Dynamic Power Management in a Mobile Multimedia System with Guaranteed Quality-of-Service

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1 Dynmc Power Mngement n Moble Multmed System wth Gurnteed Qulty-of-Servce Abstrct In ths pper we ddress the problem of dynmc power mngement n dstrbuted multmed system wth requred qulty of servce (QoS). Usng generlzed stochstc Petr net model where the non-exponentl nter-rrvl tme dstrbuton of the ncomng requests s cptured by stge method, we provde detled model of the power-mnged multmed system under generl QoS constrnts. Bsed on ths mthemtcl model, the power-optml polcy s obtned by solvng lner progrmmng problem. We compre the new problem formulton nd soluton technque to prevous dynmc power mngement technques tht cn only optmze power under dely constrnts nd demonstrte tht these other technques yeld polces wth hgher power dsspton by over-constrnng the dely trget n n ttempt to ndrectly stsfy the QoS constrnts. In contrst, our new method correctly formultes the power mngement problem under QoS constrnts nd obtns the optml soluton. 1 INTRODUCTION Wth the rpd progress n semconductor technology, the chp densty nd operton frequency hve ncresed, mkng the power consumpton n bttery-operted portble devces mjor concern. Hgh power consumpton reduces the bttery servce lfe. The gol of low-power desgn [1]-[4] for btterypowered devces s to extend the bttery servce lfe whle meetng performnce requrements. Dynmc power mngement (DPM) [5] whch refers to the selectve shut-off or slow-down of system components tht re dle or underutlzed hs proven to be prtculrly effectve technque for reducng power dsspton n such systems. A smple nd wdely used technque s the tme-out polcy [5], whch turns on the component when t s to be used nd turns off the component when t hs not been used for some pre-specfed length of tme. Srvstv et l. [6] proposed predctve power mngement strtegy, whch uses regresson equton bsed on the prevous on nd off tmes of the component to estmte the next turn-on tme. In [7], Hwng nd Wu hve ntroduced more complex predctve shutdown strtegy tht hs better performnce. However, these heurstc technques cnnot hndle components wth more thn two ( ON nd OFF ) power modes; they cnnot hndle complex system behvors, nd they cnnot gurntee optmlty. As frst shown n [8], power-mnged system cn be modeled s dscrete-tme Mrkov decson process (DTMDP) by combnng the stochstc models of ech component. Once the model nd ts prmeters re determned, n optml power mngement polcy for chevng the best power-dely trde-off n the system cn be generted. In [9], the uthors extend [8] by modelng the power-mnged system usng contnuous-tme Mrkov decson process (CTMDP). Further reserch results cn be found n [10]-[13]. In stutons where complex system behvors, such s concurrency, synchronzton, mutul excluson nd conflct, re present, the modelng technques n [8]-[10] become ndequte becuse they re effectve only when constructng stochstc models of smple systems consstng of non-nterctng components. In [14], technque bsed on controllble generlzed stochstc Petr nets wth cost (GSPN) s proposed tht s powerful enough to compctly model power-mnged system wth complex behvorl chrcterstcs. It s ndeed eser for the system desgner to mnully specfy the GSPN model thn to provde CTMDP model. Gven the GSPN model, t s then strghtforwrd to utomtclly construct n equvlent (but much lrger) CTMDP model. The polcy optmzton lgorthms n [8]-[10] 1

2 cn thereby be ppled to clculte the mnmum-power polcy for the power-mnged system wth dely constrnts. Mny Internet pplctons such s web browsng, eml nd fle trnsfer re not tme-crtcl. Therefore, the Internet Protocol (IP) nd rchtecture re desgned to provde best effort qulty of servce. There s no gurntee bout when the dt wll rrve or how quckly t wll be servced. However, ths pproch s not sutble for new breed of Internet pplctons, ncludng udo nd vdeo stremng, whch demnd hgh bndwdth nd low ltency for exmple when used n two-wy communcton scenro such s net conferencng nd net telephony. The noton of gurnteed qulty of servce (QoS) comes wth the emergence of such dstrbuted multmed systems. QoS represents the set of those quntttve nd qulttve chrcterstcs of dstrbuted multmed system necessry to cheve the requred functonlty of n pplcton [15]. Three prmeters wdely used to quntttvely cpture the noton of QoS n dstrbuted multmed systems [15]. These prmeters re: 1. Dely (D): The tme between the moment dt unt s receved (nput) nd the moment t s sent (output). 2. Jtter (J): The vrton of the delys experenced by dfferent dt unts n the sme nput strem. In mthemtcl formulton, J cn be defned s the vrnce of the dely or the stndrd devton of the dely. 3. Loss rte (L): The frcton of dt unts lost durng trnsport. In ths pper, we propose frmework of Power nd QoS (PQ) mngement (PQM) of portble multmed system clents. The PQ mnger performs both power mngement nd QoS mngement. The multmed (MM) clent s modeled s controllble GSPN wth cost (e.g., power, dely, jtter nd loss rte). Gven the constrnts on dely, jtter nd loss rte, the optml PQ mngement polcy for mnmum power consumpton cn be obtned by solvng lner progrmmng (LP) problem. Compred to prevous reserch work on power mngement nd multmed systems, our work hs the followng nnovtons: 1. Ths s the frst work to consder power nd QoS mngement n dstrbuted MM system. 2. We present new system model of n MM clent. Ths new model ccurtely cptures the dfferent behvors of the MM nd norml pplctons runnng on the MM clent. 3. The proposed optmzton soluton consders not only power dsspton nd dely, but lso jtter nd loss rte. We mnged to formulte ths problem lner progrm by mkng pproprte trnsformtons on the jtter nd loss rte constrnts. Ths remnder of the pper s orgnzed s follows. Secton 2 gves the bckground on GSPN nd MM systems. Secton 3 presents the system modelng technques for the PQ-mnged MM clent. Secton 4 ntroduces the polcy optmzton method. Sectons 5 nd 6 gve the expermentl results nd conclusons. 2 Bckground 2.1 GSPN Prmtves A GSPN conssts of four prmtve objects: plces, ctvtes, nput gtes nd output gtes. Fgure1 shows n exmple of GSPN model. 2

3 O 1 P 2 T 3 I 1 P 1 T 1 T 2 Fgure 1 An exmple GSPN model. Plces: Crcles n Fgure 1 represent plces. Ech plce my contn zero or more tokens, whch represent the mrkng of the plce. The set of ll plce mrkngs represents the mrkng of the system, M. M lso represents the stte of the system. Only the number of tokens n plce mtters. In Fgure 1, the system mrkng cn be wrtten s {P 1 +P 2 }, whch mens tht there re one token n P 1 nd one n P 2. The menng of the mrkng of plce s rbtrry. For exmple, the number of tokens n plce could represent the number of requests wtng servce n one pplcton nd request wth certn prorty level n nother pplcton. Ths flexblty n the menng of mrkng ncreses the expressveness of the GSPN for modelng wde vrety of dynmcl systems. Actvtes: Actvtes represent ctons tht tke some mount of tme to complete. There re two types of ctvtes: stochstc tmed wth n exponentl dstrbuton nd nstntneous. Hllow ovls n Fgure 1 represent tmed ctvtes. Tmed ctvtes hve durtons tht mpct the performnce of the modeled system. In GSPN, the durton of n ctvty s lwys n exponentl dstrbuton whose men vlue represents the verge durton of tht ctvty. The nverse of the men vlue s clled the trnston rte of tht ctvty. The trnston rte of n ctvty my be dfferent dependng on system mrkngs. Instntneous ctvtes represent ctons tht re completed n neglgble mount of tme compred to the other ctvtes n the system. Sold vertcl lnes n Fgure 1 represent nstntneous ctvtes. Cse probbltes, represented n Fgure 1 by smll crcles on the rght sde of n ctvty, model the uncertnty ssocted wth the completon of n ctvty. Ech cse stnds for possble outcome. Defnton A.1 A plce s clled vnshng plce f t s the only nput plce of n nstntneous ctvty; otherwse the plce s clled tngble plce. Input gte: Input gtes enble/dsble ctvtes nd defne the mrkng chnges tht wll occur when n ctvty s completed. In Fgure 1, trngles tht pont to the ctvty they control represent the nput gtes (.e., I 1 ). There exst rcs from the plces upon whch the nput gte depends (lso clled nput plces) to the bse of the trngle. Input gtes re nnotted wth n enblng predcte nd functon. The enblng predcte s Boolen functon tht controls whether the connected ctvty s enbled or not. It cn be ny functon of the mrkngs of the nput plces. The functon defnes the mrkng chnges to the nput plces tht wll occur when the ctvty s completed. If plce s drectly connected to n ctvty such s P 2 nd T 3 n Fgure 1, ths s the sme s n nput gte wth predcte tht enbles the ctvty f there s t lest one token n the nput plce nd functon tht decrements the mrkng of the nput plce. Output gte: Smlr to nput gtes, output gtes defne the mrkng chnges tht wll occur when n ctvty s completed. The dfference s tht output gtes re ssocted wth cse. In Fgure 1, trngles whose bse s connected to n ctvty or cse represent output gtes (.e., O 1 ). The trngles pont to rcs tht connect to the plces ffected by the mrkng chnges. Output gtes re defned only wth functon. The functon defnes the mrkng chnges tht wll occur when the ctvty s completed. If n ctvty s drectly connected to plce, ths s the sme s n output gte wth functon tht ncrements the mrkng of the plce. P 3 T 4 3

4 For nottonl convenence, we wll use the followng notton: plce nmes strt wth P, ctvty nmes strt wth T, nput gte nmes strt wth I, nd output gte nmes strt wth O. 2.2 Executng GSPN GSPN executon refers to the enblng of ctvtes, completon of ctvtes, nd token movement (.e., chnges of system mrkng). Actvty enblng: An ctvty s enbled t certn system mrkng M when the enblng predctes of ll the nput gtes connected to t re true nd there s t lest one token n ech plce tht s drectly connected to t. In Fgure 1, ctvtes T 2 nd T 3 re enbled n system mrkng M={P 1 +P 2 } becuse for ech of them, there s only one nput plce tht contns one token. Actvty T 4 s not enbled n M becuse there s no token n P 3. The enblng predcte of I 1 decdes the enblng of T 1. Actvty completon: An nstntneous ctvty s completed mmedtely fter t s enbled. A tmed ctvty s completed f t s enbled for ts durton tme. Every tme tmed ctvty s enbled, the durton tme s obtned by rndom smple of the exponentl dstrbuton ssocted wth ths ctvty. When tmed ctvty s enbled but not yet completed, the system mrkng my be chnged by the completon of nother ctvty. If the ctvty hs not enbled the new system mrkng, the completon of tht ctvty wll not hppen, nd ll nformton relted to ts prevous enblng wll be dsregrded n the future. Mrkng chnge: Chnge of system mrkng s only evluted when there s n ctvty completon. When n ctvty s completed, one of ts cses (notce tht there my be only one cse for the ctvty) s chosen bsed on the pre-defned cse probblty. Then the followng steps re tken: ll of the drectly connected nput plces hve ther mrkngs (.e., number of tokens) decremented; the nput plces connected through nput gtes chnge ther mrkngs ccordng to the nput gte functons; ll of the plces drectly connected to the selected cse hve ther mrkngs ncremented; the plces connected through output gtes chnge ther mrkngs ccordng to the output gte functons. Defnton: Therechblty set of GSPN from n ntl mrkng M 0, denoted s RS(M 0 ), s the set of ll possble system mrkngs tht cn be cheved s result of sequence of ctvty completons. 2.3 Controllble GSPN wth cost Defnton: A GSPN wth cost s GSPN model wth two types of cost: mpulse cost ssocte wth mrkng trnstons nd rte cost ssocted wth system mrkngs. Impulse cost occurs when the GSPN mkes trnston from one mrkng to nother. Rte cost s the cost per unt tme when the GSPN stys n certn mrkng. Defnton: A controllble GSPN s GSPN where ll or prt of the cse probbltes of ctvtes cn be controlled by externl commnds. 2.4 Dstrbuted Multmed System Fgure 2 shows smplfed vew of dstrbuted MM system wth QoS mngement [17]. The system conssts of three components: n MM server wth dtbse of multmed objects nd dtbse of QoS nformton, the trnsport system tht mnly conssts of network of communcton chnnels, routers nd swtches, nd the MM clent, whch cn be portble personl computer, pocket PC or nother moble multmed devces. 4

5 MM Server MM Clent MM Dtbse QoS Dtbse MM dt MM dt Resources: CPU, memory, etc. Locl QoS mnger Trnsport System Locl QoS mnger Resources: Network Locl QoS mnger Globl QoS mnger Fgure 2 QoS mnged, dstrbuted multmed system. Ech component hs ts own locl QoS mnger. The globl QoS mnger controls the QoS negotton nd renegotton procedure mong the components. The procedure cn be brefly descrbed s follows. The locl QoS mnger reports the vlble locl resources to the QoS mnger. The globl mnger computes the QoS tht ech component needs to delver bsed on the vlble resources nd sends the requrement to the locl mnger. The locl mnger uses ts vlble resources to enforce the locl QoS requrement nd keeps on montorng the locl QoS. If there s locl QoS volton, the locl mnger sends request to the globl mnger, who wll respond to the request by ether re-lloctng the locl QoS requrement mong the dfferent components or negottng wth the user to dopt degrded globl QoS. Becuse low power desgn s trgeted t electronc components wth lmted power source, we focus on PQ mngement for the MM clent. The ssumpton beng tht the MM clent hs lrge (or nfnte) power source. In ths context, the locl QoS mnger of the MM clent n Fgure 2 wll be referred to s the locl PQ mnger. 3 Modelng the PQ-Mnged Clent Only components relted to the PQ mngement problem re shown n ths block dgrm. Although the GSPN formlsm cn model complex systems wth multple, nterctng servce provders, n ths pper, we use smple system wth sngle servce provder. Ths s becuse the focus of ths pper s on power nd QoS mngement, not on complex system modelng. As n exmple of usng GSPN to model complex power-mnged system wth multple nterctng servce provders, plese refer to [14]. Fgure 3 gves smplfed block dgrm of our PQ-mnged clent. 5

6 MM Buffer MM Strem Servce Provder Locl pplcton Request Queue Schedulng Control Power Mode Control QoS constrnts Locl PQ Mnger Fgure 3 Block dgrm of PQ-mnged MM clent. As shown n Fgure 3, the MM clent conssts of servce provder (SP) tht my be CPU, DSP or n rry of hrd dsks. The SP provdes servces (e.g., computng, processng, communcton, dt retrevl nd storge) for servce requests comng from pplctons runnng on the MM clent. We dvde the pplctons nto two ctegores: the MM pplctons nd the other pplctons. We seprte the MM pplctons becuse of ther dstngushng fetures s explned below: 1. The dstrbuton of request nter-rrvl tmes s non-exponentl, whch requres specl tretment durng the modelng process; 2. The QoS requrement s only pplcble to the MM pplcton; 3. The prorty of the servce requests from the MM pplcton s usully hgher thn those from other pplctons. MM pplcton SR SQ TS SP Other pplcton SR SQ Fgure 4 Top-level GSPN model for the MM clent. Fgure 4 shows the top level GSPN model for the MM clent. It s dvded nto three mjor prts: 1. MM servce requester (SR) nd servce queue (SQ): The MM SR s used to model the sttstcl behvor of the nput MM strem, nd the MM SQ s used to model the behvor of the MM buffer. The GSPN model s shown n Fgure Locl SR nd SQ: These re used to model the behvor of request generton nd s buffer for other pplctons. The GSPN model s shown n Fgure 6. 6

7 3. The tsk scheduler (TS) nd servce provder (SP): The TS s used to represent the mechnsm for selectng wht request (s to be processed next. The SP s used to model the power/performnce chrcterstcs of the servce provder. We ssume tht the unt nter-rrvl tme for the MM strem cn be ny dstrbuton. Snce the exponentl dstrbuton s requred by the GSPN modelng technque, we use the stge method [14] to pproxmte the MM strem dstrbuton by usng three-stge SR model. The MM SR conssts of plces P MM, P MMb, P MM1 nd P MM2 nd ctvtes µ 1, µ 2, µ 3, α 1 (β 1 =1-α 1 ), α 2 (β 2 =1-α 2 ) connected s shown n Fgure 5. Gven dstrbuton of the nput nter-rrvl tme of the MM strem, we cn obtn the vlues of µ 1, µ 2, µ 3, α 1 nd α 2 by curve fttng. P MMBuf represents the MM SQ. Stge_3 Stge_2 Stge_1 P MM1 µ 2 β 2 P MMb P MM2 µ 3 µ 1 β 1 P MM α 2 P MMBuf α 1 G MM :{Mrk(P MM1 )+Mrk(P MM2 )=0&Mrk(P MMBuf )<MMbuffersze Fgure 5 GSPN model for the MM SR nd SQ. To emphsze the dfference between MM pplctons nd other pplctons (whch we wll denote s norml pplctons from now on), we ssume tht the request nter-rrvl tme for the norml pplctons s exponentlly dstrbuted. The GSPN model for these pplctons s shown n Fgure 6. T norm P SQ G norm :{Mrk(P SQ ) < SQ cpcty Fgure 6 GSPN model for the locl SR nd SQ. Fgure 7 shows the GSPN model of tsk scheduler nd smple SP, whch hs two dfferent power modes: ctve (denoted s ) nd sleepng (denoted s s ). When the SP s n ctve mode, t cn be processng MM pplctons, whch s denoted by mode (, MM), or processng norml pplctons, whch s denoted by mode (, norm). 7

8 T 2s T s2 P 2s T decson () T decson (s) P decson (s) P s2 P decson () P MMBuf P dle (,MM) T strt P work (,MM) T process (,MM) T redecson P dle (s) T vnsh P dle(,norm) P chngng P work (,norm) P SQ T process(,norm) Fgure 7 GSPN model for the SP nd TS. To llustrte how the GSPN n Fgure 7 works, ssume tht the ntl stte of the system s ctve-dle nd wtng for MM pplcton nd the MM buffer s empty. When token rrves t P MMBuf, whch mens tht n MM request hs rrved, the token n plce P dle (,MM) moves to plce P work (,MM), whch represents the stte of the SP when t s ctve nd servcng n MM request. The durton t of ths servce s decded by the tmed ctvty T process (,MM). After tme t, thetokennp work (,MM) moves to plce P decson (), whch represents the stte of SP when t s ctve nd cceptng commnd from the PQ mnger. After very short tme, the token n P decson () movestop 2s, P dle (,MM) or P dle (,norm) wth probblty 1, 2 nd In the controllble GSPN, these probbltes re the controllble cse probbltes of ctvty T decson (), whch re to be optmzed. The rest of the system works n smlr wy. The mechnsm of tsk schedulng s modeled by the mmedte ctvty T decson (). The PQ mnger reds the sttes of ll system components nd sends commnds to control the tsk schedulng nd the SP stte trnston. The GSPN model of the MM clent s then utomtclly trnsformed nto contnuous-tme Mrkov decson process (CTMDP), bsed on whch the optml PQ mngement polcy s solved. 4 Polcy optmzton The nput to our polcy optmzton lgorthm s the requred QoS, whch cn be represented by (D, J, L). In rel pplctons, D (dely) my be specfed n tme unts; J (jtter) my then be specfed n tme unts or squre of tme unts; L (loss rte) my be specfed n rel numbers. However, we do not use these constrnts drectly n our polcy optmzton process. Insted, we convert D nd J from the tme domn to n nteger domn relted to the number of requests wtng n the queue. Next we remove the L constrnt by buffer sze estmton bsed on the relton between L, D nd J. Fnlly we formulte lner progrmmng problem tht cn be solved for optml PQ mngement polcy, whch cheves mnmum power consumpton under the QoS constrnts. 4.1 Trnsformng the D nd J Constrnts We use the verge number of wtng requests n the queue to represent the verge request dely (D) nd the vrnce of the number of wtng requests n the queue to represent the request dely vrnce (J). We use the probblty tht the queue s full to represent the loss rte (L). The rtonle behnd these 8

9 representtons s Theorem 4.1, whch shows the reltonshp between the request dely nd the number of wtng requests n the queue. Theorem In PQ-mnged system, f the request loss rte s smll enough, then D = Q λ, whered s the verge request dely, Q s the verge number of wtng requests n the queue nd λ s the verge ncomng request speed. Furthermore, durng ny tme perod of length T, E T (d) =E T (q) T / X, where E T (d) nd E T (q) denote the verge request dely nd verge number of wtng requests n the queue durng tme T,ndX s the number of ncomng requests n ths system durng tme perod T. Proof: (omtted to sve spce). 4.2 Estmtng the Buffer Sze For the MM clent, lloctng too much memory for the MM buffer s unnecessry nd wsteful. However, we hve to mke sure tht the MM buffer s bg enough so tht the SP does not need to provde unnecessrly fst servce to cheve the gven loss rte constrnt, whch would n turn result n undesred power consumpton. Tble 1 shows smple exmple. Assume PQ-mnged MM clent nd QoS constrnt of (D, J, L) = (1.5, 0.9, 0.02). In the frst cse, we set the sze of the MM buffer to 4 nd solve the optml polcy under the constrnts of D nd J. In the second cse, we set the sze of the MM buffer to 6 nd solve the optml polcy under the constrnts of the sme D nd J. Then we smulte both polces usng UltrSAN nd obtn the smulted vlue of D, J, L nd power consumpton (P). Tble 1 Power comprson for systems wth dfferent buffer sze Buffer sze D J L Power From the bove tble we cn see tht the system wth buffer sze of 4 consumes 40% more power thn the system wth buffer sze of 6; however, n the former cse, the D nd J vlues re smller thn the gven constrnts. The reson for ths s tht, wth nsuffcent buffer spce, the SP hs to spend extr power to provde fster servce speed. Ths experment lso shows tht D, J, L nd the sze of the MM buffer re not mutully ndependent. Gven three of them, we cn estmte the fourth one. More precsely, ther reltonshp cn be formulted by equtons (4.1) to (4.4), where p s the probblty tht there re requests wtng n the queue (MM buffer) nd m nd v re the men vlue nd the vrnce of the wtng requests n the queue. n =1 n =0 n = 0 p = 2 m (4.1) ( m) p v (4.2) n = p = 1 (4.3) 0 p 1, =1,, n. (4.4) We re nterested n fndng the mnmum buffer sze n tht s needed to vod unnecessry power consumpton due to over constrnts on D nd J. Ths problem cn be solved s follows: Mn. n Subject to: n =1 p = D, (4.5) 9

10 n =0 n = 0 2 ( m) p J, (4.6) n = p = 1, (4.7) p n L, (4.8) 0 p 1, =1,, n (4.9) We cnnot solve bove problem exctly. However, fter some smplfcton, we fnd tht f n stsfes nequlty reltons (4.10)-(4.12), there wll be set of p, whch stsfes functon (4.5) (4.9). (n -2) 2 L J + D 2 4 D + 3, (4.10) (n +1) (n 2) L m 2, (4.11) (n 2) (n 1) L D 2 3 D +2+J (4.12) Therefore, we obtn n upper bound on the mnmum requred buffer sze: N up = Mx(n 1, n 2, n 3 ) (4.13) where n 1, n 2, n 3 re the solutons of equtons (4.10), (4.11) nd (4.12). If the llocted buffer sze s lrger thn N up, there wll not be extr power wste due to over-constrnng D nd J. Note tht ths buffer sze estmton s ndependent of the ncomng-dt rte nd the system servce rte, becuse we ssume tht the gven QoS constrnt (D, J, L) cn lwys be stsfed by the optml polcy. We hve performed experments to verfy our buffer estmton method, we set J = 1.5, L = 5%. By usng dfferent D vlues between 1 nd 3.5, we estmte the mnmum buffer sze, N up, usng (4.13). Fgure 8 shows the comprson between the estmted vlue nd the rel vlue tht s obtned by smulton. The results show the correctness of our method N D Fgure 8 Comprson of rel vlue nd estmted upper bound. 4.3 Polcy optmzton by Lner Progrmmng rel vlue estmted vlue The PQ mngement problem s to fnd the optml polcy (set of stte-cton prs) such tht the verge system power dsspton s mnmzed subject to the performnce constrnts for the trdtonl pplcton nd the QoS constrnts for the MM pplcton. 10

11 Frst we gve the defnton of some vrbles. The reder my refer to [14] regrdng how to clculte some of the vrbles from gven CTMDP model. p j τ x : Probblty tht the next system stte s j f the system s currently n stte nd cton s tken. : Expected durton of the tme tht the system wll be n stte f cton s chosen n ths stte : Probblty tht the next stte of the system wll be nd cton wll be tken f rndom observton of the system s tken pow : System power consumpton n stte q_mmbuf : Number of unprocessed dt n MM buffer ene j : Energy needed for the system to swtch from stte to stte j A : Set of vlble ctons n stte Our LP problem s formulted s follows: LP1: Mn { x } subject to x x p = x ( pow τ + ene p ) (4.14) j τ = x 0 x 1 ll, j j j j j 0 S x q _ MMBuf τ < x 2 ( q _ MMBuf D) τ < J (4.15) Equton (4.15) gves the constrnt on jtter, whch s represented by the jtter of q_mmbuf. Note tht the left hnd sde of (4.15) does not gve the exct jtter of q_mmbuf, whch s: 2 x ( q _ MMBuf x q _ MMBuf τ ) τ (4.16) Equton (4.16) contns nonlner terms. For computtonl effcency, we opted to use n pproxmton of jtter so tht the resultng mthemtcl progrm remns lner. Proposton: For ny set of { x }, tht stsfes (4.15), the vlue of (4.16) s less thn J. Proof: To mnmze x q _ MMBuf m) x q MMBuf D ( τ, we know tht: m = _ τ. Therefore, m, (4.16) gves the smllest vlue. From the bove proposton we know tht for ny polcy, f t stsfes constrnt (4.15), then the rel jtter of q_mmbuf usng ths polcy s less thn constrnt J. Hence we cn use (4.15) nsted of (4.16). Fgure 9 shows n llustrton of q_mmbuf dstrbuton when the system s usng the PQ-optmzed polcy nd the PD-optmzed polcy (whch n prevous work, optmzes power only under dely constrnt). In ths exmple, we set the MM buffer sze to 8. The verge length of the MM buffer s the 11

12 sme for both polces. The power consumpton of the system usng the PD-optmzed polcy s 25% less thn tht of the system usng the PQ-optmzed polcy. However, the q_mmbuf jtter nd loss rte of the system usng the PD-optmzed polcy re 3X nd 1000X lrger thn those of the system usng the PQoptmzed polcy. In the expermentl results, we cn cheve the sme q_mmbuf jtter for the system usng PD-optmzed polcy by over-constrnng the verge dely nd therefore consumng more power q_mmbuf dstrbuton usng PQ-optmzed polcy q_mmbuf dstrbuton usng PDoptmzed polcy Fgure 9 Comprson of q_mmbuf dstrbuton. Notce tht n LP1, only the QoS constrnt for the MM pplcton ws ncluded. We cn esly dd the performnce constrnt (.e. dely) for the norml pplctons. 5 Expermentl Results Our trget system s smplfed model of clent system n dstrbuted MM system. System detls re s follows. The SR hs only request generton stte. The verge nter-rrvl tme of trdtonl request s 50ms. The SQ cpcty s 3. The verge nter-rrvl tme of the MM dt s 20ms. The SP hs two p_modes: hgh-power mode nd low-power mode. It tkes 0.2J energy to swtch from hgh-power mode to low-power mode nd 0.5J energy to swtch from low-power mode to hgh-power mode. To smplfy the model, we ssume tht the tme needed for swtchng s smll enough to be neglected. In both power modes, the SP cn process both the MM pplctons nd the norml pplctons, but wth dfferent power consumpton nd speed. There s lso nother scenro n whch the SP s not processng ny pplcton. In ths cse, the servce speed of SP s 0, nd only very smll mount of power s consumed. Therefore, n our trget system, there re three _modes: MM, norml nd dle. Tble 2 nd Tble 3 gve the SP power consumpton nd verge servce tme n ech combnton of p_mode nd _mode. Here, we ssume tht the hgh-power mode s desgned specfclly for MM pplcton. For exmple, n ths mode flotng-pont co-processor s used so tht the servce speed of the MM pplcton ncreses sgnfcntly. Tble 2 SP power (w) n ech (p_mode, _mode) MM Norml Idle Hgh power Low power

13 Tble 3 SP servce speed (ms) n ech (p_mode, _mode) MM Norml Idle Hgh power Low power Tble 4 Comprson between PQ-optmzed nd PD-optmzed polces QoS PD-optmzed PQ-optmzed P Constrnts Powe r D J Powe r D J (%) (1, 1, 0.1%) (1, 1.5, 0.1%) (3, 1, 0.1%) (3, 1.5, 0.1%) (5, 1, 0.1%) (5, 1.5, 0.1%) In our experment, becuse the norml pplcton s not tme crtcl, we set the performnce constrnt of norml pplcton smply s loss rte 5%. We use dfferent QoS constrnts (D, J, L) for the lner progrmmng problem. We solve LP1 to fnd the PQ-optmzed polcy. We use the procedure n [14] to fnd the PD-optmzed polcy under the gven D constrnt. If the resultng jtter nd loss rte cnnot meet the QoS constrnts, we decrese D nd reclculte the PD-optmzed polcy untl they meet the constrnts. The results re shown n Tble 4. From the bove results, we rech the followng conclusons: 1. Our method cn clculte the PQ-optmzed polcy for the MM clent for gven QoS constrnts by solvng the LP problem only once whle the prevous DPM method hs to obtn the PD-optmzed polcy for gven QoS constrnts by solvng the LP problem multple tmes. 2. Our method cn obtn the PQ-optmzed polcy tht mtches the gven QoS constrnts whle the prevous method cn only meet the QoS constrnts by over-constrnng the dely requrement, whch results n lrger power consumpton. 6 Conclusons We hve presented new modelng nd optmzton technque for Power nd QoS mngement n dstrbuted multmed systems. QoS n ths context refers to the combnton of the verge servce tme (dely), the servce tme vrton (jtter) nd the network loss rte. We model the power mnged multmed system wth gurnteed QoS s GSPN nd the PQ-optml polcy s obtned by solvng lner progrmmng problem. Becuse jtter nd loss rte re correlted prmeters, we could not nclude both of them nto the LP formulton drectly. Insted we removed the loss rte constrnt from the LP formulton by estmtng the mxmum sze of the queue tht stores the MM dt. Furthermore, the jtter constrnt s non-lner functon of the vrbles we wnted to optmze. Therefore t could not be drectly used n the LP formulton. We were ble to substtute the orgnl jtter constrnt wth nother lner constrnt, whch we mthemtclly proved to be correct. Prevous methods only consder the dely constrnt whle obtnng the PD-optmzed polcy. They cn only meet the jtter nd loss rte constrnts by over constrnng the dely. Compred to these methods, we show tht our PQM method cn cheve n verge of 12% more power svng. 13

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