Channel-Qualty Dependent Earlest Deadlne Due Far Schedulng Schemes for Wreless Multmeda Networks Ahmed K. F. Khattab Khaled M. F. Elsayed ahmedkhattab@eng.cu.edu.eg khaled@eee.org Department of Electroncs and Communcatons Engneerng Caro Unversty, Gza 12613, Egypt ABSTRACT Provdng delay guarantees to tme-senstve traffc n wreless multmeda networks s a challengng ssue. Ths s due to the tme-varyng lnk capactes and the varety of real-tme applcatons expected to be handled by such networks. We propose and evaluate the performance of two channel-aware schedulng schemes that are capable of provdng such delay guarantees n wreless networks. In the frst proposed scheme, the Channel-Dependent Earlest-Due-Date (CD-EDD) dscplne, the expraton tme of the head of lne packets of users' queues s taken nto consderaton n conjuncton wth the current channel states of users n the schedulng decson. Ths polcy attempts to guarantee the targeted delay bounds n addton to explotng multuser dversty to make best utlzaton of the varable capacty of the channel. In the second scheme we attempt to ensure that the number of packets dropped due to deadlne volaton s farly dsturbed among users. Ths provdes farness n the qualty of servce (QoS) delvered to dfferent users. A unque feature of our work s explct provsonng of statstcal QoS as well as ensurng farness n data rates, delay bound, and delay bound volaton. We provde extensve smulaton results to show the dfferent performance aspects of the proposed schemes. Categores and Subject Descrptors C.2.1 [Computer Communcaton Networks]: Network Archtecture and Desgn Wreless Communcaton; C.4. [Performance of Systems]: Modelng Technques General Terms QoS Provsonng, Performance evaluaton and modelng. Keywords Farness, Multuser dversty, Schedulng, Wreless networks. 1. INTRODUCTION Schedulng n wreless networks have become the focus of recent research. Ths s due to the expectatons that the next generaton Permsson to make dgtal or hard copes of all or part of ths work for personal or classroom use s granted wthout fee provded that copes are not made or dstrbuted for proft or commercal advantage and that copes bear ths notce and the full ctaton on the frst page. To copy otherwse, or republsh, to post on servers or to redstrbute to lsts, requres pror specfc permsson and/or a fee. MSWIM 04, October 4 6, 2004, Veneza, Italy. Copyrght 2004 ACM 1-58113-953-5/04/0010...$5.00. networks wll combne the advantages of the Internet wth the moblty characterstcs of the wreless systems. Many schedulng algorthms, capable of provdng certan guaranteed QoS, have been developed for wrelne networks. However, these exstng servce dscplnes, such as Weghted Far Queung (WFQ), vrtual clock, and Earlest-Due-Date Frst (EDD) [1], are not drectly applcable n wreless networks because they do not consder the characterstcs of wreless channel. These characterstcs nclude hgh error rate, bursty errors, locatondependent and tme-varyng wreless lnk capacty, scarce bandwdth, user moblty, and power lmtaton of the moble hosts. All of the above characterstcs leads to the fact that developng effcent and effectve schedulng algorthms for wreless networks s very challengng. An effectve way to ncrease the capacty of a tme-varyng channel s the use of dversty. The dea of dversty s to create multple ndependent sgnal paths between the transmtter and the recever so that hgher channel capacty can be obtaned. Dversty can be acheved over tme, space, and frequency. These tradtonal dversty methods are essentally applcable to a sngle-user lnk. Recently, however, Knopp and Humblet [2] ntroduced another knd of dversty, whch s nherent n a wreless network wth multple users sharng a tme-varyng channel. Ths dversty, termed multuser dversty, comes from the fact that dfferent users usually have ndependent channel gans for the same shared medum (e.g. downlnk). Wth multuser dversty, the strategy of maxmzng the total Shannon (ergodc) capacty turns out to be a greedy schedulng rule where the scheduler allows at any tme slot only the user wth the best channel to transmt [3]. Results n [4] have shown that such schedulng technque can ncrease the total (ergodc) capacty dramatcally, n the absence of delay constrants, as compared to the tradtonally used schedulng technques. One problem wth such greedy schedulng s the unfarness n resource sharng between users n the network. Ths s due the fact that the user wth the best channel condtons wll always receve the bggest share of network resources; whle the user sufferng from bad channel condtons wll not be able to be served. The research reported n [5-10] was concerned wth the problem of achevng throughput and/or temporal farness among users. These works report on schedulng algorthms that attempt to guarantee that the dfference n the servces obtaned by users wth dfferent channel condtons are as close as possble ether on short-term bass and/or on long-term bass. However, these schemes provde no delay guarantees and thus are not sutable for delay-senstve applcatons, such as voce and vdeo. In ths paper we propose a schedulng scheme based on Earlest-Due- 31
Date Frst (EDD) that explots mult-user dversty and can provde statstcal guarantees on delays, acheves hgh throughput, and exhbts good farness performance wth respect to throughput and deadlne volatons. The rest of ths paper s organzed as follows: s secton 2 we descrbe the model of the system under consderaton. Then n secton 3, a survey of schedulng delay-senstve traffc n wreless network n the lterature s presented. In secton 4, we propose two new schedulng polces and dscus ther operaton. Whle n secton 5, an extensve set of smulaton s carred out to explore the characterstcs of these dscplnes. Secton 6 summarzes the man fndngs of ths paper. 2. SYSTEM MODEL We frst descrbe the cellular wreless network model used, and more specfcally the downlnk of such a network. A base staton transmts data to N moble termnal users, each of whch requres certan QoS guarantees. In cell-structured wreless networks, the servce area s dvded nto cells, and each s served va a base staton. A sngle cell s consdered n whch a centralzed scheduler at the base staton controls the downlnk schedulng, whereas uplnk schedulng uses an addtonal mechansm such as pollng to collect transmsson requests from moble termnals [5], [6]. We assume that the downlnk and uplnk transmsson don't nterfere wth each other. We consder a tme slotted system, where tme s the resource to be shared among users. A tme-slotted cellular system can have more than one channel (frequency band), but at any gven tme, only one user can occupy a gven channel wthn a cell. Here, we focus on the schedulng problem for a sngle channel over whch a number of users could be tme-dvson multplexed. Tme dvson multple access (TDMA) systems dvdes the tme nto tme slots of length Ts, durng whch data transmsson of a sngle user, the scheduled user, s carred out usng all resources avalable to the base staton at that tme nstant. For downlnk schedulng, packets destned to dfferent users are put n separate queues, one correspondng to a user's data flow. The tme varyng channel condtons of wreless lnks are related to three basc phenomena: fast fadng on the order of mllseconds, shadow fadng on the order of tens to hundreds of mllseconds, and fnally, long tme-scale varatons due to user moblty. The channel fadng processes of the users are assumed to be statonary, ergodc and ndependent of each other, and we also assume that the channel gans are constants over one tme slot's duraton. Snce our algorthm wll explot the users channel condtons n makng the schedulng decson, we consder wreless systems wth mechansms to make predcted channel condtons avalable to the base staton as s commonly the case wth technologes such as HDR [11], UMTS-HS-DPA [12], (E)GPRS [13], etc. The partcular mechansm employed by a system depends on the communcaton standard. In general, the faster and more precsely the channel qualty can be predcted, the better the scheduler can ncorporate ths nformaton nto ts decson as to whch user to schedule next [5]. Thus, we wll assume that base staton has the current (or delayed) channel state nformaton of each user. An mportant and challengng problem n the desgn of hgh speed communcatons networks s that of provdng Qualty of Servce (QoS) guarantees, usually specfed n terms of rate guarantees, loss probabltes or delays of packets n the network. The control of delays s often of crucal mportance, especally for real-tme applcatons such as audo and vdeo streamng. Real-tme traffc classes are modeled as a stream of packets, wth each packet havng an expry tme beyond whch the packet s of no use to the end user. The objectve of the scheduler s to transmt each packet before ts expry, and f ths s not possble, to mnmze the number of lost packets due to deadlne expry. Expry occurs when a packet have been watng n the base staton queue for a tme greater than ts deadlne wthout beng served. Such a packet s dropped by the system. Such QoS requrements can be specfed n terms of deadlne T (determnstc QoS requrements) or accompaned wth allowed volaton probablty δ (statstcal QoS) for each user traffc flow. In ths paper, we wll use the followng model n defnng QoS requrement of user ( ) > (1) P W T δ for = 1, 2,., N, where W to be the delay encountered by user packets. Under ths constrant, the problem s to mnmze the volaton occurrences. 3. PREVIOUS WORK In ths secton, we present a survey of exstng schedulng dscplnes applcable n wreless networks wth delay-senstve users' traffc. In [14], the authors proposed to apply the wrelne EDD dscplne schedulng n wreless networks. The scheme s called Feasble Earlest Due Date (FEDD) schedulng. They assumed a smple channel state model n whch the channel can be ether "good" or "bad". Thus, FEDD schedulng chooses to schedule the packet whch has the earlest tme to expry from the set of queues whose channels are marked good only. The authors n [16] proposed a modfcaton to the Largest Weghted Delay Frst (LWDF) schedulng dscplne that takes the tme varyng characterstcs of wreless channels nto account. The LWDF [15] dscplne s a parameterzed verson of the frstnput frst-output (FIFO) that works as follows: at the begnnng of the tme slot startng at tme t, serve at the maxmal possble rate the queue of user j, where j = argmax{ aw ()} t (2) where W (t) s the watng tme of head of lne (HoL) packet of the th user at the tme slot startng at tme t, and a > 0, = 1,2,., N, are a fxed set of constants. If the delay QoS requrements for all users are as expressed by (1), t was proved n [15] that the choce of weghts a that makes LWDF dscplne nearly throughput optmal (note however that ths choce of weghts s vald only for large values of the delay bound T and very small values of δ ) s: δ a = log (3) T 32
The proposed modfcaton of [16] was to use multuser dversty n order to ncrease the effcency of channel utlzaton (and hence the system throughput) and also compensate delayed users. The proposed Modfed Largest Weghted Delay Frst (M- LWDF) dscplne schedules the j th user, where j = argmax{ γµ () tw ()} t (4) where μ (t) s the state of the channel of user at tme t,.e. the actual rate supported by the channel. Ths rate s assumed to be constant over one slot. It had been proven n [16] that settng γ = a / µ,where a s gven by (3) and µ s the mean rate supported over the th channel, makes the M-LWDF dscplne throughput optmal. In practce, the mean rate can be measured over a certan, but relatvely long, tme wndow [4] by averagng the rate actually gven to that user n that wndow. The M-LWDF schedulng rule could be rewrtten as schedule the j th user, where µ () t j = argmax{ a W ()} t (5) µ The exponental rule schedulng dscplne have been also proposed n [16] (further nvestgated and mplemented n [17] for CDMA/HDR system and modfed n [18].) Ths scheme schedules the j th user at the tme slot startng at tme t for transmsson, where and aw ( t ) aw µ () t 1+ aw j = argmax{ a e } (6) µ N = 1 N 1 aw = aw () t (7) Ths polcy attempts to equalze the weghted delays a W (t) of all the queues when ther dfferences are large. If one of the queues would have larger (weghted) delay than the others by more than order aw, then the exponent term becomes very large and overrdes the channel consderatons (as long as ts channel can support a non-zero rate), hence gvng prorty to that queue. On the other hand, for small weghted delay dfferences (.e. less than order aw ), the exponental term s close to unty, and the polcy behaves as the proportonally far rule. Hence, the exponental rule polcy gracefully adapts from a proportonally far one to one whch balances delays [16], [17]. Smulaton results n [17] showed that the exponental rule schedulng exhbts better delay tals compared to any other schedulng polcy n the sense that the delays of all users are about the same and are all reasonably small. Ths occurs, however, for large values of T and very small values of δ, whch s not desred practcally. Moreover, the exponental rule schedulng was found to be hghly dependent on parameter settngs. Therefore, It was advsed that dentfyng good schedulng rules whch are less dependent on the "proper" parameter settng would be desrable [16]. 4. THE PROPOSED SCHEDULING SCHEMES The goal of our work s to desgn schedulng schemes for delay senstve traffc that exhbts good performance n wreless networks. From the above study of such a problem, we mean by the word "good performance" that such a dscplne should attempt to acheve the followng objectves: 1) Maxmzng the overall system throughput by utlzng multuser dversty, 2) Provdng a mechansm to compensate queues whose packets are experencng long delays n the system n order to prevent ther packets from beng lost, 3) Achevng farness n resource sharng, and 4) Exhbtng weak dependency on the parameters settng. 4.1 Channel Dependent Earlest Deadlne Due (CD-EDD) Schedulng Dscplne In classcal wrelne earlest due date schedulng, each packet s assgned a deadlne, and the scheduler serves packets n order of ther deadlnes. The queue wth the smallest deadlne s served frst by the maxmum avalable rate. If the scheduler s overcommtted, then some packets mss ther deadlnes. Ths polcy was shown to be optmal n the wrelne case (for ndependent dentcally dstrbuted Bernoull arrval and channel processes). EDD cannot be effcently employed n wreless networks snce t does not consder the tme varyng characterstcs of wreless lnks. It was not reported n the lterature the exstence of a schedulng dscplne that combnes the EDD schedulng concept wth a mechansm to adapt wth the characterstcs of wreless networks (wth the excepton of the attempt n [14] whch does not actually adapt wth the tme varyng nature of wreless channel, snce t assumed the smplfed channel model of good or bad). We propose a new schedulng dscplne, whch we call the Channel Dependent Earlest Due Date frst (CD-EDD) polcy. Ths s bascally a channel-state dependent EDD polcy where the scheduler chooses to schedule the queue whose HoL packet has the earlest tme to expre and the best channel condtons, and consequently the hghest transmsson rate, among all queues. The proposed CD-EDD schedulng polcy s as follows: At the tme slot startng at tme t, schedule wth the maxmum possble rate the queue of the j th user, where where µ () t W () t j = argmax{ a } (8) µ d () t a s the weghtng parameter reflectng the statstcal QoS requrements of the th user. μ (t) s the actual rate that could be used for transmsson by the th user at tme t, whch reflects the current channel state of the user's channel. µ s the mean rate supported or prevously offered to the th user. 33
W (t) s the delay experenced by the HoL packet snce ts entrance to the th user queue n the base staton. d (t) s the tme to expre of the th user HoL packet, whch s the dfference between the deadlne, T, and the delay experenced tll tme t, W (t),.e. d () t = T W () t (9) The behavor of the CD-EDD polcy can be explaned as follows: when a certan queue has ts HoL packet watng n the system for a relatvely long perod (but have not expred yet), ts tme to expre wll decrease sgnfcantly. n such a stuaton, the term W ()/ t d () t wll grow sgnfcantly due to the contrbuton of 1/ d () t untl t overcomes other terms n (8). Ths has an effect akn to reducng the number of dropped packets due to deadlne volaton. On the other hand, f the delay characterstcs of all users are about the same,.e. ther tme to expre and watng tmes are close, the term W ()/ t d () t wll be common to all users, and the polcy then reduces to a proportonally far one that explot multuser dversty to effcently utlze the channel bandwdth of multuser systems n a far manner. It s worth mentonng that weghts a doesn't contrbute sgnfcantly n the decson. A rule of thumb for choosng a whch works n practce s the one gven n (3) snce ths choce s suggested by large devatons of optmalty results. In other words, the CD-EDD s a schedulng dscplne that can be used to provde QoS guarantees, defned n terms of delay bounds, for real-tme traffc n wreless networks. Ths s acheved by ncreasng the prorty of delayed users to get access to the medum over tme. An mportant feature of the CD-EDD polcy s ts weak dependency on the value of QoS requred, and thus can be used for a wde varety of QoS requrements. 4.2 A Set of Volaton Far Rules Another new dea than can be appled n conjuncton wth any schedulng dscplne n order to enhance the farness characterstcs of these polces s proposed here, whch s based on the number of deadlne volatons occurrng to packets of dfferent queues. Ths requres that each queue n the base staton to be accompaned wth a counter that counts the number of packets lost n ths queue's flow. Ths may be mplemented practcally be means of sldng wndows bass. Let us defne NV (t) to be the number of deadlne due date volatons encountered n the flow of the th user up to tme t. NV() t to be the average of the number of volatons n all N queues,.e. N = 1 N 1 NV() t = NV () t (10) The scheduler may use the number of deadlne volatons to fnd a way to compensate users sufferng from unfarness n the number of dropped packets. For example the scheduler could gve more credt or ncrease the prorty level so that such a user could access the system resources. Ths could be acheved be a schedulng dscplne that uses a term lke NV ()/ t NV() t n makng the schedulng decson. We call such a schedulng dscplne a volatons-far (VF) dscplne. Intally, we appled ths dea drectly to the proportonally far [4] schedulng dscplne, yeldng the volatons-far proportonally far polcy. So, n each tme slot the scheduler chooses the j th user, where µ () t NV () t j = argmax{ } (11) µ NV() t Ths reduces the number of packets lost for users wth bad channel condtons, therefore, enhancng the farness characterstcs of the proportonally far polcy. On the other hand, t stll lacks a mechansm for provsonng of QoS guarantees for delay senstve traffc. We further apply the proposed modfcaton to both the M-LWDF and the exponental rule polces. In the volatons-far modfed largest weghted delay frst (VF-M-LWDF) dscplne, the schedulng decson s such that at the tme slot startng at tme t, schedule wth the maxmum possble rate the queue of the j th user, where µ () t NV () t j = argmax{ a W ()} t (12) µ NV() t In the volatons-far exponental (VF-EXP) dscplne, the schedulng decson s such that at the tme slot startng at tme t, schedule wth the maxmum possble rate the queue of the j th user, where aw ( t ) aw µ () t NV () t 1+ aw j = argmax{ a e } (13) µ NV() t The proposed modfcaton enhance ther performance snce the addton of the volatons-far term wll ensure farness n both the delay tmes and throughput. Ths could be explaned snce both the M-LWDF and the exponental dscplnes mnmze the packet delay, and when the number of dropped packets s farly dstrbuted among the users, the long term servce rate wll be equal for all users. Another very mportant gan of the volatonsfar verson of these dscplne, s that ther performance s not much dependent on the parameter settng as was the case n the orgnal rules (ths wll be seen n the smulaton results). Fnally, f the proposed volatons-far technque s appled on the proposed CD-EDD, we can get a schedulng dscplne applcable n wreless network that explctly provde QoS to delay senstve traffc, wth excellent farness characterstc wth respect to data rate, delay bound, and delay bound volaton. The volatons-far channel-dependent earlest deadlne due date (VF-CD-EDD) scheduler chooses, at the tme slot startng at tme t, the j th user for transmsson, where 34
µ () t W () t NV () t j = argmax{ a } (14) µ d () t NV() t In the next secton, we provde an extensve set of smulaton that explore the performance of the proposed CD-EDD dscplne compared wth the M-LWDF and the exponental rule dscplnes as a reference. We also show the advantages acheved by ther volatons- far versons, namely the VF-CD-EDD, the VF-M- LWDF, and the VF-exponental schedulng dscplnes. 5. PERFORMANCE EVALUATION 5.1 Smulaton Setup Frst, we descrbe the smulaton setup used. We chose the Hgh Data Rate (HDR) CDMA system model. HDR technology has recently been proposed as a TDM-based overlay to CDMA wth the goal of provdng packet data servces to moble users. A very attractve feature of HDR s enablng the use of effcent schedulng algorthms snce t provdes a mechansm for lnk status montorng. The cell serves N moble users each recevng a data flow. The base staton contans N queues, one correspondng to a dfferent data flow and an assocated scheduler. The scheduler makes a decson every 1.667 mllsecond based on the current nformaton avalable at the start of the tme slot. Arrval process of the real-tme traffc s modeled as a Bernoull processes wth a mean rate of 28.8 Kbps for each of the N user's queues. Ths rate corresponds to the typcal rate requred for streamng audo over the Internet. The HDR packet sze s 128 bytes. We assume for smplcty that all users requre the same servce qualty,.e. they all have the same deadlne (T ) and the same volaton probablty (δ ) of 95%. Even thought all users share a common channel, the channel capacty of that channel seen by dfferent users s dfferent. Ths s due to the wreless lnk characterstcs descrbed above. The nstantaneous capacty of a wreless channel s gven by 2 () log (1 () ) 2 Ct = B + ht SNR (15) where C(t) s the channel capacty or the data rate (n bts per second) that can be transmtted on a channel of bandwdth B (Hertz). The bandwdth of HDR/CDMA channel s 1.25 MHz. The term h(t) s the normalzed gan (or fadng level) of the wreless channel at tme t, and SNR s the requred sgnal to nose rato at the recever antenna (13 db for HDR/CDMA system). For smulaton purposes, we use the typcal HDR and cell parameters gven n [11]. The average fade level dstrbuton of a typcal moble n HDR cell can be easly found. The fadng process of each user's channel can be represented by a Raylegh process. So, n order to smulate N channels, we pck N fadng levels accordng to the above dstrbuton, and generate N Raylegh processes wth means equal to these fadng levels after beng normalzed. It s worth mentonng that HDR doesn't not support arbtrary transmsson rates,.e. the scheduled user cannot transmt wth the rate computed above but wth the maxmum possble rate from a set of dscrete rates. An HDR user can transmt data at a rate of 9.6 * 2 Kbps, = 0, 1,, wth a maxmum rate of 2 Mbps. Thus the state of channel µ () t at the start of the tme slot at tme t wll be the actual rate that the channel can support, rather than the channel capacty at that tme nstant. We have assumed that the channel condtons do not change sgnfcantly wthn a tme slot duraton. Fnally, all smulatons wll be carred out for a duraton of 10 mnutes. 5.2 Performance Metrcs For real-tme traffc, a good measure of performance s the delays packets ncur at the base staton. A good schedulng algorthm should keep all delays below the delay bound T wth hgh probablty. The delay dstrbuton curves can be used to llustrate the delay behavor of the schedulng dscplnes under consderaton. Some parameters of the delay dstrbuton, such as the worst-case delay, the mean delay, or the 95-percentle delay, could be used to evaluate the QoS receved by a user. We wll consder the 95-percetle delay as our measure of the delay guarantees offered by a schedulng dscplne. Our measure of the throughput performance of the schedulng dscplnes at hand wll be the total throughput acheved by the system. The farness of bandwdth sharng among users s also a good ndcaton of the effcency of any schedulng dscplne. The fracton of packets dropped, due to deadlne volaton, for a user can be used to evaluate the loss performance of a schedulng dscplne. For real-tme traffc, ths fracton s requred to be as small as possble. From farness pont of vew, t s better to equalze the fracton of packets lost n dfferent queues. 5.3 Results and Dscussons Frst, we estmate the number of users, wth traffc lke the one descrbed above, that can be supported by a sngle HDR cell under each of the prevously mentoned schedulng polces. In ths experment, we smulate N users, unformly dstrbuted throughout the cell, and montor the average servce rate receved by a sngle user for dfferent values of N. As N ncreases, and as long as the channel capacty can support such a number of users, t s expected that the servce rate receved by each user wll be close to ts arrval rate. Any further ncrease of the number of user, whle keepng the channel capacty unchanged, wll make the scheduler unable to serve such users n the approprate tme so more packets wll be dropped and thus the average throughput share of each user wll decrease. So, we wll take the number of users beyond whch the average servce rate receved by any user n the system start to decrease as the system capacty. Smulaton results showed that the consdered schedulng dscplnes allow the system to support from 12 to 16 users dependng on the value of the deadlne. In our second experment, we nvestgate the delay performance of varous schedulng dscplnes. We begn wth a comparson of the proposed CD-EDD schedulng dscplnes versus to both the M-LWDF and the exponental rule schedulng dscplnes reported as the most sutable polces for schedulng delay senstve traffc n the lterature. In order to be able to evaluate the performance of the schedulng technques, the system should be loaded wth ts maxmum capacty. Based on the results of the frst experment, we assume that the cell s servng 14 moble termnals,.e. N =14. The delay dstrbuton tals for both user 1 (wth the best channel condtons) and user 14 (wth the worst channel condtons) for the M-LWDF, exponental rule, and the 35
(a) The maxmum and mnmum 95% delays. (a) The maxmum and mnmum 95% delays. (b) The maxmum and mnmum percentage of packets lost. Fgure 1. Farness Behavor of the orgnal dscplnes. (b) The maxmum and mnmum percentage of packets lost. Fgure 2. Farness Behavor of the volaton far dscplnes. proposed CD-EDD schedulng dscplnes for delay bounds of 60, 100, 200, and 400 mllseconds have been studed. These bounds are encountered practcally n multmeda streams. However, due to space constrants, we are not able to show these curves. We refer the reader to [20] for further detals. We observe that for moderate delay bounds, e.g. 60 and 100 mllseconds, the performance of the exponental rule schedulng slghtly outperforms both the M-LWDF and CD-EDD dscplnes. In ths case, all delays are kept at small value and about the same for all users. For hgher bounds, e.g. 200, and 400 mllseconds, we fnd that the delay performance of the CD-EDD scheduler does not change sgnfcantly. On the other hand, the performance of both the M-LWDF and the exponental rule schedulers degrades severely as the gab between the tals of the best user and the worst user becomes wder. Ths severe degradng n performance s caused by the dependency of both rules on the qualty of servce requred, whch affects the value of the weghts {a } that controls the performance of these rules. (Keep n mnd that the goal of the M-LWDF s to mnmze the weghted delays whle the exponental rule schedulng tres to keep all the delays around the average of these weghted delays (aw ), and they both do not target a certan delay bound to serve as much packet as possble before ths bound s volated.) On the other hand, the CD-EDD polcy does not suffer from such a dependency on the QoS, and consequently the weght values, snce the phlosophy of ths rule s manly to serve more packets before ther deadlnes expre. Ths may cause the packets of the best channel users to experence relatvely hgher delays than n the case of other rules, but stll lower than the worst user. Ths occurs on the expense of preventng more packets from beng dropped due to deadlne volaton. Ths can be further demonstrated when we plot the maxmum and the mnmum (correspondng to the best and worst users) 95- percentle delay and percentage of packets dropped due to deadlne volatons versus the delay bounds as shown n Fgure 1-a and 1-b, respectvely. It s clear that t s not desrable to keep one or some users' delays below a value much smaller than the requred bound whle leavng one or some users sufferng from droppng a large percentage of ther packets as the case 36
wth both the M-LWDF and exponental rule schedulers. Whle n CD-EDD dscplne, the maxmum and the mnmum 95 percentle delay are about the same and so close to the delay bound, besdes the packet loss ratos are very small and very close to each other. So, the base statons can guarantee strong delay bounds for all delay senstve users n a far manner by usng the CD-EDD schedulng dscplne, regardless of the value of these bounds. When the same experments were carred out for the volatonsfar versons of the above dscplnes, t was found that the performance of all the volatons-far polces s not much dependent on the QoS requred (ncludng the dscplnes whch are orgnally sufferng from that dependency). The delay dstrbuton tals of the best user and the worst user for dfferent delay bounds have been studed [20]. It s observed that the tals became much more closer for the VF-CD-EDD, but wth a lttle bt hgher delays than those of ether the VF-M-LWDF or the VF-EXP polces. As shown n Fgures 2-a and 2-b, where the maxmum and the mnmum 95-percentle delay and percentage of packets dropped due to deadlne volatons are plotted versus the delay bounds, the servce qualty offered to dfferent users, n terms of 95% delay, s about the same. Furthermore, the amount of packets dropped n the system due to deadlne volatons becomes very small. Moreover, ths amount s dstrbuted among all users n a far manner. Lke the CD-EDD, the VF-CD-EDD has the superorty snce t acheves the smallest number of packets lost due to deadlne volatons. Fnally, we study the throughput characterstcs of the aforementoned schedulng dscplnes. Here we are nterested n studyng the overall throughput of the system as well as how the throughput s dvded among users wth dfferent channel condtons,.e. farness n throughput sharng. The results of ths experment are llustrated n Fgure 3-a for 100 mllseconds bound by plottng the overall throughput of the system versus the number of users usng the smulaton setup of the frst experment. When the system s operatng wth number of users less than the system capacty, the total throughput of the system equals the sum of the arrval rates. When the system s servng more users than the system capacty, we observe that, regardless of the delay bound, the total throughput acheved usng the CD- EDD s hgher than any other rule because ths polcy causes the smallest number of packet to be lost due to deadlne expry. Moreover, the total throughput acheved usng any volatons-far dscplne s less than the throughput acheved wth the nonvolatons far counterpart. Ths s because n order to acheve farness n the rato of packets dropped among dfferent user, the volatons-far polces may prevent users wth good channel condtons from transmttng ther data for the sake of users wth bad channel condtons (such channels support low transmsson rates only). So the overall throughput acheved by the system wll be lower than the case where the schedulng polcy do not ntend to make users wth good channel condton drop some packet for the purpose of farness. In Fgure 3-b, we compare the average throughput share of a sngle user aganst the actual throughput shares of both the best channel user and the worst channel user for 100 mllseconds delay bound for both the orgnal dscplnes and ther volaton far counterparts. In ths experment, we use the same smulaton (a) The total throughput acheved. (b) Throughput Farness. Fgure 3. Throughput behavor at 100 m sec delay bound. model used n the second experment where the base staton serves the 14 used above. As seen n these fgures, the CD-EDD dscplne acheves the greatest average throughput per user, besdes, t keeps the actual throughput share as close as possble to that average. Note that the throughput shares of the best channel user and worst channel user are always close to each other for varous delay bounds for CD-EDD schedulng. Ths means that the CD-EDD dscplne s the most throughput far polcy that can guarantee delay bounds for real-tme users. On the other hand, even though the volaton far dscplnes leads to a slghtly lower throughput per user as prevously dscussed, they ensure farness n throughput sharng among all users regardless the delay bound. Ths s because n such dscplnes, the number of packets dropped due to deadlne expry s almost equal for all users. We summarze the man results of our smulaton experments n Table 1. 37
Table 1. Smulaton results summary CD-EDD M-LWDF EXP VF-CD-EDD VF-M- LWDF Delay bound guarantee X X Independency on QoS X X Total throughput X Less than orgnal Rules Delay farness Depend on QoS Throughput farness X Volaton farness X X 6. CONCLUSIONS Ths paper addresses the problem of schedulng real-tme users over TDM-based wreless multmeda networks. We ntroduced the Channel Dependent Earlest-Due-Date frst (CD-EDD) schedulng dscplne, a dscplne that provdes statstcal delay bound guarantees for tme-senstve traffc n networks wth tme-varyng channels. Gans n throughput and realzed delay are acheved by explotng mult-user dversty technques n whch the schedulng decson takes nto account the current channel state for each user n the system. By consderng the packet loss due to deadlne volaton, we also presented a set of schedulng polces that acheve farness n delays, throughput, and packet loss ratos among dfferent users regardless of the value of the delay bound. The proposed dscplnes outperforms other exstng polces n the sense that the servces receved by dfferent real-tme users, namely, delays, rates, and loss ratos, are farly acheved for a wde of applcatons. The proposed polces have low computatonal complexty and are sutable for applcaton n future broadband fxed or moble wreless systems such as 802.16a and 802.20. 7. REFERENCES [1] S. Kashave. An Engneerng Approach to Computer Networkng: ATM Networks, the Internet, and the telephone Network. Addson Wesley, 1997. [2] R. Knopp and P. A. Humblet. Informaton capacty and power control n sngle-cell multuser communcatons. In Proceedngs of IEEE ICC 95, Seattle, USA, June 1995. [3] D. Wu and R. Neg. Utlzng multuser dversty for effcent support of qualty of servce over a fadng channel. In Proceedngs of IEEE ICC'03, Anchorage, Alaska, USA, May 2003. [4] A. Jalal, R. Padovan, R. Pankaj. Data throughput of CDMA-HDR a hgh effcency-hgh data rate personal communcaton wreless system. In Proceedngs of Vehcular Technology Conference 2000-sprng, vol. 3. [5] Y. Lu, S. Gruhl, and E. Knghtly. WCFQ: An opportunstc wreless scheduler wth statstcal farness bounds. IEEE Transactons on Wreless Communcaton, September 2003. VF-EXP [6] Y. Lu and E. Knghtly. Opportunstc far schedulng over multple wreless channels. In Proceedngs of IEEE INFOCOM, 2003. [7] X. Lu, E. K. P. Chong, and N. B. Shroff. Transmsson schedulng for effcent wreless utlzaton. In Proceedngs of IEEE INFOCOM, 2000. [8] X. Lu, E. K. P. Chong, and N. B. Shroff. Optmal opportunstc schedulng n wreless networks. In Proceedngs of IEEE INFOCOM, 2000. [9] S. S. Kulkarn and C. Rosenberg. Opportunstc schedulng polces for wreless systems wth short term farness constrants. In Proceedngs of IEEE GLOBECOM, December 2003. [10] Z. Jang and N. K. Shankaranarayana. Channel qualty dependent schedulng for flexble wreless resource control. In Proceedngs of GLOBECOM, Texas, 2001. [11] P. Bender, P. Black, M. Grob, R. Padovan, N. Sndhushayana, and A. Vterb. CDMA/HDR: a bandwdth effcent hgh speed wreless data servce for nomadc users. IEEE Communcatons Magazne, vol. 38, no. 7, July 2000, 70 77. [12] 3rd Generaton Partnershp Project; Techncal Specfcaton Group Rado Access Network, Physcal layer aspects of utra hgh speed downlnk packet access (release 4) tr25.848 v4.0.0, Avalable: http://www.3gpp.org, Mar. 2001. [13] 3rd Generaton Partnershp Project; Techncal Specfcaton Group Rado Access Network, Servces provded by the physcal layer (release 4) ts 25.302 v4.1.0, Avalable: http://www.3gpp.org, June 2001. [14] S. Shakkotta and R. Srkant. Schedulng real-tme traffc wth deadlnes over a wreless channel. In Proceedngs of ACM Workshop on Wreless and Moble Multmeda, Seatle, WA, August 1999. [15] A.L. Stolyar and K. Ramanan. Largest Weghted Delay Frst Schedulng: Large Devatons and Optmalty. Annals of Appled Probablty, 2001, Vol.11, No.1, 1-48. [16] M. Andrews, K. Kumaran, K. Ramanan, A. L. Stolyar, R. Vjayakumar, P. Whtng. CDMA data QoS schedulng on the forward lnk wth varable channel condtons. Bell Laboratores Techncal Report, Aprl, 2000. [17] S. Shakkotta and A.L. Stolyar. Schedulng Algorthms for a Mxture of Real-Tme and Non-Real-Tme Data n HDR. In Proceedngs of ITC-17, Salvador da Baha, Brazl, September 2001, 793-804. [18] K. Chang and Y. Han. QoS-based adaptve schedulng for a mxed servce n HDR system. In Proceedngs of PIMRC, 2002. [19] S. Shakkotta and A. L. Stolyar. Schedulng for Multple Flows Sharng a Tme-Varyng Channel: The Exponental Rule. Analytc Methods n Appled Probablty, vol. 207, 2002, 185-202. [20] A. Khattab. Channel-Aware Schedulng of Delay-Bounded Multmeda Traffc n Wreless Networks Beyond 3G. M.Sc. Thess, Caro Unversty, Egypt, 2004. 38