty slots n*(1-(a +1)*p b ) unblocked emty slots n slots n s large Fgure 2 Smplfed llustraton of the prncple of AIFS dfferentaton off countdown, are modelled as beng smeared out randomly and dstrbuted unformly over all slots. Ths assumpton s requred to be able to treat the A slots wthn the Markov model. (In realty, an A slot wll only occur after another A slot, or after a successful or unsuccessful packet transmsson.) Usng ths smple assumpton, t s possble to scale down the probablty of detectng an empty slot. Ths down-scalng can be llustrated n Fgure 2. Here a large number of n slots are grouped nto three groups; busy slots (due to successful transmssons or collsons), empty slots that are blocked (due to the AIFSN settng of the AC n consderaton) and other empty slots that are not blocked. Each busy slot leads to a proportonal share of empty slots beng blocked, where A yelds the proporton of blocked slots for the AC n queston. By replacng p b wth the new scaled expresson (A +1)p b, we derve a new scaled expresson for p, whch s denoted p * : (1 p )= 1 (A +1)p b 1 τ However, to mantan consstency n the model, a mnmum bound s ntroduced: p =mn(1,p + A p b 1 τ ) Thus, starvaton occurs when p * 1 n Eq. (17) or when p * = 1 n Eq. (18). Snce at ths pont τ > 0, starvaton can be roughly predcted to occur when: (20) (21) p b 1 (22) 1+A Although ths approxmate expresson seems rather rough, ts usefulness s strkng. In the sem-saturated case, an AP s normally nterested n adjustng channel access parameters (such as contenton wndows, AIFSN etc.) for each traffc class to control the share of the channel allocated to each AC. By means of the above expresson, the AP can smply predct from the traffc load that t pours nto the transmsson queues, whether any AC wll face starvaton when the traffc s handled by the VCH. An alternatve approach s to nclude AIFS countdown explctly n the Markov chan [11]. However, the model becomes all too complex to be useful except for the smplest settngs of the AIFS parameters. For example, n [11] the lowest prorty AC s confgured wth AIFSN = 3, whle for all other ACs the AIFS s set equal to DIFS. More flexble confguratons of the AIFSNs seem complcated wthn ths framework. IV Estmaton of the traffc parameters ρ, q and q * A Delay and Servce Tme under saturaton condtons and nfnte queues In order to be able to determne an expresson for ρ we frst need expressons for the packet delays under both saturated and non-saturated condtons. Under saturaton condtons, the queue s always full of packets ready to be transmtted (.e. the utlzaton, ρ, of the queue s equal to 1). To study delay under these condtons, we frst deal wth the delay assocated wth countng down backoff slots for the packets to be transmtted. The probablty of a successful transmsson exactly n the j-th stage s p j (1 p ). In each stage, h, the average countdown delay s T c * (W,h 1) / 2, and the accumulated delay for a packet sent n the j-th stage s found by summng all h stages up tll j. In summary, the expected countdown delay, D CD, s: D CD L = T e p j (1 p ) j=1 (23) Whle the backoff nstance s countng down, the probablty of facng an empty slot s 1 p * whle the probablty of beng blocked s p *. Hence, p * / (1 p * ) represents the share of slots where the countdown process s beng blocked. Whle beng blocked, the average delay s p s T s + (p b p s )T c. In summary, the expected blockng delay, D B, s: D B = D CD p 1 p j h=0 W,h 1 2 ( ( ) ) ps p b T s + 1 ps p b T c T e (24) Telektronkk

9 Furthermore, each tme a backoff nstance goes from the (h 1)-th to the h-th stage, there s a collson delay, T c * = T c + T TO, assocated wth the transmsson attempt that a backoff nstance must wat after experencng a collson before t can sense the channel dle agan. (Here, T TO s smply defned as the dfference between the collson delay, T c *, of a staton that partcpates n a collson and that of a staton not partcpatng, T c. When valdatng aganst smulatons, ts settng should reflect the mplementaton of the smulator.) The number of retry attempts s found by fndng the average of j. In summary the expected retry delay, D R, s: D R L = T c (1 p ) (25) Moreover, we must add the average transmsson delay, T s, assocated wth the successfully transmtted packets (occurrng at a probablty of (1 p L +1 ), resultng n the delay, D T : D T j=1 = T s (1 p L+1 ) Fnally, we must also take nto account the delay D drop assocated wth dropped packets (occurrng at a probablty of p L +1 ). We have: D CD,drop D B,drop = T e L h=0 = D CD,drop jp j W,h 1 2 p 1 p D R,drop = T c (L +1) D drop (26) (27) In concluson, we fnd that the total delay under saturaton condtons between packets that are ether successfully transmtted or dropped, s: D SAT (28) B Delay and Servce Tme on a non-saturated channel Under extreme non-saturaton condtons, however, the post-backoff s completed before a packet arrves n the transmsson queue to be transmtted. Thus, under these condtons the post-backoff wll not add to the transmsson delay, as t dd when we calculated the saturaton delays above. The easest way to handle ths s to subtract the post-backoff delay from the expressons above. D NON SAT ( T e + ( ( ) ) ps p b T s + 1 ps p b T c T e = p L+1 (D CD,drop + D B,drop + D R,drop = D CD + D B + D R + D T + D drop = D SAT W,0 1 2 p ( ( (1 p ) D CD,drop ps T s + p b ( 1 p ) ))) s T c p b (29) C Estmatng ρ Frst, for a G/G/1 queue, the probablty that the queue s non-empty, ρ, s gven by ρ = λx, where λ represents the traffc rate n terms of packets per second and x s the average servce tme. For smplcty, we assume here that the traffc rate faced by all backoff nstances of a class s the same on all statons and use λ to denote the traffc rate (n terms of packets per seconds) of traffc class on one staton. Then we have ( mn ) (30) It s possble to use arguments to determne ρ wth hgher accuracy. In all scenaros we studed and valdated, however, we dd not experence any sgnfcant dfferences between settng ρ = mn(1, λ D SAT ) and ρ = mn(1, λ D NON-SAT ). Hence, elaboratng on ths ssue s beyond the scope of ths paper. If we measure the delay parameters n terms of µs and the rate, R, n terms of Mbps and all packets are of 1024 bytes, we fnd that: (31) D Estmatng q and q * To estmate q of the non-saturaton model we assume that the traffc arrvng n the transmsson queue s Posson dstrbuted,.e. that we have an M/G/1 queue. q s the probablty that at least one packet wll arrve n the transmsson queue durng the followng generc tme slot under the condton that the queue s empty at the begnnng of the slot. Startng out wth the pdf of the length of a generc slot, b(t), we have: b(t) = p s δ(t T s ) + (1 p b )δ(t T c ) + (p b p s )δ(t T c ) (32) Consequently, q s calculated as: q =1 1,λ D NON SAT λ (µs) = R (Mbps) ) ( ρ mn e λt b(t)dt =1 ( ps e λts +(1 p b )e λte +(p b p s )e λtc) (33) Notng, however, that the model s approxmate by nature, t s possble to fnd the probablty based on the average length of the tmeslot. Hence, as a smplfcaton we mght approxmate: q 1 e λ((1 p b)t e+p st s+(p b p s)t c) 1,λ D SAT (34) 140 Telektronkk

10 Both expressons for q were valdated n a number of scenaros, and we dd not observe any sgnfcant dfferences between ether of them. Ideally, q * should be estmated dfferently, snce t expresses the probablty of recevng a packet n the tmescale of the countdown of one backoff slot, n contrast to q *. We tested a number of dfferent expressons for ths, but observed that settng q * equal to q for smplcty worked as a good approxmaton n all the scenaros we explored. V Throughput A Throughput wthout Vrtual Collson Handlng Let p,s denote the probablty that a packet from any of the backoff nstances of class s transmtted successfully n a tme slot. p,s = Let also p s denote the probablty that a packet from any class s transmtted successfully n a tme slot. p s = (35) (1 τ h ) n h(36) Then, the throughput of class, S, can be wrtten as the average real-tme duraton of successfully transmtted packets by the average real-tme duraton of a contenton slot that follows the specal tme scale of our model: p,s T,MSDU S = (37) (1 p b )T e + p s T s +(p b p s )T c T e denotes the real-tme duraton of an empty slot, whle T s,t c denote the real-tme duraton of a slot contanng a successfully transmtted packet and of a slot contanng two or more colldng packets, respectvely. The length of the longest colldng packet on the channel determnes T c. If all packets are of the same length, whch we wll consder n ths paper, T c = T s. (Otherwse refer to [12] to calculate T c based on the average duraton of the longest colldng data packet on the channel.) Fnally, T MDSDU denotes the average real-tme requred transmttng the MSDU part of a data packet. Frst, we notce that the share s of the total data bandwdth (that s gven by the current traffc load) allocated to a class s gven by: s = n N 1 τ (1 τ c ) nc (1 τ ) N 1 =0 N 1 =0 p,s = c=0 N 1 =0 n τ (1 τ ) T,MSDU n τ (1 τ ) T,MSDU N 1 n τ (1 τ ) h=0 (38) B Throughput wth Vrtual Collson Handlng If there s one transmsson queue of each AC on each staton, on the contrary, there wll be Vrtual Collson Handlng between the queues on each staton. Then, hgher prorty traffc does not need to take transmsson of lower-prorty queues on the same staton. The probablty of ther transmssons wll not affect the throughput of the hgher prorty AC. Thus, Eq. (35) above must be replaced by: p,s = n τ (1 τ ) N 1 c=0 (1 τ c) nc c=0 (1 τ c) (39) Usng ths expresson for p,s, p s s calculated, as before, by summng over all p,s,.e. p s = N 1 =0 p,s. S s also calculated as above. C Throughput of the Vrtual Collson Handler One can use expresson (39) to look at behavour wth only one staton by settng n = 1 for all. Then we get: p,s = τ (1 p ) (40) Here, we note that the expresson descrbes the specal case wth only one staton contendng for the channel, whch s the case when the channel refers to the vrtual channel represented by the VCH. Usng ths new expresson for p,s, both p s and S of the VCH are calculated as earler. VI Valdatons A Parameters used for valdatons For valdatons, we compared numercal computatons n Mathematca of the model presented above wth ns-2 smulatons, usng the TKN mplementaton of e n ns-2 [8]. In Table 1 we can see the parameter settngs for a, b, g. Note however that parameters such as CWmn and CWmax are overrdden by the use of e [2]. For our valdatons, we smply used the default e values summarzed n Table 1. (Hence, a scenaro where the HC adjusts these parameters dynamcally, was not consdered.) The scenaro selected for valdatons s b [9], snce ths s the most wdely deployed confguraton per se. A confguraton wth the mandatory long preamble was explored [9]. Accordng to the standard the long preamble and physcal PLCP header are Telektronkk

11 802.11a b g Nom. BW 54 Mb/s 11 Mb/s 54 Mb/s SIFS 16 us 11 us 10 us (+ 6 us) SLOT 9 us 20 us 9 us (11g-only) 20 us (legacy) CWmn CWmax Retry lmt (long/short) 7/4 7/4 7/4 PHY-header 20 us 192 us (long) 20 us 96 us (short) Retry lmt (long/short) 7/4 7/4 7/4 Table 2 Parameter settngs for a, b and g always transmtted at 1 Mbps, and takes 192 µs n total. In our selected scenaro, we also consder that all data payloads (.e. MSDU) are of 1024 bytes of length and are transmtted at the maxmum b rate of 11 Mbps. Furthermore, we consder a case wth the basc transmsson mechansm of sendng a data packet followed by an acknowledgement (ACK) wthout the ntaton RTS/CTS-mechansm. Accordng to the standard, the MAC-part of the ACK shall be transmtted at the same rate as the proceedng frame,.e. at 11 Mbps. However, n our scenaro we consder an mplementaton where the MAC-part of the ACK s transmtted at 1 Mpbs. The reason that we make ths choce s to match wth the mplementaton of the ns-2 network smulator that s beng used to valdate our results. B Determnng the b parameters for numercal calculatons Wth a transmsson range n the order of 30 m the propagaton delay wll be around 0.1 µs, and s neglected n the estmaton of the parameters (whch s often normal practce also wth varous smulator mplementatons). Conceptually, the propagaton delay can be consdered as an already ncluded part of the value for the SIFS, eq. (41) see below. Here T c denotes the tme a non-colldng staton has to wat when observng a collson on the channel, whle T c * denotes the tme a colldng staton has to wat when experencng collson. A non-colldng staton has to wat for a perod determned by the fxed EIFS parameter, whle a colldng staton has to wat by a perod determned by the confgurable Ack- Tmeout nterval. For smplcty, we have set the AckTmeout equal to EIFS (whch s also a normal practce wth many smulators, such as ns-2), such that T c equals T c *, and T TO = 0. (Xao [5] sets T TO = EIFS DIFS = 314 µs.) Note also that the calculaton of T c (and T c * ) ncludes the element T 1024 snce all packets on the ar are of the same sze. In a system where there are packets of dfferent length T c (and T c * ) should nstead consder the transmsson tme of the longest packet, whch s not dffcult to estmate (e.g. see [12]). If we had consdered transmsson wth the RTS/CTS mechansm, on the contrary, we would have had the changes as shown n Eq. (42) see below. T e = 20 µs T,MSDU = T 1024 = 8 * 1024 / 11 µs = µs T s T c = (T PHY + T MAC + T 1024 ) + SIFS + (T PHY + T ACK-MAC ) + mn(aifs[0],..., AIFS[3]) = (192 µs + 8(24 + 4) / 11 µs + 8 * 1024 / 11 µs) + 10 µs + (192 µs + 8 * 14 / 1 µs) + 50 µs = (957.1 µs) + 10 µs + (304 µs) + 50 µs = µs = (T PHY + T MAC + T 1024 ) + (EIFS) = (957.1 µs) + (SIFS + (T PHY + T ACK-MAC@1Mbps + DIFS) = (957.1 µs) + (10 µs µs + 8 * 14 / 1 µs + 50 µs) = µs (41) T s RTS/CTS T c RTS/CTS = (T PHY + T RTS-MAC ) + SIFS + (T PHY + T CTS-MAC ) + SIFS + T s = (192 µs + 8 * 20 / 2 µs) + 10 µs + (192 µs + 8 * 14 / 2 µs) + 10 µs + ( µs) = µs = (T PHY + T RTS-MAC ) + DIFS = (192 µs + 8 * 20 / 2 µs) + 50 µs = 322 µs T c *,RTS/CTS = T s RTS/CTS + SIFS + T CTS-Tmeout (42) 142 Telektronkk

12 C Valdaton of the full-range model wth starvaton (Uplnk Scenaro) Frst we look at a typcal uplnk scenaro wth a number of statons, QSTAs, contendng for channel access (Fgure 3 ). In ths scenaro, the role of the access pont, QAP, s smply to acknowledge packets sent by the QSTAs. QAP Ths scenaro corresponds to the uplnk scenaro presented n the frequently cted paper by Mangold et al. [10], except that here we consder b nstead of a. Each staton has four actve queues and sends 250 kbps of traffc of each of the four ACs. For smplcty, the packets of all ACs have the same length of 1024 bytes (.e. IP header and IP payload). QSTA 1 QSTA 2 QSTA 4 QSTA 5 The throughput values of our ns-2 smulatons were measured over three mnutes of smulaton tme. The smulatons were started wth a 100 seconds transton perod to let the system stablze before the measurements were started. Each QSTA generated 250 kbps Posson dstrbuted traffc for each of the four ACs. The dot11rtsthreshold was set so hgh (e.g bytes) that the optonal RTS/CTS mechansm of e was not used. Fgure 4 compares numercal calculatons of the analytcal model wth the actual smulaton results. We observe that our full-range model, whch models e on the full range from a non-saturated to a saturated medum, gves a qualtatvely good match when compared wth smulatons. We also observe naccuraces n the model n the sem-saturaton part (mddle part) of the fgure. The numercal calculatons of Mathematca have dffculty n convergng n ths regon, for example for n = 8. In Fgure 4 we also observe that the starvaton of AC[0] and AC[1] experenced wth smulatons s QSTA 3 Fgure 3 Smulaton setup to valdate numercal results of uplnk traffc descrbed wth relatvely good accuracy by the analytcal model. We wll take a closer look at the mportance of the expresson to the analytcal model. Fgure 5 shows how the probablty of a busy slot on the channel, p b, changes as a functon of the traffc load. Here, the curve for p b s taken from exactly the same numercal calculatons as were drawn n Fgure 4. The horzontal lnes llustrate the starvaton condtons of the two classes accordng to Eq. (19);.e. when p b = and when p b = 0.5. The vertcal lnes map these freeze ponts down onto the x-axs, and translate them nto the correspondng traffc loads. Despte nteger resoluton of the x-axs, we have lnearly nterpolated down to non-nteger ponts on the axs, for llustratve purposes only. Returnng to Fgure 4 above, we observe that the starvaton ponts were predcted wth satsfactory accuracy. Throughput per AC [Kb/s] Generated traffc (pr. AC) AC[3] (Smulaton) AC[2] (Smulaton) AC[1] (Smulaton) AC[0] (Smulaton) AC[3] (Numercal) AC[2] (Numercal) AC[1] (Numercal) AC[0] (Numercal) Number of statons Fgure 4 Comparng analyss (numercal) wth smulatons. Four ACs per staton and 250 kbps per AC per staton Telektronkk

13 Pb (%) Pb (numercal) Starvaton condton for AC[1] 20 Starvaton condton for AC[0] Predcted freeze ponts Number of nodes Fgure 5 Usng the analytcal model to predct at whch traffc loads starvaton wll occur D Valdaton of the performance of the Vrtual Collson Handler (Downlnk Scenaro) Most related works on analytcal modellng of e seem to focus on uplnk scenaros when t comes to valdatons. However, here we argue that n daly lfe, s manly used for Internet Access or for access to a wred Local Area Network (LAN) nfrastructure. In both cases, the wreless staton (QSTA) s often a clent that retreves large amounts of nformaton from the wred network. In other words, traffc patterns are normally asymmetrc, wth lttle uplnk traffc from the STAs, but a large amount of downlnk traffc from the access pont (QAP). Indeed, many networks are desgned and optmzed wth respect to ths feature. Asymmetrc Dgtal Subscrber Lne (ADSL), for example, whch connects the majorty of households to the Internet, often QAP allocates a sgnfcantly larger share of the avalable bandwdth for the downlnk traffc, assumng that the uplnk traffc wll be lmted. Ensurng qualty of servce and approprate dfferentaton of the downlnk traffc s therefore of utmost mportance. In ths secton we look at a typcal downlnk scenaro. Here we go to the extreme and assume that all traffc s downlnk traffc. Ths assumpton means that the QAP s always free to use the wreless channel and wll not experence collson from any other staton. Ths actually means that all traffc contenton wll occur n the Vrtual Collson Handler (VCH), whch wll represent a vrtual traffc channel. An underlyng assumpton s that the QAP uses EDCA for downlnk traffc, and not HCCA. For our valdaton, we consder a scenaro wth QAP, mplementng a VCH and four transmsson queues for the four possble ACs. Ths confguraton s depcted n Fgure 6. It corresponds to the downlnk scenaros presented n the frequently cted paper by Mangold et al. [10], except that here we consder b nstead of a. QSTA 1 QSTA 5 Fgure 6 shows that a number of dfferent statons (QSTAs) mght be lstenng for traffc on the rado channel n order to receve any downstream traffc from the access pont (QAP). However, t s only the QAP that sends data traffc, whle the QSTAs are not actvely ntatng traffc. Hence, the role of the QSTAs s only to acknowledge all MAC frames that the QAP successfully transmt on the channel. QSTA 2 QSTA 4 QSTA 3 Fgure 6 Smulaton setup to valdate numercal results of downlnk traffc Fgure 7 compares numercal calculatons of the analytcal model wth the actual smulaton results. As before, we use Posson dstrbuted traffc consstng of 1024 byte packets sent wthout the optonal RTS/CTS mechansm. Here we are only dealng wth 144 Telektronkk

14 Throughput per AC [Kb/s] Traffc generated per AC [Kb/s] AC[0] (Smulaton) AC[1] (Smulaton) AC[2] (Smulaton) AC[3] (Smulaton) AC[0] (Numercal) AC[1] (Numercal) AC[2] (Numercal) AC[3] (Numercal) Fgure 7 Comparson between analytcal results and smulaton results. (Recommended e parameter settngs) one node. Instead of ncreasng the number of nodes (as we dd n the Uplnk Scenaro above) we ncrease the traffc generated per AC. For smplcty, we assumed that the QAP generated the same amount of downlnk traffc for each of the four ACs. In Fgure 7 we observe that our full-range model, whch models e on the full range from a non-saturated (fnte queue) to a saturated (nfnte queue) system, gves a good match when compared to smulatons. In Fgure 8 we repeat the valdatons usng dfferent values for the contenton wndow. Here we have doubled all mnmum and maxmum contenton wndows compared to the recommended values gven n Table 1. We have also shown the results on a larger scale (up to 20,000 kbps per AC) to llustrate the remarkably good accuracy between model and smulaton results n the saturaton part of the fgure. However, there are ranges of Fgure 7 and Fgure 8 where there are notceable dscrepances between the curves. For Fgure 8, ths range s expanded and shown on a smaller scale n Fgure 9. Here we observe that the model probably the AIFS-approxmaton s a lttle too rough on the lowest prorty AC, AC[0]. Due to the fact that AC[0] and partly also AC[1] are underestmated here, the model ncorrectly gves a throughput of AC[3] that exceeds the 1-to-1 Throughput per AC [Kb/s] Traffc generated per AC [Kb/s] AC[0] (Smulaton) AC[1] (Smulaton) AC[2] (Smulaton) AC[3] (Smulaton) AC[0] (Numercal) AC[1] (Numercal) AC[2] (Numercal) AC[3] (Numercal) Fgure 8 Comparson between analytcal results and smulaton results (doubled CW values) Telektronkk