QoS Provisioning in Wireless Data Networks under Non-Continuously Backlogged Users

Transcription

1 os Provsonng n Wreless Data Networks under Non-Contnuously Backlogged Users Tmotheos Kastrnoganns, and Symeon Papavasslou, Member, IEEE School of Electrcal and Computer Engneerng Natonal Techncal Unversty of Athens Athens 5780, Greece tmothe@netmode.ntua.gr, papavass@mal.ntua.gr Abstract Ths paper addresses the problem of effcent resource allocaton n CDMA wreless networks, supportng non-real-tme servces wth varous long-term os requrements, by explotng the advantages of opportunstc schedulng. Most of the exstng work covers the analyss of the system under the assumpton of nfnte backlogs. In ths paper, we remove ths assumpton and analyze the behavor of the system wth respect to ts overall achevable performance and ts ablty to gratfy users ndvdual os requrements under dfferent fundamental opportunstc schedulng polces, for the more realstc case of noncontnuously backlogged users. Motvated by the correspondng results that ndcate the unsatsfactory performance of these schedulers when consderng fnte backlogs, and n order to overcome these neffcences, a new non-work-conservng opportunstc schedulng framework s proposed whch s seamlessly ntegrated wthn the operaton of the varous schedulers. The correspondng results demonstrate that the proposed approach results n the fulfllment of users os prerequstes whle stll mantanng the opportunstc nature of the schedulers and thus achevng hgh system throughput. Keywords- CDMA wreless networks, opportunstc schedulng, fnte backloggs. I. INTRODUCTION Towards optmzng system s throughput performance over fast-fadng wreless envronments n code dvson multple access (CDMA) networks, channel-aware opportunstc schedulng polces have been adopted that postvely explot mult-user dversty affect []-[0]. However, most of the related exstng work on opportunstc schedulng algorthms covers the analyss of the system for statc user populaton and assumng nfnte backlogs. The potental nstablty effects and the correspondng sub-optmal system s throughput performance under dynamc user confguraton, when greedy opportunstc polces are appled to maxmze system s overall throughput performance, s addressed n []. However, n that study only a certan class of polces, based on Proportonal Far algorthm [4], has been consdered. Moreover n [2], t s further shown that opportunstc TDMA based schedulng schemes do not always lead to optmalty, n terms of overall power consumpton, when fnte users backlogs are consdered. In ths paper we remove the assumpton of contnuously backlogged users, snce n real envronments users may often experence empty queues, due to ther potentally good channel Ths work was partally supported by EC EFIPSANS proect (INFSO ICT 25549) condtons, the bursty nature of ther traffc, as well as the possbly low or moderate system load. Therefore, we ntally study the performance of fundamental opportunstc schedulng approaches under non-contnuously backlogged users scenaros. The under consderaton algorthms acheve system s performance maxmzaton, whle ether assertng weghted users long-term access tme farness [7] or long-term utltaran farness [8], when consderng nfnte backlogs. The correspondng results ndcate ther nsuffcency n supportng users ualty of Servce (os) prerequstes under noncontnuously backlogged users scenaros. Furthermore, the underlyng reasons and common desgn optons that lead them n achevng sub-optmal solutons and break the farness n realstc envronments are also revealed and dscussed. Motvated by the above observatons we ntroduce a generc Non-Work-Conservng Opportunstc Schedulng (NWCOS) framework, whch can be seamlessly ntegrated wth varous exstng schedulng polces, and asserts users os requrements satsfacton, whle stll schedulng them n an opportunstc way even n the case where the assumpton of nfnte backlogs s removed. Ths s accomplshed by decouplng the operaton of the onlne tunng mechansm that controls users os from the operaton of users selecton procedure that controls ther actual transmsson n an opportunstc schedulng polcy. The rest of the paper s organzed as follows. In secton II, the system model and some background nformaton wth respect to the operaton of basc opportunstc schedulers are presented. Secton III, dscusses the basc reasons that lead these schedulng schemes to unsatsfactory behavor under noncontnuously backlogged users whle n secton IV, the operaton of the proposed non-work-conservng opportunstc schedulng framework s descrbed. Fnally, n secton V, the effcacy of the proposed approach n assertng user s os requrements whle stll achevng hgh system performance s demonstrated va modelng and smulaton. II. SYSTEM MODEL & BACKGROUND INFORMATION We consder a sngle cell tme-slotted CDMA wreless system accessed by a statc populaton of N non-contnuously backlogged actve users. A tme slot s a fxed nterval of tme and could consst of one or several packets. Users channel condtons, whch are affected by shadow fadng and fast fadng, are consdered to be fxed wthn the duraton of a tme

2 slot. In each tme slot t the base staton, whch s assumed to have perfect knowledge of users nstantaneous channel condtons, transmts wth maxmum power P max to only one user from the set S of N actve users, n accordance to a specfc schedulng polcy (.e. * ( t) = t where S ). Moreover, let us denote as R( t) = ( R, ( t),..., R, N( t)) the users transmsson rate vector under polcy at tme slot t. Furthermore, due to ther dverse servce demands as well as ther varyng channel condtons, actve users are dstngushed wth respect to ther queues amount of data n two tmevaryng complementary sets, a set of nstantaneously backlogged users and a set of users wthout data to transmt denoted as S B (t) and S E (t), respectvely. Each moble user s assocated wth a proper utlty functon U (t) whch represents hs degree of satsfacton wth respect to the level of performance that he would experence f he s served at tme slot t. Followng the approach of [7], a user s utlty s a general functon of hs nstantaneous channel condtons, n terms of nstantaneous sgnal to nose rato (SNR) ρ (t), and s assumed to be non-negatve and bounded. Intutvely, a user s utlty s also a functon of hs nstant transmsson rate R, (t). In the rest of ths secton, we outlne the operaton of two fundamental representatve opportunstc schedulng polces. A. Temporal Farness Schedulnng Scheme () Temporal farness scheduler ams at the maxmzaton of the total expected system performance whle assertng a mnmum amount of tme slots that an actve user wll have access at the system s resources wth respect to pre-assgned weghts φ S. The correspondng optmzaton problem can be defned as follows: max E U t I = s.. t Pr( () t = ) φ S (2) ( ) () t () S where I () t = denotes the ndcator functon wth value f user s selected to receve servce a tme slot t and 0 otherwse. Satsfyng nequalty φ S asserts feasblty. The optmal soluton to the above optmzaton problem can be expressed as [7]: { } () t = argmax U () t + w () t (3) * SB () t ( () = φ ) w ( t+ ) = w ( t) a( t) I S ( t) (4) t B where we can set a(t)=/t. Accordng to (3), a user s prorty of beng selected at tme slot t s not only affected by the temporal value of hs utlty functon but also by hs tme-varyng weght w () t. Users weghts reflect ther acheved servce performance nto the schedulng polcy, and hence converge at such optmal values through a stochastc approxmaton procedure that forces the scheduler to acheve users long-term access tme goals. Let us underlne that only users havng data to transmt partcpate at the comparson performed n each tme slot and thus update ther weghts, snce the polcy s optmal under nfnte backlogs. Moreover, when users are contnuously backlogged then SB () t S. B. Utltara Farness Schedulng Scheme() The goal of utltaran farness schedulng scheme s to maxmze the overall expected system performance whle assertng that each user receves at least a certan share of the entre resources, n terms of average system s performance, accordng to hs pre-assgned weght g. Therefore, the optmal schedulng problem can be stated as: max E U t I = ( ) () t (5) S s.. t E U() t I () () t = ge U t I () t = S (6) S where nequalty g S declares feasblty. Moreover, the optmal schedulng polcy can be wrtten as [8], [0]: { } ( t) = arg max ( k+ w ( t)) U ( t) (7) * SB () t w ( t+ ) = w ( t) a( t) EU () ti g ( w ( t) mn ( w ( t))), S ( t) () t = B SB () t g E U() t I () t = S S where k g w ( t) SB =, mn( ( )) 0 (8) w t = and w () t = 0 f E U() t I () () t = ge U t I () t =. S Furthermore, n order to approxmate E U () t I () t = a S smooth factor can be used whch s updated as Ut ( + ) = β Ut ( ) + ( β ) U ( ti ) () t = where 0<β<. S Lettng U (t)=r, (t), long-term throughput farness can be acheved. III. OPPORTUNISTIC SCHEDULING UNDER NON- CONTINIOUSLY BACKLOGGED USERS SCENARIO As the system evolves, the stochastc nature of users channel condtons that result n tme-varyng servce performance necesstates the exstence of an on-lne updatng mechansm to reflect ther servce experence nto the schedulng polcy. Therefore, the examned opportunstc schedulng schemes share a common desgn prncple even f ther os goals dffer. Specfcally, both temporal farness and utltaran farness approaches use a stochastc approxmaton mechansm to ntroduce users channel condtons as well as ther up to date performance, nto the schedulng polcy (.e. as

3 n (4),(8)). Through the stochastc approxmaton users weghts are perodcally fne-tuned, pursung a set of optmal fxed values that balance ther average utlty performance and hence keep the farness, whle maxmzng overall system s performance. The proper convergence of users weghts, forced by parameter a(t), requres to be correctly updated at every tme slot. In a system wth contnuously backlogged users (.e. S () B t = S t ) the effcacy of all user s weghts convergence reles on ther partcpaton at every slot s comparson whch also permts ther mmedate weghts update, accordngly. Under moderate or lght system s or ndvdual user s load, or due to the potentally bursty nature of the traffc, users probabltes of experencng empty queues ncreases along wth ther overall probabltes of belongng to the set S E (t). Moreover, f we let a user S whch has no amount of data to transmt at tme slot t to be excluded from the comparson process, then hs weght s not properly tuned. The prevous schedulng opton leads to fault users weghts update, and as a result to the falure of the stochastc approxmaton procedure and the break of the farness. Unexpectedly, the better a user s channel condtons are, the hgher s hs probablty of experencng an empty queue and therefore beng un-favored. Fnally, let us underlne the fact that, as the system evolves the current nformaton used towards updatng users weghts, affects less ther fnal values due to factor a(t). Therefore, t s vtal that all users weghts are properly tuned, and thus echo ther average channel condtons n ntal tme slots, whether are served or not, and ndependently of ther nstantaneous backlog state. IV. A NON-WORK-CONSERVING OPPORTUNISTIC SCHEDULING FRAMEWORK In order to overcome the dentfed drawbacks emergng n the vew of non-contnuously backlogged users scenaro, we ntally propose a basc non-work-conservng framework - n the followng we refer to as B-NWCOS - whch can be ntegrated n a seamless way wth the under consderaton opportunstc schedulng schemes. B-NWCOS lets all actve users to partcpate n the weghted utltes comparson procedure at every tme slot whether havng data to transmt or not. Furthermore, f a user s relatvely better than others at tme slot t under polcy but he lucks of data to transmt (.e. * () t =, SE), then the base staton would reman dle wthn the duraton of that tme slot. However, user s weght w () t, as well as all actve users weghts are updated, as f user was normally accessng the system s resources at the consdered slot. Such desgn opton allows users weghts to be properly tuned and the stochastc approxmaton mechansm to meet ts goal, n terms of reflectng users average channel condtons and ther expected servce performance at the values of the weghts, thus leadng the schedulng polcy to accomplsh ts os demands. The followng algorthm llustrates the operaton of the proposed B-NWCOS framework under a general polcy, where { TP, }. For presentaton purposes, we denote as the nformaton used to update users weghts at each tme slot t, whch s further expressed as a functon of the ndcator I. () t = Algorthm B-NWCOS IN tme slot t, let * () t = where S. IF S () t then B I =, = I () t = = 0 S and () t R ( t) = (0,..., R ( t),...,0), ELSE IF S () t then I () t = () t = E = Iˆ =, I () t = = 0, S and R () 0 t =. The system remans dle. w ( t+ ) = w ( t) ( I ) S f { TP, } () t = Indcator I ˆ () t = s when user s relatvely better than others n tme slot t but he lucks of data to transmt. In order to satsfy non-contnuously backlogged users os performance demands, B-NWCOS keeps the base staton dle when the maxmum prorty user has no backlogs, and thus system s scarce rado resources are not fully utlzed. To overcome the problem of wastng the avalable resources, we modfy B-NWCOS framework n a way that maxmzes system s utlzaton. Under the enhanced framework, referred to as E-NWCOS, when the relatvely best user (as selected by polcy ) has no data to transmt the scheduler permts the allocaton of system s resources to the one wth the hgher prorty among those belongng to the set of actve users wth data to transmt (.e. set S B (t)). Addtonally, both users weghts are updated n order to properly reflect the correspondng servce performance devatons. The proposed modfcaton s stll a non-work-conservng scheme from the perspectve of the nstantaneously hghest prorty user, but s work-conservng to the whole system, when S B t. The operaton of E-NWCOS under a general polcy s llustrated bellow. Algorthm E-NWCOS IN tme slot t, let * () t = where S, let * () t = k where k SB () t. IF S () t then B = k therefore, I = (), t = I () 0 t = = S and R ( t) = (0,..., R ( t),...,0), ELSE IF SE () t & SB then I = Iˆ =, I () = =, () t = () t = t k I 0,, () t = = k S, R() t = (0,..., R, k(),...,0) t. ELSE The system remans dle. w ( t+ ) = w ( t) ( I ) S f { TP, } () t =

4 V. NUMERICAL RESULTS In ths secton, the operaton of the proposed B-NWCOS and E-NWCOS frameworks over temporal farness and utltaran farness schemes s evaluated va modelng and smulaton, under both contnuously backlogged and noncontnuously backlogged users scenaros. In order to better llustrate the performance effcacy of the proposed schemes, we assume lnear relatonshp between users utltes and ther correspondng transmsson rates (.e. U (t)=r, (t) S ). Hence, all schedulers am at system s throughput maxmzaton. Throughout our study we consder a sngle cell tme-slotted CDMA system. The duraton of a slot s assumed to be.67 msec and the smulaton lasts for slots. The total number of actve users n the system s N=20, and we consder two types of users wth respect to ther average channel condtons, namely good users, users to 0, and bad users, users to 20, wth average SNR ρ G = 4 (6dB) and ρ B = 2 (3dB), respectvely. To consder the mpact of users channel condton varatons on the system s performance, we model ther channels through an 8-state Markov Raylegh fadng channel model [3]. Moreover, the nstantaneous transmsson rate of a user s determned from the nstantaneous SNR (db) value accordng to Table as used n the CDMA xev-do system [7]. TABLE I. DATA RATE (Kbps) AS FUNTCION OF SINR (db) SNR Rate (Kbs) SNR Rate (Kbs) Fgure. On Average Good to Bad Users' Weghts Rato CB_T F NCB_T F 7 B-NWCOS_T F 20 2 E-NWCOS_ Users access-tme percentage under polcy CB_ NCB_T F B-NWCOS_T F E-NWCOS_ Schedulng Schemes Actve users are assumed to submt fle transfer requests accordng to a Posson process wth rate λ S and average fle sze F (F =480Kbps S ). In order to represent both nfnte and fnte backlogs throughout our experments we consder two dfferent user rates of submttng fle transfer requests, as follows: λ = 2 fles/sec or λ = 0.2 fles/sec S, respectvely. Therefore, for every schedulng polcy { TP, } the system performance s demonstrated under four schedulng scenaros. The frst depcts scheduler s performance under contnuously backlogged users case (λ = 2 fles/sec, referred as CB_), the second under noncontnuously backlogged users case (λ = 0.2 fles/sec, NCB_), whle the thrd and the fourth scenaros concern ts correspondng performance under fnte backlogs over the two versons of our proposed framework, namely B-NWCOS_ and E-NWCOS_, respectvely. A. Assertng Temporal Farness () os Crtera For demonstraton purposes, the provsonng of long-term access-tme farness among all actve users was consdered under scheme (that s Pr( ( t) = ) = N S ). Fg. llustrates all users percentage of tme at whch they had access at system s resources wthn the duraton of the smulaton. Each radus n the fgure represents an actve user (.e. user =, 2,..., 20), whle the value of ts radus length Fgure 2. Good to bad user s weghts rato under polcy Total System's Throughput (Kbps) CB_ NCB_ B-NWCOS_ E-NWCOS_ Schedulng Schemes Fgure 3. Total average system s throughput under polcy determnes user s correspondng access tme percentage. Under nfnte backlogs (CB_, grey lne), all users access tme percentages are almost the same (.e. approxmately 5%) under algorthm, whch confrms ts ablty of achevng users desrable long-term os goals. On the other hand, under non-contnuously backlogged users scenaro (NCB_, black lnes), where actve users percentage of experencng empty queue s 9.5% of the total smulaton tme on average, fals to provde farness among them. The results ndcate that the

5 nner reason for such an unsatsfactory behavor s users weghts fault values. Therefore, Fg.2 demonstrates the average weghts rato of good to bad user s after convergng to ther fnal values, under all schedulng scenaros. The optmal weghts rato that effcently reflects nto the schedulng polcy good and bad users channel condtons, can be determned by the one acheved under CB_ scenaro. Moreover, we can observe that the correspondng average users weghts rato s much smaller than the optmal acheved under NCB_; therefore good users are hghly un-favored n terms of tme slots allocaton compared to bad users as s llustrated n Fg. (black lne). Under the proposed B-NWCOS and E-NWCOS frameworks access tme farness among actve users s accomplshed under fnte backlogs, as the cycle-shape lnes n Fg. confrm. Moreover, the correct functon of the stochastc approxmaton procedure that leads to proper users weghts convergence, s verfed by the resultant good to bad users weghts ratos values whch are very close to the one acheved under n CB_ scenaro, as presented n Fg.2 (two last columns). Fnally, the effcent utlzaton of system s rado resources under E-NWCOS s shown n Fg.3 (last column compared to others) where system s total average throughput s demonstrated. Let us underlne, that even when the system s load s low (.e. users ncomng fles rato s 0.2 fles/sec) whch leads to empty queues effects, t s stll suffcent to mantan the system fully occuped. Moreover, under E-NWCOS_ framework system s slot utlzaton approxmates 00%, n contradcton to the 9% slot utlzaton acheved under B-NWCOS_ and therefore, system s correspondng throughput performance approxmates the one acheved under nfnte backlogs case, whle stll assertng farness. B. Assertng Utltaran Farness () os Crtera In the followng, we study the system s performance under utltaran farness scheme when long-term throughput farness os requrements among all actve users are set (.e. g = and g = N S ). Fg.4 shows all users S achevable average transmsson rates consderng nfnte backlogs (CB_, gray lne) and fnte backlogs (NCB_ black lnes) under the basc schedulng scheme as well as over B-NWCOS_ and E-NWCOS_ frameworks. Moreover, Fg.5 depcts the average weghts rato of good to bad users after convergence. When algorthm operates under non-contnuously backlogged users scenaro fals to provde long-term performance farness by over-provsonng bad users whle restrctng the allocaton of system s resources to good users, as t s ndcated by the correspondng devatons on ther acheved average throughput (Fg. 4, black lne) and confrmed by the value of ther weghts rato (Fg.5, NCB_ column). On the other hand, over B-NWCOS framework accomplshes ts os goal (Fg.4, trangle marks), whle under E-NWCOS framework acheves to further mprove both the overall system and ndvdual user performance by approxmately 8% (Fg.4, rhombus marks) CB_ NCB_ B-NWCOS_ E-NWCOS_ Fgure 4. Users average throughput under polcy On Average Good to Bad Users' Weghts Rato CB NCB_ B-NWCOS_ E-NWCOS_T F Schedulng Schemes Fgure 5. Good to bad user s weghts rato under polcy It should be emphaszed that E-NWCOS framework acheves to utlze the dle system s tme slots occurred under B- NWCOS, (.e. slot utlzaton under B-NWCOS_ s 85%), whle stll satsfyng the users os prerequstes snce ther correspondng weghts that control the farness stll converge at ther proper values. Fnally, t should be noted that the effectveness and effcency of the proposed framework has also been studed under Proportonal Far [4] and Mnmum Performance guaranty [8] schedulng schemes, and smlar observatons have been made. However the correspondng analyss and results are omtted here due to the space lmtatons. VI. CONCLUDING REMARKS In ths paper, we address the problem of effcent resource allocaton n CDMA wreless networks. The common assumpton of nfnte backlogged users s removed n ths work and an extensve analyss of system s behavor, n terms of overall performance as well as the ablty to gratfy users ndvdual os requrements s performed. Our study and correspondng results obtaned under two fundamental opportunstc schedulng polces ndcate nsuffcent system s performance when consderng fnte backlogs and thus, the

6 nner reasons for ths behavor are dentfed and dscussed. Therefore, a non-work-conservng opportunstc schedulng framework, seamlessly ntegrated and n lne wth all consdered scheduler s operaton s devsed, that leads to users os prerequstes fulfllment whle mantanng ther opportunstc schedulng character even under noncontnuously backlogged users scenaro. Moreover, through smulaton and expermentaton, the advantages of the proposed framework are revealed whle the revsed polces effcency n supportng users os requrements under both nfnte and fnte backlogs are llustrated. Throughout our analyss we consder fnte users backlogs whle stll assumng statc users populaton. The system performance evaluaton under tme varyng users populaton along wth the approprate users farness crtera re-defnton requred n such case s a problem of a great mportance towards desgnng schedulng polces that profcently operate under realstc scenaros. REFERENCES [] S. Lu, V. Bharghavan, and R. Srkant, Far schedulng n wreless packet networks, IEEE/ACM Trans. Netw., vol. 7, no. 4, pp , Aug [2] P. Bender, P. Black, M. Grob, R. Padovan, N. Sndhushyana, and S. Vterb, CDMA/HDR: a bandwdth effcent hgh speed wreless data servce for nomadc users, IEEE Commun. Mag., vol. 38, no. 7, pp.70-77, Jul [3] M. Andrews, L. an, and A. Stolyar, "Optmal utlty based mult-user throughput allocaton subect to throughput constrants," n Proc. IEEE INFOCOM, vol. 4, pp , March [4] A. Jalal, R. Padovan, R. Panka,"Data throughput of CDMA-HDR a hgh effcency-hgh data rate personal communcaton wreless system," n Proc. IEEE VTC 2000-Sprng, vol. 3, pp , [5] F. Berggren and R. Jantt, "Asymptotcally far transmsson schedulng over fadng channels," IEEE Trans. on Wreless Commun., vol. 3, no., pp , Jan [6] Y. Lu, S. Gruhl, and E. Knghtly, "WCF: An Opportunstc Wreless Scheduler wth Statstcal Farness Bounds," IEEE Trans. Wreless Commun., vol. 2 no. 5, Sept [7] X. Lu, E. Chong, and N. Shroff, Opportunstc Transmsson Schedulng Wth Resource-Sharng Constrants n Wreless Networks, IEEE J. Sel. Areas n Commun, vol. 9, no.0, pp , Oct [8] X. Lu, E. Chong, and N. Shroff, A framework for opportunstc schedulng n wreless networks, Computer Networks, vol. 4, pp , March [9] J.-W. Lee, R. R. Mazumdar, and N. B. Shroff, Opportunstc Power Schedulng for Dynamc Mult-server Wreless Systems, IEEE/ACM Trans. Netw., vol.5, no.6, pp , June [0] C. L, S. Papavasslou, Far Channel-Adaptve Rate Schedulng n Wreless Networks Supportng Mult-Rate Multmeda Servces, IEEE J. Sel. Areas n Commun, vol. 2, no.0, pp , Dec [] S. Borst, User-level performance of channel-aware schedulng algorthms n wreless data networks. IEEE/ACM Trans. Netw. Vol.3 no.3, p.p , June [2] N. Ahmed, M. Khoastepour, A. Sabharwal, B. Aazhang, Fnte Backlog Effects on Downlnk Schedulng, IASTED Communcatons, Internet and Informaton Technology Conference, pp , Scottsdale, AZ, Nov [3] H. Wang and N. Moayer, Fnte-state Markov channel a useful model for rado communcaton channels, IEEE Trans. Vehc. Tech., vol. 44, pp. 63 7, March 995.