Characterization and Optimization of Delay Guarantees for Real-time Multimedia Traffic Flows in IEEE WLANs

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1 Characterzaton and Optmzaton of Delay Guarantees for Real-tme Multmeda Traffc Flows n IEEE 802. WLANs Yan Gao, Member, IEEE, Chee We Tan, Senor Member, IEEE, Shan Ln, Yng Huang, Member, IEEE, Zheng Zeng, Member, IEEE, and P. R. Kumar, Fellow, IEEE Abstract Due to the rapd growth of real-tme applcatons and the ubquty of IEEE 802. MAC as a layer-2 protocol for wreless local area networks (WLANs), t becomes ncreasngly mportant to support delay-based qualty of servce (QoS) n such WLANs. In ths paper, we develop a smple but accurate enough analytcal model for predctng the queueng delay of real-tme multmeda traffc flows n non-homogeneous random access based WLANs. Ths leads to tractable analyss for meetng queueng delay specfcatons of a number of flows. In partcular, we address the feasblty problem of whether the mean delays requred by a set of User Datagram Protocol (UDP) flows supportng real-tme multmeda traffc can be guaranteed n WLANs. Based on the model and feasblty analyss, we further develop an optmzaton technque to mnmze the delays for the traffc flows. Moreover, we present a decentralzed algorthm and report ts mplementaton and present extensve smulaton and expermental trace-based results to demonstrate the accuracy of our model and the performance of the algorthms. Index Terms Delays n 802. WF, Optmzaton, Delay Guarantees, Qualty of Servce, WLAN. I. INTRODUCTION The recent rapd growth of real tme applcatons has led to a strong need to provde delay-based qualty of servce (QoS) for moble computers and portable devces n wreless local area networks (WLANs). Ths has to be supported over the IEEE 802. snce t has ganed wdespread popularty and become the de facto WLAN standard. However, the mechansms employed n the IEEE 802. MAC, namely random access and the dstrbuted coordnaton functon (DCF), render t substantally more dffcult to ensure delay guarantees because of channel contenton and the random back-off mechansm used. Therefore, as the frst task confrontng researchers n ths feld, t s necessary to characterze the delays n such networks. Second, t s mportant to devse solutons that Ths materal s based upon work partally supported by NSF Contract CNS , AFOSR Contract FA , NSF Scence & Technology Center Grant CCF , and the Research Grants Councl of Hong Kong, Project No. RGC CtyU 224. Y. Gao, Y. Huang and Z. Zeng are wth the Department of Computer Scence at the Unversty of Illnos at Urbana-Champagn, Illnos (e-mal: gaoyan.hrb@gmal.com, huang23@llnos.edu, cedarzeng@gmal.com). C. W. Tan and S. Ln are wth the College of Scence and Engneerng at Cty Unversty of Hong Kong, Tat Chee Ave., Hong Kong (e-mal: cheewtan@ctyu.edu.hk, shanln8-c@ctyu.edu.hk). P. R. Kumar s wth the Department of Electrcal and Computer Engneerng at Texas A&M Unversty, College Staton, TX (e-mal: prk.tamu@gmal.com). provde the requred delay performance. We address both ssues n ths paper. Exstng studes on the performance analyss of the IEEE 802. MAC have focused on ts throughput capacty n networks wth saturated traffc, and not delay; see Banch [?], Cal, Cont, and Gregor [?]. In [?], a M/G/ queue s analyzed under network saturaton. Models for unsaturated homogeneous networks have also been reported n the lterature. For example, Medepall and Tobag [?] present a unfed model for mult-hop networks that approxmates each queue by an ndependent M/M/ queue. However, ths approxmaton may not be adequate for an accurate delay analyss n WLANs. Tkoo and Skdar [?] present a G/G/ queueng model for delay analyss n homogeneous networks. Ther focus s on the performance analyss of the standard IEEE 802. DCF. There has also been varous studes usng M/G/ queue to analyze the performance n WLANs, see for example [?], [?]. Also, most work consder centralzed pollng technques based on the pont coordnaton functon (PCF). For example, Coutras, Gupta and Shroff [?] analyze the performance of PCF n support of voce servces. However, they do not address the fact that both best-effort traffc and real-tme traffc can coexst n WLANs, and IEEE 802. DCF s the de facto settng used n most WLANs. Provdng delay-based QoS requres WLAN networks to support servce dfferentaton under non-homogeneous traffc dynamcs. The networks should also reallocate lmted resources from the over-provsoned flows to the underprovsoned flows. IEEE 802.e has been proposed to enhance the orgnal standard to support QoS. However, IEEE 802.e classfes flows only by ther applcatons (e.g., voce, vdeo, etc.) and provdes the same servce to flows that fall n the same class. Moreover, t only dfferentates prorty among flows, but does not actually provde delay guarantees,.e., t s only best effort servce. A non-homogeneous and adaptve WLAN s preferred over one that operates n a fxed homogeneous manner. However, an accurate model of nonhomogeneous flows n random access WLANs, especally wth respect to ther delay characterzaton, s stll elusve. In ths paper, we develop a smple but suffcently accurate analytcal model based on an M/G/ queueng model for nonhomogeneous unsaturated IEEE 802. networks. We characterze the mean servce tme wth respect to the contenton wndow and the probablty that the queue s nonempty. Both the probablty of beng non-empty and the access delay can

2 2 be jontly obtaned by solvng a coupled system of nonlnear equatons through a fxed pont teraton wth a carefully chosen ntal pont so that t converges. Moreover, we show that, n random access networks, the second moment of the access delay s determned only by ts frst moment f the packet sze s suffcently large. Ths approxmaton smplfes the formula of the queueng delay. Usng ths analyss, we determne whether the network can provde the mean delay guarantees requred by the QoS flows. The contrbutons of the paper are summarzed as follows: ) We derve a smple but accurate model for mean queueng delay n non-homogeneous IEEE 802. MAC based networks. We use t to determne the feasblty of usng a random-access based WLAN to serve a set of real-tme flows wth mean delay requrements. 2) We provde a characterzaton of the average delay and access rate, and propose a fxed pont algorthm to compute them. A lnear system approxmaton s derved to complement the analyss. 3) We provde an algorthm to mnmze the mean delays for a set of User Datagram Protocol (UDP) traffc flows whle meetng mean delay requrements. 4) We desgn a dstrbuted algorthm based on the proposed queueng model and show that the dstrbuted algorthm performs as well as the centralzed algorthm. 5) We valdate our algorthm to provde performance guarantees through extensve NS-2 smulatons and tracebased experments. We motvate the non-homogeneous IEEE 802. flows problem n Secton??. In Secton??, we characterze the mean servce tme and the mean queueng delay. In Secton??, we study fxed pont teratons related to the queueng model. We show how to optmze the mean delay performance n Secton??. Smulaton results and numercal results are compared n Secton??. Furthermore, we derve a dstrbuted algorthm based the analytcal model and address several desgn ssues n Secton??. Results of trace-based experments are gven n Secton??. Fnally, we conclude the paper n Secton??. II. PROBLEM STATEMENT A. Non-homogeneous IEEE 802. networks In IEEE 802. DCF networks, each node wth a packet to transmt selects randomly a back-off tmer counter BC from [, CW ], where CW denotes the contenton wndow. If the channel s sensed dle, these nodes decrement ther tmers untl one of them expres. Then that node attempts to access the channel whle the remanng nodes pause ther tmers. The decrementng mechansm resumes when the channel s dle once agan. If more than one node attempts to transmt n the same slot, a collson occurs. A collded transmsson s tred agan untl a retransmsson lmt s reached before t s dscarded. In the standard IEEE 802. network, the contenton wndow of each node s set to be the same. Ths homogeneous or unform settng works well for best-effort traffc where farness s taken nto account. However, the ncreasng need to support the QoS requrements of dfferent flows requres networks to have the ablty to provde servce dfferentaton especally delay guarantees to real-tme flows. The standard IEEE 802.e has been proposed to enhance the orgnal standard to support QoS. However, IEEE 802.e categorzes flows only by ther applcatons (e.g., voce, vdeo, etc.) and provdes the same servce to all the flows that fall n the same class. It s mportant to note that IEEE 802.e only dfferentates prortes to flows but does not actually provde delay guarantees. Our goal s to provde mean delay guarantees n random access WLANs. Towards ths end, a nonhomogeneous and adaptve wreless network s preferable. We consder wreless networks wth nodes that are capable of changng ther backoff parameters. In other word, we tune only CW. Thus, our scheme s compatble wth the IEEE 802. standard. In other word, we analytcally show that CW alone can effectvely be used for resource allocaton and performance dfferentaton. B. Soft Deadlne Guarantees In ths paper, we focus on the soft deadlne related to the mean delay of a flow. Soft-deadlne guarantees are mportant for several real-tme applcatons such as voce over Internet Protocol (VoIP), onlne games and Internet protocol televson (IPTV), snce they often requre a fxed bt rate but are senstve to average delays. Consder a WLAN where N nodes are actve and each has a QoS flow to the access pont (AP). These flows dffer n rate and mean delay requrements. Assume that for each node the packet arrval s a Posson process and the nter-arrval tme s exponentally dstrbuted wth mean /λ. Let λ = [λ, λ 2,..., λ N ] be the arrval rate vector. Addtonally, each flow has a soft deadlne D to meet. The average queueng delay of the packet for flow s requred to be less than D. Let D = [D, D 2,..., D N ] denote the target delay vector. Now, suppose both λ and D are gven. Does there exst an assgnment of contenton wndows CW = [CW, CW 2,..., CW N ] for the N flows such that all the deadlnes of all the nodes are met? Ths queston s mportant to admsson control that decdes whether t s feasble to accommodate a flow n the network wthout hurtng the performance of exstng hgher prorty flows. Furthermore, f t s feasble, a natural queston s how to acheve all these mean delays,.e., how to assgn CW to each node. We answer these two key questons n ths paper. III. ANALYTICAL MODEL OF NON-HOMOGENEOUS IEEE 802. NETWORK A. Meda Access Delay We begn by frst analytcally addressng the access delays n a non-homogenous WLAN. We do not consder the exponentally ncreasng back-off mechansm mplemented n the IEEE 802. protocol because our scheme explctly determnes the contenton wndow for each flow so as to meet the delay requrements for all the flows. Imposng an addtonal CW adjustment mechansm, e.g., exponental backoff algorthm, may complcate the analyss and s left for future work. In the lterature, the schemes proposed n [?], [?] dsable the exponental backoff mechansm, and drectly adjust

3 3 the contenton wndow. However, ther goal s to maxmze throughput, whle ours s to provde mean delay guarantees for nonhomogeneous flows. We wll consder an access rate for node that s equal to 2/CW. Ths corresponds to IEEE 802. DCF wth BC chosen randomly from [, CW ] [?], [?], [?], [?]. Snce our flows are not saturated, the queues may be empty, and n ths case they do not transmt. Let NE denote the event that queue s not empty and E denote the event that queue s empty. Then, the uncondtonal channel access (CA) probablty of node s P[CA] = P[CA E]P[E] + P[CA NE]P[NE]. It s obvous that P[CA E] s equal to zero because a node has no packet to transmt when the queue s empty. In 2 partcular, we approxmate P[CA NE] by CW. Note that ths s an approxmaton only when the backoff mechansm s enabled to choose unformly wthn [, CW ], but otherwse ths s exact (and not an approxmaton) f transmsson s attempted after an exponentally dstrbuted nterval. Denotng p = 2/CW, and ρ as the probablty that the queue s not empty, we have P[CA] = 2ρ CW = ρ p. () Let p be the vector [p, p 2,..., p N ], notng that 0 p. Lkewse, let ρ := [ρ, ρ 2,..., ρ N ]. Next, we need to compute the probablty PI that the channel s dle when node has a packet to send, the probablty PS that the channel s successfully carryng a packet of node, and the probablty PO that node sees the channel as busy though tself s not transmttng a successful packet. Note that PI + P S + P O = for all. All these quanttes are n fact functons of the vector p. We now focus on the dependence of ρ on p. Note that node competes for the channel access only when t has a packet to transmt. Thus, node fnds the channel dle n a tme slot f t tself does not attempt and no other node attempts at the begnnng of ths slot. Hence, N PI = ( p ) ( ρ j p j ). (2) Node successfully transmts a packet f only t attempts and no other node attempts n the same slot. Ths probablty s j N PS = p ( ρ j p j ). (3) j Otherwse, node sees the channel occuped by other actvtes, consstng of ether successful transmssons of other nodes or collded transmssons. Snce the collded transmssons consst of both the transmssons nvolvng node as well as those not nvolvng node, we have N PO = PI PS = ( ρ j p j ). (4) j In the sequel we wll employ a fxed pont analyss snce p tself depends on ρ. Let us defne the servce tme x of a packet as the tme from the nstant the packet reaches the head of the queue n the node tll the nstant t successfully departs from the queue. Ths servce tme ncludes two parts, the channel contenton delay and the packet transmsson tme. For smplcty, we assume that all the packets are of the same sze and all nodes employ the same bt rate for transmssons. Thus, they have the same packet transmsson artme, denoted by T. More formally, n the IEEE 802. network, the packet transmsson artme s T := DIFS + PACKET + SIFS + ACK, (5) where DIFS denotes the duraton of the dstrbuted nterframe space, PACKET denotes the transmsson tme of a data packet, SIFS denotes the duraton of the short nterframe space, and ACK denotes the transmsson tme of an acknowledgement. There are two access modes used n IEEE 802. DCF, namely the basc access mode and the request to send/ clear to send (RTS/CTS) access mode. The RTS/CTS access mode s usually dsabled n practce due to ts large overhead. Thus, n ths paper, we focus only on the basc access mode. In the basc access mode, a collson s detected when a node does not receve an ACK wthn an ACK-tmeout. Ths ACKtmeout s defned to be the tme to transmt an ACK frame plus SIFS. Thus, we assume that the artme spent on a collded transmsson s the same n duraton as that of a successful transmsson. We denote a slot-tme duraton by τ. Let t k denote the tme nstant when the k-th dle slot begns,.e., the nstant that the channel s dle at the begnnng of the correspondng slot. There are two possble events followng ths nstant: a) the channel contnues to be dle for a duraton of τ untl the next dle slot begns; b) at least one of the nodes attempts to transmt n ths slot that results n a T tme unts channelbusy perod. We assume the ntervals S (k) = t k+ t k are ndependent and dentcally dstrbuted random varables and refer to these ntervals as vrtual slots. Assume that the tme nterval from the tme the packet reaches the head of the queue to the tme t starts to depart from the queue conssts of K vrtual slots, where K s a random varable ndependent of S. Its dstrbuton s geometrc and thus s gven by It follows that P[K = n] = ( P S) n P S, for n = 0,, 2,... (6) For node, ts servce tme s therefore E[K ] = P S PS. (7) K x = S (k) + T, (8) k= where the S (k) are Bernoull random varables that are ether equal to τ f the channel s dle or equal to T f a transmsson of a node other than occurs: P τ wth probablty I S (k) = T wth probablty PS P O. PS (9)

4 4 Then, we have E[S ] = P I τ + P O T P S. (0) It s easy to see that both E[S ] < and E[K ] <. From the ndependence of S and K, we can apply Wald s equaton [?] to obtan X := E[x ] = E[K ]E[S ] + T. () Substtutng (??) and (??) nto (??) yelds X = P I τ + P O T PS + T. (2) Hence, (??) expresses the nterestng relatonshp between the expected servce tme and the access rate n carrer sense multple access based (CSMA-based) random access wreless networks. Snce the network s unsaturated, we need to determne the probablty ρ that the queue s non-empty. Snce each node s an M/G/ queue, we have ρ = λ X. (3) Substtutng (??) nto (??), we thus obtan N equatons wth N unknowns [x, x 2,, x N ]. Solvng ths N dmensonal vector fxed pont problem gves us the servce tmes for nonhomogeneous flows n the WLAN. In summary, we have obtaned the fundamental relatonshp that allows us to compute the mean servce tmes for nonhomogeneous flows n random access WLAN: Gven the contenton wndows CW, the mean servce tmes are gven by (??), where P I, P S and P O are gven by (??,??,??), wth p defned by (??). In addton, the quanttes ρ s n (??) satsfy (??). B. Queueng Delay In the prevous secton, we have derved an analytcal model that can be used to compute the servce tme f the access rates of all nodes are gven va ther contenton wndows. Snce many real-tme applcatons such as onlne games, VoIP and IPTV mpose requrements on jtter and delay, we next study how the non-homogeneous contenton wndow settngs and the non-homogeneous throughput requrements jontly affect the average queueng delay. Defne the queueng delay of a packet to be the tme from the nstant that the packet arrves at the queue to the nstant that the packet successfully departs from the queue. The average queue sze of the M/G/ queue s gven by [?]: E[Q ] = λ X + λ2 E[x2 ] 2( λ X ), (4) where Q denotes the queue sze and E[x 2 ] s the second moment of the servce tme. Usng Lttle s law, the average queueng delay Y s Y = E[Q ] λ = X + λ E[x 2 ] 2( λ X ). (5) To determne the average queueng delay (??), we need to also determne the second moment of the servce tmes. In (??), we have characterzed the servce tme x as a sequence of the vrtual slots S plus a transmsson artme T. Next, takng squares on both sdes of (??), we have K x 2 = ( S [k] + T ) 2 k= K K k K = S 2 [k] + 2 S [k]s [l] + 2T S [k] + T 2. k= k=2 l= Applyng Wald s equaton, we get k= E[x 2 ] = E[K ]E[S 2 ] + E[K 2 K ]E 2 [S ] + 2T E[K ]E[S ] + T 2. Usng the dstrbuton of S n (??), we compute (6) (7) E[S 2 ] = τ 2 PI + T 2 PO PS. (8) To determne E[K 2 K ], we frst obtan the moment generatng functon of K from (??) as follows: M K (B) = B n ( PS) n PS PS = ( PS. (9) )B n=0 It s easy to verfy that d 2 M K (B) d B 2 B= = = n(n )B n 2 ( PS) n PS B= n=0 n(n )( PS) n PS = E[K 2 K ]. n=0 Hence, from both (??) and (??), we get (20) E[K 2 K ] = 2( P S )2 (P S )2. (2) Fnally, substtutng (??), (??), (??) and (??) nto (??), we get the second moment of the servce tme for node as follows: E[x 2 ] = τ 2 P I + T 2 P O P S + 2T τp I + T P O P S + 2(τP I + T P O )2 (P S )2 + T 2. (22) After substtutng (??) and (??) nto (??), we obtan the average queueng delay wth respect to vector p. Queueng delays as a functon of contenton wndows Y (p): In summary, for a non-homogeneous flows n the random access WLAN wth contenton wndows CW and packet transmsson tme T, the mean queueng delay s gven by (??), where E[x ] s gven by (??), E[x 2 ] s gven by (??), PI, P S and P O are gven by (??,??,??), and ρ = [ρ, ρ 2,, ρ N ] s a fxed pont of (??).

5 5 C. Queueng Delay and Servce Tme for Small Slot Tmes We smplfy our above analyss by usng some practcal assumptons. Substtutng (??) nto (??), we have E[x 2 ] = 2(X T ) 2 + 2T (X T ) + T 2 + P I τ 2 + P O T 2 P I τ + P O T (X T ). (23) Snce lm τ 0 E[x 2 ] = 2(X T ) 2 + 2T (X T ) + T 2 + T (X T ), f we assume that the packet transmsson artme T s suffcently large compared to the slot-tme τ, then we get a smplfed formula for E[x 2 ] gven by: E[x 2 ] = (2X T )X. (24) Note that (??) mples that the second moment of x can be determned only by ts frst moment. We beleve that ths ntrgung property s an nherent characterstc of the random access mechansm n WLAN. Therefore, the average delay reduces to Y = (2 λ T )X 2( λ X ). (25) Now, (??) s equvalent to X = 2Y 2 λ T + 2λ Y. (26) Interestngly, (??) llustrates an mportant characterstc under the small slot-tme assumpton: The queueng delay n a random access network s determned only by the servce tme. IV. ANALYSIS OF FIXED-POINT PROBLEMS A. Nonlnear Characterzaton of Delay and Access Rate We have determned that when the transmsson artme T s suffcently large compared to the slot tme τ, the queueng delay Y can n fact be determned by X. Recall that the delay X can be characterzed by (??). Based on (??), we derve a set of fxed pont equatons gven by p X + ( p )(T τ) = T j ( λ jx j p j ). (27) There are two perspectves to vewng (??): analyss or desgn. The analyss part (or the performance analyss problem analyss below) conssts of determnng the delay, gven the access rates. The desgn part (or the access rate assgnment problem below) conssts of determnng the access rates for the flows so as to meet all the delay constrants. Both parts can be solved usng the fxed pont equaton n (??). Performance Evaluaton (PE): We fx the access rate p, and evaluate the servce tme X. For node, ts delay can be wrtten as X = I P E (X) T := p j ( λ jx j p j ) ( p )(T τ). p (28) We denote by X as a fxed pont of (??), assumng that t exsts. Thus, we consder the followng fxed pont teraton to solve (??): X(k + ) = I P E (X(k)). (29) Access Rate Assgnment (ARA): From a protocol desgner s vewpont, t can be nterestng to compute the access rate assgnment such that all the flows meet ther requred delays. In other word, we adapt the access rate p such that all the delays X are fulflled. For node, the access rate s gven by p = I ARA (p) T := (X T + τ) j ( λ jx j p j ) T τ X T + τ. (30) f We denote by p a fxed pont of (??), assumng that t exsts. Thus, we consder the followng fxed pont teraton to solve (??): p(k + ) = I ARA (p(k)). (3) B. Lnear System Approxmaton Note that λ X p < for all f the queueng system s stable. Now, usng the fact that /( z) + z for nonnegatve z <, we can lower bound the RHS of (??) by an affne expresson. Thus, we have p X + ( p )(T τ) T ( + j λ j X j p j ). (32) Furthermore, we can approxmate the nequalty n (??) by an equalty f we assume small 2 p X for all, and apply a Taylor expanson for the RHS of (??). Ths leads us to consder the followng fxed pont equaton: p X j λ j T p j X j = p T + ( p )τ. (33) Now, we can consder two dfferent lnear fxed pont equatons n the form of (??): One n terms of X for the performance evaluaton assumng a fxed p, and the other n terms of p for the access rate assgnment assumng a fxed X. The followng result shows that each of these two lnear fxed pont teratons has a unque soluton. Theorem 4.: Suppose that p, p 2,..., and p N are gven, (??) has a unque soluton for [ X, X 2,..., X N ]. Proof: Let y denote the vector [p X, p 2 X2,, p N XN ] T and b denote the vector [p T + ( p )τ, p 2 T + ( p 2 )τ,, p N T + ( p N )τ] T. Then, we represent (??) by y = F y + b, (34) where F s an rreducble nonnegatve matrx wth entres: { 0, f l = j F lj = (35) λ T, f l j. We now apply nonnegatve matrx theory to characterze the soluton to (??). Let Λ A denotes the spectral radus of a nonnegatve matrx A. By the Collatz-Welandt theorem (see, e.g., [?]), Λ F max λ j T < λ T <, (36) j 2 A suffcently small condton on X p n order for (??) to hold s λ X p <. We omt the detal here for the lmt of space. n

6 6 where the last nequalty follows from the necessary condton that the M/G/ system s stable only f the workload s strctly less than,.e., λ T <. Next, we state the followng result from [?]. Lemma 4.2: A necessary and suffcent condton for a soluton z 0, z 0 to exst to the equatons (I A)z = c, for any c 0, c 0 s that Λ A <. In ths case there s only one soluton z, whch s strctly postve,.e., z 0 and z 0, and gven by z = (I A) c. Applyng Lemma?? to (??), ths mples that (I F ) b has a unque postve soluton. Ths proves the theorem. Lemma 4.3: Assume that X s gven. If p s the fxed pont of (??), and p s the fxed pont of (??), then we have, component wse, p p and p p. Proof: Suppose the followng holds: p X + ( p )(T τ) = T ( + j λ j X j p j ), (37) p X + ( p T )(T τ) = j ( λ jx j p. (38) j ) For each, we subtract (??) from (??) to obtan (X T + τ)(p p ) T = j ( λ jx j p j ) T ( + λ j X j p j ) j > T ( + j = j λ j T X j (p j p j ). λ j X j p j ) T ( + j λ j X j p j ) (39) Let u denote the vector [X (p p )]. Now, (??) for all can be wrtten n a compact form as (I C)u = v > 0, (40) where v denotes some postve vector (wth the postve slack of the nequalty (??) as ts th entry), and C s a postve matrx wth entres { (T τ)/xl, f l = j C lj = (4) λ T, f l j. Snce C s a postve matrx, usng the Perron-Frobenus theorem, Λ C s strctly postve. Now, Λ C satsfes Λ C (a) max ( j λ jt + T τ (b) < max ( j T X j + T τ X X ) ) (c) < T X (d) <, (42) where nequalty (a) s due to the Collatz-Welandt theorem, nequalty (b) s due to the servce rate /X beng strctly larger than the arrval rate λ (as (??) enforces ths constrant), nequalty (c) s straghtforward, and nequalty (d) s due to the necessary stablty condton for a M/G/ queue. Applyng Lemma?? to (??), u s strctly postve. Ths proves the lemma. We pont out that the lnear approxmaton analyss only holds under certan regme, and s useful for tractable analyss. There are however lmtatons on the approxmaton. For example, ncreasng the number of nodes wll ncrease servce tme. As future work, t s mportant to study other (nonlnear) approxmatons under whch (??) can be further smplfed. C. Convergence We establsh below the convergence result related to the algorthms for the ARA and the PE. Theorem 4.4: If p exsts, then startng from p, the ARA algorthm produces a monotone ncreasng sequence of vectors p(k) that converges to a fxed pont. Proof: By Lemma??, we know p < p. Note that I ARA (p) s a monotone non-decreasng functon. Thus, startng from p, we have p() = I ARA ( p) < I ARA (p ) and p() = I ARA ( p) p. Suppose p() p(2) p(n) p. Then, monotoncty mples that p = I ARA (p ) I ARA (p(n)) = p(n + ) I ARA (p(n )) = p(n). (43) That s, p p(n + ) p(n). Hence, the sequence p(n) s nondecreasng and bounded above by p. Thus, p(n) converges. One can use a smlar approach to prove the convergence of the PE algorthm (??), and the proof s omtted. A. Feasblty Problem V. APPLICATIONS To demonstrate the utlty of the proposed model, we use the above algorthm to address the followng ARA queston: In an IEEE 802. WLAN, suppose that the arrval rates λ and the requred delays D = [D, D 2,..., D N ] T are gven. Does there exst a set of access rates [p, p 2,, p N ] T such that the resultng delay for each node s guaranteed to be smaller than D? We refer to ths problem as the average delay feasblty problem. Formally, we say that {(λ, D ), (λ 2, D 2 ),, (λ N, D N )} s feasble f there exst [p, p 2,, p N ] T such that Y (p) D. (44) We argue that f there exsts a p such that the equalty holds n the above (.e., Y D, for =, 2,..., N), then {(λ, D ), (λ 2, D 2 ),..., (λ N, D N )} s feasble. We mplctly assume n the followng that f a vector of delays s feasble, then any set of component-wse larger set of delays s also feasble. Equvalently, we have the expected channel access delay as 2D X =, (45) 2 λ T + 2λ D where we substtute Y = D. Note that both D and λ are nputs, and hence X can be completely determned by them. Consequently, ρ = λ X s also determned. Substtutng ρ nto (??) yelds a fxed pont problem to yeld the contenton wndows p. One can use the ARA algorthm proposed n the prevous secton to solve ths fxed pont problem. After obtanng the fxed pont p, f 0 < p < for all, then we can deduce that the flows are feasble, and a feasble contenton wndow CW s then gven by the maxmum nteger that s smaller than 2/p. Otherwse, we conclude that the flows are not feasble because f the fxed pont had exsted, the ARA algorthm s guaranteed to converge.

7 7 B. Mnmzaton of Delay We now consder a scheme for the delay mnmzaton problem that s solved by a central controller, e.g., an access pont n a WLAN, whch collects the QoS requrements {(λ, D ), (λ 2, D 2 ),..., (λ N, D N )} from all the nodes. 3 The WLAN access pont frst solves the feasblty problem n Secton??, and then optmzes the delay performance. Assume that the th node has a cost functon f (Y ) that s dfferentable, non-decreasng and strctly convex. Now, from (??), Y s convex n X. We substtute (??) nto f (Y ) to yeld a convex functon n X, whch we denote as f (X ). Consder the followng optmzaton problem: mn N f (X ) (46) = s.t. 0 X ˆX 2D := 2 λ T + 2λ D, (47) X = I P E (X(p)), (48) 0 < p. (49) In the above, the constrant (??) guarantees that the average delay s less than the requred delay. However, the constrant (??) that relates p to X s nonconvex, thus (??) s generally hard to solve. To obtan numercal soluton, we use the barrer method (nteror-pont method) n optmzaton theory [?] to compute a local optmal soluton. Snce the barrer method yelds a soluton n the nteror of the feasble set, ths can be useful to fnd a feasble soluton that meets the delay requrements,.e., the delay constrants (??) as they are satsfed at all the ntermedate soluton terates. From (??) and (??), we consder the followng barrer functon: B (p) := ˆX X (p) + +. (50) p p Note that ths barrer functon ncreases to + when any th constrant approaches ts boundary. Let ɛ be a postve weght assocated wth B (p) for all. Consder the optmzaton problem: max J(p) := N f (X (p)) + N ɛ B (p). (5) The soluton to (??) yelds a suboptmal soluton that s feasble to (??). We present the followng algorthm based on the gradent method to solve (??) [?]. Gradent Algorthm ) Obtan an ntal pont p 0 by solvng the feasblty problem n Secton??. 2) For a fxed p k (soluton of the feasblty problem), run the PE algorthm tll convergence to obtan X k. 3) For fxed p k and X k, obtan d J(pk ) from (??) and (??). d p k 4) Update p by p k+ = p k d J(p k ) β d p k, where β s a postve dmnshng stepsze [?]. 3 We assume that each node has only a sngle QoS flow for the AP. 5) Repeat from Step 2 untl convergence to a small tolerance. Due to the nonconvexty n (??), ths gradent algorthm yelds a soluton that n general s not the global optmal soluton of (??). However, by explotng the lnear system approxmaton n Secton??, we can obtan a relaxaton to (??) that yelds a lower bound to the (unknown) global optmal value of (??): mn N f (X ) (52) = s.t. 0 X ˆX, (53) X ((I F ) b(p)) /p, (54) 0 < p, (55) where (Ax) denotes the th element of the vector Ax, and b(p) = [(T τ)p + τ, (T τ)p 2 + τ,, (T τ)p N + τ] T. Note that (??) s obtaned by relaxng the constrant (??) n (??) usng (??). Now, (??) s stll nonconvex. However, by makng the logarthmc change of varable p := log p for all, we obtan the followng convex problem that s equvalent to solvng (??): mn N f (X ) (56) = s.t. 0 X ˆX, (57) X ((I F ) b(e p )) /e p, (58) p 0, (59) where e p = [e p, e p2,, e pn ] T. In practce, t s observed through our smulatons n the followng secton that (??) often yelds an optmal value that s only slghtly smaller than the objectve value evaluated at the suboptmal soluton obtaned by the gradent algorthm. Ths demonstrates that the gradent algorthm can compute a near-optmal soluton. A. Smulaton Setup VI. SIMULATION RESULTS We perform our smulaton usng the NS-2 network smulator (verson ns2.3) [?]. Table?? summarzes the system parameters used n the smulaton. As we do not employ the exponental back-off mechansm, after obtanng a CW from the analyss, we just set CW mn = CW max = CW to dsable the exponental back-off. These values of CW mn and CW max shown n Table?? are referred to as the default baselne settngs for comparson purpose. No other parameters are changed n any smulaton. Collocated topologes are created n whch all nodes can carrer-sense one another. Each sender node s attached to a Posson traffc generaton agent n whch packet nter-arrval tmes can be customzed. The nterface queues at each node use a Droptal polcy and the queue sze s set at 5000 packets. Each smulaton runs for 400 seconds n smulaton tme. Two metrcs, namely the servce tme and the queueng delays, are measured for each flow. For the servce tme, the tme nterval from the nstant that the packet arrves at the head of the queue to the nstant that the packet successfully

8 8 fg/accessdelay_vs_cw-eps-converted-to.pdf fg/accessdelay_fx_rato-eps-converted-to.pdf Fg.. Saturated condtons: servce tme v.s. CW, where CW 2 = CW 3 = 32. Fg. 2. Saturated condtons: servce tme v.s. CW, fx the rato CW : CW 2 : CW 3 = : 2 : 3. Packet payload 024 bytes UDP header 20 bytes MAC header 28 bytes PHY header 24 bytes ACK frame 38 bytes Channel bt rate Mbps PHY header bt rate Mbps Slot tme 20 µs SIFS 0 µs DIFS 50 µs CW mn 3 CW max 023 Retransmsson lmt 7 TABLE I SYSTEM PARAMETERS departs from the queue s measured. For the queueng delay, the tme nterval from the nstant that a packet s sent by the applcaton layer (labeled by AGT n trace fles) to the nstant that the packet s successfully receved s measured. B. Accuracy of the Analytcal Model The accuracy of the model s measured through three scenaros: servce tme under saturated condtons, servce tme under unsaturated condtons, and queueng delays. For each smulaton, both the smulaton results (denoted by smulaton ) and the theoretcal results obtaned from our model (denoted by theoretcal ) are plotted for comparson. ) Servce tme under saturated condtons: We show that our model can be appled to saturated condtons as well. In these smulatons, three lnks are examned. The sender of each lnk sends a saturated traffc to the recever. The theoretcal results are obtaned by applyng (??), where ρ = due to the saturated condtons. Two scenaros are studed. In the frst scenaro, CW of lnk s vared between 4 and 6, whle the contenton wndows of lnk 2 and lnk 3 are fxed wth CW 2 = CW 3 = 32. Fgure?? plots the smulaton results as well as the theoretcal results. One can observe that as CW s ncreased, lnk s access delays ncrease. Even though CW 2 and CW 3 are not changed, ther correspondng access delays decrease because CW s ncreased. In the second scenaro, CW s changed, whle mantanng the fxed rato CW : CW 2 : CW 3 = : 2 : 3. The results are shown n Fgure??. One can observe that except for the nonlnear part where CW s very small, the channel access delays agree wth the theoretcal values. The nonlnear part of the curves s due to the fact that the collson probablty becomes larger when every node has a small CW for contenton resoluton. 2) Servce tme and queueng delays under unsaturated condtons: For the unsaturated condtons, three scenaros are examned. The frst scenaro s ntended to study how traffc arrval rates affect the servce tme. The nter-arrval tme of flow 3 s vared, whle keepng the other two lnks arrval rates fxed. The fxed packet nter-arrval tmes are λ = 0.03 and λ 2 = For the contenton wndow, CW = CW 2 = CW 3 = 32 s set. Fgure?? plots the results. The theoretcal results are obtaned by solvng (??) usng the PE algorthm. In the second scenaro, t s examned how CW affects the channel access delays. The traffc arrval rates, and CW and CW 2 are fxed. Only CW 3 s changed from 2 to 44. The results are shown n Fgure??. One can observe that as CW 3 s ncreased, the delays of flow 3 ncrease. One can also observe that the delays of flow and flow 2 drop. The thrd scenaro s used to demonstrate how servce tme changes n response to the number of nodes. Each lnk has the same traffc rate and the same CW. In partcular, λ = 0.03 and CW = 32 for all. Only the number of lnks s changed. Fgure?? plots the results. As expected, the access delays ncrease as the number of lnks grows. 3) Queueng delays: We repeat the same three scenaros for the queueng delays. One can observe smlar trends n these fgures to ther counterparts for the servce tme. From the three scenaros, we conclude that the theoretcal results are accurately verfed by the smulaton results. The accuracy

9 9 fg/servcetme_vs_arrval-eps-converted-to.pdf fg/servcetme_vs_cw-eps-converted-to.pdf fg/servcetme_vs_num-eps-converted Fg. 3. Unsaturated condtons: servce tme v.s., where = 0.03, = 0.005, and CW λ 3 λ λ = 2 CW 2 = CW 3 = 32. Fg. 4. Unsaturated condtons: servce tme v.s. CW 3, where = 0.03, = 0.005, = λ λ 2 λ and CW = CW 2 = CW 3 = 32. Fg. 5. Unsaturated condtons: servce tme v.s. the number of lnks, where all = 0.03 and all λ CW = 32. s not only reflected n the trend but also n the quanttatve values. C. Performance Evaluaton In the followng smulatons, two case studes are examned to demonstrate the applcablty of the model and to evaluate the performance of the proposed algorthm. Each pont n the fgures s a tme-average of the queueng delay over every 50 smulaton seconds. ) Feasblty: In the frst case, when the capacty s nsuffcent, the default 802. settng cannot meet the delay guarantees of all the QoS flows. But, wth the proposed scheme, one can fnd an approprate settng n whch all the delay requrements are met. The three requred delays are assumed to be 0.02 seconds. Note that ths delay requrement s realstc accordng to [?]. The data rates of the UDP traffc flows are fxed as follows: λ = 0.025, λ 2 = and λ 3 = The ARA algorthm s run to obtan a set of feasble contenton wndows: CW = 66, CW 2 = 23 and CW 3 = 8. Fgure?? plots the smulaton results. One can see that the baselne default IEEE 802. can guarantee the mean delay requrements only for flows and 2, whereas the mean delay of flow 3 s much larger than the allowed mean delay. However, the WLAN can actually guarantee all the mean delays f the contenton wndows are approprately adjusted. In fact, one sees that the mean delays of all flows are met when the WLAN uses the contenton wndows that are computed usng our algorthms. 2) Mnmzng delays: In ths case study, the performance of the scheme that mnmzes the average delays for UDP traffc flows, whle preservng ther delay guarantees, s evaluated. We consder the followng cost functon ˆf (Y ) = Y 2. (60) λ The UDP traffc flows have fxed arrval rates λ = 0.04, λ 2 = and λ 3 = The delay requrements are stll fxed at 0.02 seconds. Compared to the nput of the frst case, one can observe that the network capacty s suffcent for ths nput. Thus, there should be room for the flows to mprove ther performance (.e., queueng delays n ths case). Usng the gradent algorthm presented n Secton??, the optmal CW s are computed to be CW = 9, CW 2 = 23, and CW 3 = 9. The comparsons are plotted n Fgure??. We observe that when confgured wth the CW s computed by our algorthms, the WLAN does acheve the optmzed mean delays and does at the same tme provde a certan level of farness. In contrast, n the baselne default IEEE 802., flow 3 suffers from bad delay performance and experences serous unfarness. 3) Scalng up wth nodes: In ths case, we have studed how the number of nodes affects the performance of the proposed algorthm n the network. The delay requrements are stll fxed at 0.02s. The data rates of the UDP traffc ( λ ) are randomly generated between 0.05 and 0.. Each smulaton runs for 00 seconds. For a fxed number of nodes, we have repeated each smulaton for 5 tmes and have compared dfferent approaches usng the averages. If the number of the contenton wndow s not feasble (smaller than ), CWmn s used for smplcty. Fgure?? shows the percentage of the nodes that meet the delay requrement (0.02s) and Fgure?? shows the average queueng delay. From both fgures, we observe that the proposed algorthm demonstrates the ablty to lower the average queueng delay as comparng to the tradtonal 802. exponental backoff mechansm. Furthermore, we observe that the proposed algorthm can allow the nodes to meet the delay requrements as the number of nodes scalng up. Therefore, the proposed algorthm s applcable even when the number of nodes n the newtork ncreases beyond tens or twentes of nodes (a typcal number n exstng WF network). VII. DESIGN OF DISTRIBUTED ALGORITHM Our results n the prevous sectons address the feasblty queston. In practce, t can be nterestng to fnd the approprate contenton wndow allocatons n a dstrbuted manner. To ths end, we derve a dstrbuted algorthm that adapts the servce rates to meet the demands through the contenton wndow adjustment.

10 0 fg/qdelay_vs_arrval-eps-converted-to.pdf fg/qdelay_vs_cw-eps-converted-to.pdf fg/qdelay_vs_num-eps-converted-to.p Fg. 6. Unsaturated condtons: Queueng delays v.s., where = 0.03, = 0.005, and λ 3 λ λ 2 CW = CW 2 = CW 3 = 32. Fg. 7. Unsaturated condtons: Queueng delays v.s. CW 3, where = 0.03, = 0.005, λ λ and CW = CW 2 = CW 3 = 32. λ 3 = Fg. 8. Unsaturated condtons: Queueng delays v.s. the number of lnks, where all = 0.03 and λ all CW = 32. fg/feasblty-eps-converted-to.pdf fg/mn_delay-eps-converted-to.pdf Fg. 9. A feasble soluton: Illustraton of the queueng delay dynamcs. Fg. 0. Mnmzng delays: = λ 3 λ = 0.04, λ 2 = and A. Dervaton of the Dstrbuted Algorthm The expectaton of n s We have defned three probabltes PI, P S and P O n (??) (??). Let us assume that there s an observer who s montorng the channel actvtes. The observer sees one of two possble states n a vrtual slot: ether the channel s dle durng the vrtual slot or the channel s busy due to the other nodes transmsson. Denote P I as the probablty that the observer sees an dle slot. Then, we have P I = N ( ρ j p j ). (6) j Denote the number of consecutve dle slots between any two transmssons as n. Snce n follows a geometrc dstrbuton, the probablty that n = k s P [n = k] = ( P I) k ( P I). (62) Rearrangng (??), we have Now, substtutng (??) nto (??) yelds Replacng P I P I E[n ] = P. (63) I P I = E[n ] + E[n ]. (64) X = ( p ) P I τ + ( P I )T p P I + T. (65) n (??) by (??), we have p (X T + τ) = T + τ. (66) E[n ] An unbased estmaton of E[n ] s the average of ts samples. In partcular, the observer n node counts n [k] and estmates

11 fg/centr_perc_b.pdf fg/centr_aver_b.pdf Fg.. Percentage of nodes satsfyng the delay requrements (0.02s) usng the gradent algorthm wth respect to the number of nodes n the network. Fg. 2. Average queueng delay usng the gradent algorthm wth respect to the number of nodes n the network. E[n ] by E[n ] =. K k= n = n [k]. (67) K Ths suggests that one can use (??) to desgn a dstrbuted algorthm because all the varables, p, X and n, are locally avalable at node. Rearrangng (??) and substtutng CW = 2 p yelds B. Implementaton Issues The dstrbuted algorthm has been mplemented and tested n the ns-2 smulator. Frst, we ntroduce a countng mechansm to count n, the number of dle slots between two consecutve nodes transmssons. Then, the contenton wndow can be adapted by (??) based on n. X = 2 ( T n + τ)cw + T τ. (68) If we consder CW as the varable, (??) defnes a mappng from CW to X. Assume that the target access delay s X. The objectve s to adapt CW such that X (CW ) meets X. In ths regard, we consder the followng optmzaton problem: mn (X X (CW )) 2 (69) s.t. CW 2. (70) The target access delay s met when X s equal to X (CW ) for all. As the objectve s a quadratc functon of CW, the problem s convex n the feasble regon of CW > 2. Therefore, a gradent algorthm can readly be used to solve (??). The dervatve of the objectve functon n (??) wth respect to CW s d dcw (X X (CW )) 2 = (X X (CW ))( T n + τ). Thus, we derve a dstrbuted algorthm from: CW (t + ) = max{cw (t) + α(x X (CW (t)))( T n + τ), 2}, (7) (72) where α s an approprately chosen stepsze [?]. In summary, CW s gradually drven to the optmal pont such that the dfference between X and X s mnmzed. In fact, as we adopt the gradent descent method to solve the dstrbuted optmzaton problem, we can derve the convergence result usng the property of gradent descent method. fg/dle_count-eps-converted-to.pdf Fg. 3. Transton of channel states. ) Idle Counter: The channel state changes when a packet transmsson begns or ends. Each node can carrer-sense the change of the channel state. At each nstant, when channel state changes, the dle counter s trggered to update the count of the number of dle slots between two consecutve transmssons. To llustrate how the dle counter works, the transton of channel state s plotted n Fgure??. Frst, a wreless node senses the channel. When t detects that a

12 2 transmsson has ended, the dle counter s reset and starts to ncrement by one for every slot tme (e.g., 20µs); when t detects a new transmsson, the dle count stops and the counter s used to compute the average number of dle slots n. Denote the counter at the j-th count as c[j]; then we can update n by an exponental movng average update: n[j + ] = ( η) n[j] + ηc[j], (73) where the parameter η s a constant smoothng factor that les between 0 and. 2) Contenton Wndow Adaptaton: We assume that the target delays (or deadlnes) Y are provded by the upper layer applcatons. The delay Y conssts of bufferng delay, servce tme and transmsson delay. Accordng to our analyss, the end-to-end delay s determned by the servce tme X. Recall that we have derved (??) that maps Y to X. Thus, applyng (??) gves the target servce tme X T f Y s specfed. Fnally, a sender node can adapt ts contenton wndow CW by usng (??), where n s provded by the dle counter. 3) Performance of Dstrbuted Algorthm: We have performed a ns-2 smulaton to evaluate the dstrbuted algorthm. In our smulaton, the data rates of the UDP traffc flows are fxed as follows: λ = 0.025, λ 2 = and λ 3 = Assume that the target delays of these flows are 0.02 second. The theoretcal contenton wndows are computed by the centralzed algorthm ARA for comparson: CW = 66, CW 2 = 23 and CW 3 = 8. These contenton wndows are shown by the sold lnes n Fgure??. The evoluton of contenton wndows drven by the dstrbuted algorthm s llustrated n the fgure. One observes that startng from an ntal condton 3, each contenton wndow gradually moves towards ts theoretcal value. The contenton wndows of flow 2 and flow 3 converge n a few seconds. The converged values are also observed to be close to the theoretcal values. However, the convergence of flow s not as obvous as the other two. In fact, because the contenton wndow of flow s much larger than the other two, t fluctuates wthn a larger range. The other two contenton wndows also fluctuate, but wthn a smaller range and thus appear to reman constant after convergence. The fluctuaton s an artfact of the gradent algorthm snce n practce we use a constant stepsze α. In Fgure??, the average delays of the three flows wth the dstrbuted algorthm are shown. One can compare the result of the delays wth the centralzed algorthm, as shown n Fgure??. We have further studed the performance of the dstrbuted algorthm when the number of nodes n the network ncreases. The confguraton of the experment s the same as that n Secton V for studyng the dstrbuted algorthm. The experment results show that the delay performance of the dstrbuted algorthm s almost the same as that of the centralzed algorthm except that the dstrbuted algorthm converges slghtly longer (after a few seconds). VIII. VIDEO-BASED EXPERIMENTAL EVALUATION In ths secton, we use a vdeo transmsson smulator EvalVd [?] to evaluate the performance of the algorthm when MPEG (movng pcture express group) vdeo s transmtted. Fg. 4. fg/cw_converge-eps-converted-to.pdf Convergence of dstrbuted contenton wndow adaptaton. fg/dst_delay-eps-converted-to.pdf Fg. 5. Average end-to-end delay performance acheved by the dstrbuted algorthm. A. Overvew of EvalVd The structure of the EvalVd framework [?], [?] s shown n Fgure?? that llustrates how EvalVd measures the vdeo qualty-of-servce metrcs. For more nformaton, we refer the readers to [?], [?]. B. Vdeo Dstorton We focus on three metrcs assocated wth vdeo dstorton for three types of vdeo frames namely I-frames, P-frames and B-frames and ther calculaton. Packet loss: For each type of data, we compute the packet loss rate as follows. Let T denote the type of data n the packet (one of I, P, B frames), P R T denote the number of type T packets receved, and P S T denote the number of type T packets sent, then the packet loss rate P L T s

13 3 fg/evalvd-eps-converted-to.pdf Fg. 6. Overvew of the vdeo transmsson smulaton of EvalVd system. gven by P L T = P R T P S T 00%. (74) Frame loss: The frame loss calculaton s ntroduced because we can not easly deduce the frame loss rate from packet loss rate. Let F R T denote the number of type T frames receved and F S T denote the number of type T frames sent, then the frame loss rate s F L T = F R T F S T 00%. (75) Delay and Jtter: Frames n dgtal vdeos have to be dsplayed at a constant rate. Dsplayng a frame before or after the defned tme leads to a phenomenon called jerkness [?]. Ths ssue s addressed by play-out buffers that can be used to absorb the jtter ntroduced by network delays. The buffer sze s predefned based on the playback tme n our experment. use both format vdeo sources. Furthermore, we set MTU to 000 bytes. The packet arrvals are shown n Fgure?? and??. The vdeo frame s sent every ms for 30 frames/sec vdeo. The frst experment s descrbed as follows: we assume two groups of users coexstng n a wreless network. Users n Group download whle playng a vdeo n YUV CIF format. Users n Group 2 download whle playng the same vdeo n YUV QCIF format. Each group conssts of two users. All users adopt the default IEEE 802. DCF. Each vdeo provder frst encodes the YUV fle to obtan the compressed MPEG-4 fle. Then, users use MP4.exe (from Evalvd) to record the tracefle for a sender. The tracefles are lnked to a ns-2 UDP agent attached n the sender node. Smulated packets are generated based on the tracefle and then sent to the recever. The sender records when these packets are sent out and the recever records when these packets are receved. After the smulaton, the two records are compared to produce the receved compressed MPEG-4 fle. Fnally, the decoder decodes the fle and reconstructs the receved vdeo. The second experment dffers from the frst only n usng the proposed algorthm. The mprovement can be observed from the qualty of the receved vdeo. The comparson s shown n Fgure??. fg/foreman-eps-converted-to.pdf C. Experment Desgn Our experments are based on real vdeo data usng raw data downloaded from the Vdeo Trace Lbrary [?]. The vdeo traces are provded n two formats, namely YUV QCIF (76 x 44) and YUV CIF (352 x 288). Snce the two formats have dfferent resolutons, the amount of data that needs to be transmtted per unt tme are dfferent for the same vdeo sequence. For example, the sze of 300-frame-long Foreman vdeo n YUV CIF s 44M, whle the sze of the same vdeo n YUV QCIF s M. For comparson purpose, we conduct two experments usng dfferent algorthms n EvalVd. We use the default IEEE 802. DCF for the frst experment whle usng the proposed algorthm for the second experment. In both experments, we Fg. 9. The llustraton of vdeo qualty for dfferent contenton wndows. Three consecutve frames are selected from the receved vdeo n group. The upper three frames are taken from the vdeo transported n the default IEEE 802. DCF network, and the lower three frames are taken from the vdeo reconfgured by parameters derved from our scheme. Observe that the lower three frames have neglgble dstorton, because the contenton wndow s approprately adjusted to guarantee the delay requrement of the vdeo n CIF format. In contrast, we see that the upper three frames are corrupted. Furthermore,