Optimal Resource Sharing for Integration of Unicast and Multicast Data on TDM Radio Channels

Size: px

Start display at page:

Download "Optimal Resource Sharing for Integration of Unicast and Multicast Data on TDM Radio Channels"

Derick Cross
6 years ago
Views:

1 Optimal Rourc Sharing for Intgration of Unicat and Multicat Data on TDM Radio Channl Vladimir Vukadinović Laboratory for Communication Ntwork TH, Royal Intitut of Tchnology 0044 Stockholm, Swdn Gunnar arlon Laboratory for Communication Ntwork TH, Royal Intitut of Tchnology 0044 Stockholm, Swdn Abtract Futur intgration of multicat and unicat data on tim-lottd radio channl will rquir fficint rourc haring mchanim. Th mchanim nd to b optimizd to provid th bt poibl prformanc for th ur. In thi papr, w conidr th ca whr mmbr of a vido traming multicat group har th common rourc with unicat ur on a HSDPA-lik TDM channl. W dfin prformanc mtric and driv a ytm modl to tudy th ur prformanc for variou rourc allocation undr fairn contraint. Our rult how that th prformanc gain of rourc-optimal multicat could b ubtantial and hould b xploitd in practical chduling chm. yword-multicat, rourc haring, vido traming, MBMS, HSDPA I. INTRODUCTION Multicat may improv th rourc fficincy whn dlivring th am information to many ur. Mobil ntwork hav an inhrnt broadcating capability du to th natur of wirl mdia. Rcnt tandardization ffort, uch a Multimdia Broadcat and Multicat Srvic (MBMS), aim at upporting multicat in 3G cllular ntwork. Futur multimdia multicat application might rquir tight intgration of multicat and unicat to allow additional contnt to b dlivrd togthr with th multicat tram to individual mmbr of th multicat group. Th bundling of multicat with th xiting mobil rvic, uch a voic and data, will nabl a nw rvic to mrg - intractiv multicat. In th Evolvd Univral Trrtrial Radio Acc (E-UTRA), which i th focu of 3GPP Long Trm Evolution (LTE) projct, uch intgration will b prformd by multiplxing th MBMS and unicat data on a hard TDM channl []. Thi intgration rquir nw chduling algorithm that nabl rourc haring btwn multicat and unicat flow (in th ca of TDM, rourc ar tim-lot). Th rourc haring nd to b optimizd to provid th bt poibl prformanc for ur. Thi i th contxt for th work prntd hrin. Intgration of unicat and multicat data in wird ntwork ha bn prviouly addrd in th contxt of IP multicat. Th intgration ffort wr mainly focud on digning appropriat chduling and quuing algorithm for input quud [2], combind input and output quud [3], and combind input and crobar quud witch [4]. Th main objctiv of th algorithm i to maximiz th utilization of th witch, but om of thm alo aim at providing fair bandwidth haring btwn unicat and multicat flow, or to achiv crtain trad-off btwn th two objctiv. In [5], th author propo a nw chdulr to har bandwidth btwn unicat TCP flow and multicat flow in a TCPfrindly mannr. In [6], th author dfin a atifaction factor for ach flow, which dpnd on th numbr of ur that rciv th flow. Intgration objctiv i to maximiz th um of th atifaction factor of all flow. Thi work i cloly rlatd to what w ar trying to achiv in th wirl domain. At prnt, multimdia multicat in mobil radio ntwork i offrd via traming tchnology ovr point-to-point connction. Thr ar currntly no pcific tranport channl in 3G for dlivring multicat: th MBMS tandard rcommnd that xiting channl hould b r-ud to th xtnt poibl and with minimal modification. W aum a HSDPA channl a a man to dlivr multimdia multicat contnt. HSDPA i currntly ud for unicat rvic du to it point-to-point natur, but th rich fatur uch a adaptiv coding and modulation, fat chduling, and hybrid ARQ mak th HSDPA a good candidat for multicat. Enhancmnt to HSDPA to upport multicat hav bn th focu of th IST B- Bon projct [7], [8]. HSDPA achiv high rourc fficincy by multiplxing ur on a hard channl in a timlottd TDM, which facilitat concurrnt rvic and, thrfor, th futur intgration of multicat and unicat data. In th ca undr tudy, w aum that th HSDPA channl i hard by a vido tram, which i dlivrd to a multicat group, and a numbr of latic unicat flow. Our objctiv i to allocat th channl rourc in a way that maximiz th ovrall ur prformanc. Optimization i prformd undr th contraint that th rourc allocation hould b fair. Th rmindr of thi papr i organizd a follow: Th ytm modl i dcribd in Sction II. In Sction III w dfin rlvant prformanc maur. Th rourc optimization problm and th rult ar prntd in Sction IV. Finally, concluion ar givn in Sction V. II. SYSTEM MODEL In thi Sction w dcrib th radio rourc modl, traffic charactritic, and nod mobility.

2 A. Radio Rourc Modl W conidr a ingl circular cll with a ba tation at th cntr. W rtrict our analyi to th ingl cll bcau, rourc-wi, a handovr i conidrd imply a an incra or dcra of th numbr of cutomr in th cll. Th cll provid on downlink channl that i hard in tim among activ ur. Th ba tation offr a finit t of poibl tranmiion rat R = { Rk }, k, which i dfind by th combination of availabl modulation chm and rror corrction cod rat. Th ba tation monitor th channl quality of a mobil trminal and dcid on it achivabl rat bad on th maurd ignal-to-noi ratio γ. Th achivabl rat i lctd from R o that th block rror rat at th mobil trminal i blow crtain thrhold (0% in HSDPA). Th dcribd rat adaptation mchanim i known a adaptiv modulation and coding. Mobil trminal xprinc variabl channl condition and, hnc, variabl achivabl rat a a rult of propagation lo, hadowing and mall-cal fading. In thi papr, w aum that th channl condition dpnd on propagation lo only. Th mall-cal fading i not of particular intrt bcau th tim-cal on which it affct th achivabl rat i typically much mallr than th tim-cal of rourc chduling algorithm. W adopt a common fr-pac propagation lo modl, whr th ignal trngth dpnd on th ditanc btwn th ba tation and th mobil trminal a γ ( d)~ d β, whr β i th path lo xponnt (typically 2 < β < 4). Bad on th vctor of achivabl rat R and dcribd mapping btwn th ignal-to-noi ratio and ditanc from th ba tation, th cll ara can b dividd into concntric ring (Fig. ) o that th achivabl rat of a nod locatd in ring k with innr and outr diamtr d k- and d k, rpctivly, i R k. An xampl of mapping btwn achivabl rat and ignal-to noi ratio to th diamtr of th ring i givn by Tabl. Firt thr column ar obtaind from th HSDPA pcification [9], whil th rlativ ring diamtr in th fourth column of Tabl ar calculatd bad on th adoptd propagation modl: β dk γ k γ ( d)~ d = d γ / β for k =,...,, () whr th propagation lo xponnt β = 4. If th hadowing ffct wr conidrd, uch a impl mapping would not b poibl inc th communication rang would not b an idal circl. Th modl prntd in th following ction can b aily xtndd to includ om of th tandard hadowing modl, uch a th log-normal hadowing, but our analyi would not bnfit from uch a modl. B. Traffic Modl W aum that thr ar N ur in th cll. Each ur blong ithr to th traming or latic cla and may gnrat only on flow at a tim (not, howvr, that on mobil dvic may hot a numbr of logical ur ). All traming ur ar ubcribd to th am multicat group and rciv a vido tram ncodd at a contant rat R. Th vido tram i aumd to b pritnt (long-livd) and, thrfor, rvic dmand of traming ur ar infinit. Elatic unicat ur ar downloading fil of avrag iz σ. Onc th download i finihd, th latic ur go into a thinking pha of avrag duration ν, aftr which a nw download i initiatd. W dfin contllation of traming and latic ur a N = ( N,, N,2,..., N, ) and N = ( N,, N,2,..., N, ), whr N,k and N,k ar th numbr of traming and latic ur in ring k, rpctivly. Auming that th mobility of th ur i uch that th ur location ditribution i uniform, probability of contllation N i whr N p( N) = p p p N! N! N!,,2, N, N,2 N, 2, (2) TABLE I. MAPPING BETWEEN SIGNAL-TO-NOISE RATIOS Γ AND ACHIEVABLE RATES R IN HSDPA. Fig.. Cll ara i dividd into a t of concntric ring. Maximum achivabl rat for a nod in ring k i R k. k γ k (db) R k (kb/) d k /d ~ ~ ~ ~

3 p k d = 2 2 k dk 2 d i th probability of finding a ur in ring k. Analogou xprion can b writtn for th contllation of latic ur. Furthr, w aum that th ratio of multicat traming ur in th total population i α, and thrfor N = α and N = ( α ) N. Similarly to th ur contllation, contllation of traming and latic flow ar dnotd by n = ( n,, n,2,..., n, ) and n = ( n,, n,2,..., n, ). From th dcription of th adoptd traffic modl, it i obviou that n = N and n N inc om of th latic ur might b in th thinking pha. C. Nod Mobility Whn a nod mov in th cll, it rcivd data rat i modulatd by an indpndnt tochatic proc. Du to th xtrm difficulty of analyzing uch ytm, w rtrict our analyi to two limiting ca of ur mobility, fluid and quaitatic [0]. Fluid rgim aum that th nod mov vry quickly compard to th tim cal of th flow dynamic and, thrfor, thir achivabl rat avrag out ovr tim. Th achivabl rat of all ur in th fluid rgim ar th am and givn by 2 2 dk dk FL = [ ] = k k = 2 k k= k= d R E R p R R N. (3) A uitabl modl to dcrib rourc haring among activ flow in th fluid rgim i a procor haring quu. Th quai-tatic rgim aum that th nod mov vry lowly compard to th tim cal of th flow dynamic and, thrfor, thir achivabl rat rmain roughly contant for th rvic tim duration. Th achivabl rat of a ur in th quai-tatic rgim dpnd on it ditanc d from th ba tation A. Straming Ur Utility A traming ur utility i th prcptual vido ditortion and can b dcribd a an -curv []. Th hap of th curv dpnd on th proprti of th vido ncodr and th rat at which th vido tram i ncodd (R ). A function that w u to dcrib th traming ur utility i givn by r C R C U() r = and hown in Fig. 2. For th contnt tord at a mdia rvr, contant C and C 2 can b dtrmind offlin. In th ca of fin-granularity calabl coding, ditortion curv i mooth and can b aily fittd by (5). In th ca of layrd coding, ditortion curv i a tairca function with th numbr of tp qual to th numbr of layr in th vido tram. It can only b roughly approximatd by (5). Finally, non-calabl coding giv a impl tp function, which i obtaind for C2. Th avrag traming utility of a multicat group with contllation n i givn by: C2 C2 φ rk C R ( n,, φ) =, k C n k = U r n (5), (6) whr r i th tranmiion rat at th ba tation, r k i th achivd rat for a ur in ring k: r, r Rk rk =, 0, r > Rk and φ i th har of channl rourc (tim-lot) allocatd to th multicat group. Finally, th traming ur utility i obtaind by avraging (6) ovr all poibl contllation and R ( d) = R, if d < d d. (4) QS k k k Rourc haring among activ flow in th quai-tatic rgim can b modld a a multi-cla procor haring quu, whr th numbr of cutomr cla i qual to th numbr of ring in th cll (i.. to th numbr of poibl tranmiion rat). Sinc traming flow ar aumd to b pritnt (tim cal of th flow dynamic tnd to infinity), thir prformanc i analyzd in th fluid rgim only. Elatic flow hav finit iz dmand and, thrfor, thir prformanc hould b analyzd both in th fluid and quai-tatic rgim. III. USER UTILITIES AND OVERALL USER PERFORMANCE In thi ction, w dcrib th utiliti for multicat traming ur U and latic ur U, and dfin an ovrall prformanc maur, which w dnot a powr (Π). Fig. 2. Exampl of poibl traming utility function.

4 by lcting th optimal tranmiion rat at th ba tation U( φ) = max p( n) U( n, r, φ), (7) r { R, R2,..., R } n whr 0 U ( φ). B. Elatic Ur Utility Elatic ur aim at minimizing th tim ndd to download a fil. Thrfor, th utility of latic ur i throughput. In ordr to calculat th throughput of latic ur, w modl th cll a a clod quuing ntwork compod of on procor haring nod (PS) and on infinit rvr (IS) nod (Fig. 3). Activ latic ur ar rvd in th PS nod; thir rvic tim dpnd on whthr th ytm i in th fluid or quai-tatic rgim. Aftr thy finih rvic, thy ntr th IS nod, which modl th thinking tag; man rvic tim in th IS nod i ν. Th contllation in PS and IS nod ar n and N n, rpctivly. Thi quuing ntwork ha a pcial form to which th BCMP thorm appli [2], [3]. Th thorm tat that th tationary ditribution of th numbr of flow in th PS nod ha th following product form: p( n N ) = A( N ) h ( n ) h ( N n ), (8) PS IS whr A( N ) i a normalization contant and hps () and his () ar charactritic function of PS and IS quu, rpctivly. In th quai-tatic rgim, a ur blong to on of th cla bad on it location in th cll and, hnc, it achivabl data rat. Th man rvic tim of a cla-k ur in th PS nod i σ (( φ) Rk ), whr σ i th avrag fil iz, R k i th achivabl rat in ring k, and factor (-φ) i to account for th har of th channl rourc allocatd to th latic ur. Th man rvic tim in th IS nod i ν. Th charactritic function of multi-cla PS and IS nod ar givn by h h PS IS σ ( n) = n! k= nk,! ( φ) Rk ( Ν n) = ν ( N n )! k= k, k, nk, Nk, nk, A convnint proprty of BCMP ntwork i that th tationary ditribution p( n N ) do not dpnd on th rvic tim ditribution in th PS and IS nod. Hnc, ytm prformanc i innitiv to th fil iz and thinking tim ditribution. Thr ar a numbr of algorithm (convolution algorithm, man valu analyi (MVA), tc.) that can b ud to olv (8) and (9) and to obtain rlvant prformanc maur, uch a (9) th cla-k throughput Tk ( N, φ). W ud th Bard- Schwitzr approximation of th MVA algorithm to obtain th rult dcribd in Sction IV [4]. Onc th cla throughput ar known, w can calculat th ovrall throughput of latic ur by avraging th um of cla throughput ovr all poibl ur contllation: k k= T( φ) p( N ) T ( N, φ). (0) = N Finally, w dfin th latic ur utility a normalizd throughput pr ur: ( ) θ U φ = T ( φ ). () N Th normalization contant θ i introducd to nur that 0 U ( φ). Fig. 3. Th ytm can b modld a a clod quuing ntwork with on PS and on IS nod. In th fluid rgim, th dcribd quuing ntwork implifi to a ingl-cla BCMP ntwork: th man rvic tim in th PS nod i σ (( φ) RFL ), whr R FL i givn by (3). Rult can b obtaind a a pcial ca of th prviou. C. Ovrall Ur Prformanc W dfin an ovrall prformanc maur that w rfr to a powr : α α Π ( φ) = U ( φ) U ( φ), (2) whr 0 Π( φ). It i a wightd product of traming and latic utiliti and, thrfor, powr maximizing allocation opt φ i proportionally fair with rpct to th multicat/traming and unicat/latic cla. Hr w xplain th intuition bhind th powr a a prformanc maur. Lt g dnot th drivativ of a function g(φ) with rpct to φ. It i obviou that U > 0 and U < 0 : a w incra th har of channl rourc φ allocatd to th traming cla, th prformanc of traming

5 ur incra and th prformanc of latic ur dcra. Thrfor, w can think of α U U a a wightd rlativ gain in traming utility and ( α ) U U a a wightd rlativ gain in latic utility. At th point of maximal prformanc, th two gain mut b qual. Hnc, th optimality condition i givn by: U U α = ( α) (3) U U By finding th drivativ of th powr function dfind by (2), w can that th optimality condition (3) i atifid at th point of maximum powr: Π U U Π ' = 0 = α + ( α) = 0 Π U U (4) IV. OPTIMAL RESOURCE SHARING Our objctiv i to find an optimal tratgy for rourc haring btwn multicat (traming) and unicat (latic) ur that maximiz th powr Π(φ) ubjct to th following contraint: n φ + n n + n. (5) Th contraint nur that rourc haring i don in a fair mannr. W aum that a rourc allocation i fair if ach ur i allocatd at lat /N of channl rourc, whr N i th total numbr of ur multiplxd on th channl. Unlik Fig. 4. Powr Π(φ) for variou prcntag of multicat ur α in fluid (FL) and quai-tatic (QS) rgim. Fig. 5. Optimal rourc allocation φ for variou prcntag of multicat ur α. unicat ur, all mmbr of a multicat group acc th channl imultanouly and w hav crtain flxibility in allocating th xc rourc. A rourc-conrvativ tratgy would b to conidr th multicat group a bing (rourc-wi) a ingl ur. In that ca, fair har of rourc for th multicat group i givn by th lowr bound in (5). W may, howvr, argu that ach mmbr of th multicat group i ntitld to it own fair har of rourc. In that ca, fair har of rourc for th multicat group i givn by th uppr bound in (5) and it i th am a in th ca of multipl-unicat. In th rmaining part of thi Sction, w prnt om of th rult obtaind from th modl dcribd in Sction II and III. Our aumption ar: Th total numbr of ur in th cll i N = 50. Multicat ur ar fd with a vido tram ncodd at R = 64 kb/. Paramtr of th traming utility function (5): C = C 2 = 6. Unicat ur ar downloading fil of avrag iz σ = 50 kb. Th avrag thinking tim btwn two concutiv download i ν = 5. Powr curv for variou prcntag of traming ur in th cll α ar hown in Fig. 4. Th powr i plottd only for allocation φ that atify th contraint (5). W may notic fl q that Π ( φ) > Π ( φ), which i conitnt with prviou finding that quai-tatic and fluid rgim provid rpctivly conrvativ and optimitic timat of ur prformanc [0]. Powr curv ar non-mooth and oftn do not hav pronouncd maxima. Th non-moothn i du to th dicrtn of th t of tranmiion rat upportd by th ba tation. It rult in tp-lik chang in th optimal rourc allocation (Fig. 5), which man that th allocation rmain contant for rlativly wid intrval of α. Thrfor,

6 givn that th prcntag of multicat ur do not vary much during a multicat ion, which i oftn th ca, frqunt rallocation of rourc ar not ndd. Rourc rquirmnt of th multipl-unicat and rourc-conrvativ multicat, which ar givn by th bound in (5), ar alo indicatd in th figur. Innitivity to ur mobility in th cll would b a vry dirabl fatur from th viwpoint of a practical chduling algorithm that implmnt th rourc haring. Although Fig. 5 rval ignificant dicrpanci btwn optimal allocation in fluid and quai-tatic rgim, thy would not ncarily rult in ignificantly diffrnt prformanc. Th raon i that powr function Π(φ) oftn do not hav a pronouncd maximum. In th fluid rgim, th ytm modl rduc to a ingl-cla quuing ntwork and, thrfor, optimal allocation fl φ can b aily obtaind. It would b convnint if, rgardl of ur mobility lvl, th am allocation could b maintaind without a ignificant lo in ur prformanc. In Tabl 2, w valuat th lo for th quai-tatic rgim: Π Δ= q fl q q ( φ ) Π ( φ ). (6) q q Π ( φ ) Th lo i blow % rgardl of th proportion of multicat ur in th cll. Thi rult indicat that it might not b ncary to adjut th rourc allocation in rpon to varying mobility in th cll inc any rourc allocation fl q φ φ φ i ufficintly clo to optimal. A. Optimal powr for variou proportion of multicat ur Optimal powr for variou prcntag of multicat ur in th cll i hown in Fig. 6 (top). Rult for th rourcconrvativ multicat and th multipl-unicat ar alo indicatd. For th mall prcntag of multicat ur in th cll (α < 0 %), th ovrall ur prformanc dpnd largly on th prformanc of unicat ur and all thr tratgi convrg to th am powr lvl. Howvr, a th prcntag of multicat ur in th cll α incra, ur prformanc bcom incraingly dpndant on th way th channl rourc ar hard. A xpctd, vn though it conum th largt amount of rourc, multipl-unicat prform th TABLE II. USER PERFORMANCE IN THE QUASI-STATIC REGIME FOR φ =φ q AND φ =φ fl. Λ Π q (φ q ) Π q (φ fl ) diff(%) Fig. 6. Powr (top) and powr gain (bottom) for variou α. wort: th powr furthr dcra with α a th numbr of rdundant tranmiion of th am contnt incra. Two multicat chm, rourc-optimal and rourcconrvativ, xploit th inhrnt multicat capability of th radio channl: th har of rourc allocatd to th multicat group φ incra lowr than th iz of th multicat group, a it can b n from Fig. 5. Th amount of rourc lft for unicat ur dcra in total, but incra pr ur and th ovrall ur prformanc improv. Th powr-maximizing tratgy outprform th rourc-conrvativ a it can b n from Fig. 6 (top). Thi illutrat th diadvantag of a tratgy that only aim at conrving th rourc intad of allocating thm in a way that maximiz th ur prformanc. Thi i oftn ovrn inc conrvation of rourc ha alway bn th prvailing motiv for multicat dlivry. To illutrat th advantag of th rourc-optimal ovr rourc-conrvativ multicat, w dfin powr gain for th fluid and quai-tatic rgim a G q / fl q / fl Π φopt q / fl φrc ( ( α )) ( α ) =, (7) Π ( ( α ))

7 whr φ = + n ( α ) q / fl rc ( α ) q / fl. A hown in Fig. 6 (bottom), th prformanc gain can b ignificant: up to 65 % in th quai-tatic and up to 25 % in th fluid rgim. B. Srvic guarant On of th major problm whn dlivring multimdia multicat ovr common channl i to provid rvic guarant. A larg amount of rourc nd to b ddicatd to th multicat rvic if full cll covrag i rquird, which might cau th tarvation of unicat flow. In th following cnario w tudy rourc haring with oft rvic guarant for multicat ur. W aim at maximizing th ovrall ur prformanc Π with an additional contraint that th traming utility of ach multicat ur hould b abov 0.5 with 90% probability. Hnc, intad of th fairn contraint (5), w introduc th contraint Pr{ 0.5} 0.9 U > >. In Fig. 7, w compar th rourc rquirmnt of multicat ur φ (top) and ovrall prformanc Π (bottom), with and without rvic guarant. For mall α, a larg har of channl rourc ha to b allocatd to atify th dmand of a rlativly mall numbr of multicat ur, which dtriorat th prformanc for th majority of th ur. Th ytm powr dcra compard to th ytm without guarant. Whil thi rult wa xpctd, it i intrting to notic that th guarant that w introduc in thi cnario do not improv th ovrall ytm prformanc, rgardl of th proportion of multicat ur in th cll. A th numbr of multicat ur incra, th guarant tnd to b atifid anyway bcau th objctiv (powr) function (2) nur that th prformanc of th majority i maximizd. V. CONCLUSIONS Futur multimdia rvic will rquir tight intgration of multicat and unicat data. In th volvd UMTS, TDM channl ar propod for multiplxing of multicat and unicat data tranmiion. In thi papr, w dcrib a modl that can b ud to tudy rourc haring in uch channl. W dfin prformanc mtric for traming multicat and latic unicat flow and u th modl to optimiz th rourc allocation in trm of th ovrall ur prformanc ( powr ) in a HSDPA cll. Th rourc-optimal multicat i contratd to two othr common tratgi for dlivring multicat data: multiplunicat and rourc-conrvativ multicat. Our rult how that th prformanc gain of rourc-optimal multicat can b ubtantial, which may prompt th dvlopmnt of intllignt chduling algorithm for intgration of multicat and unicat data. Our rult alo indicat that optimal rourc haring might b innitiv to ur mobility in th cll. Finally, w valuatd th cot of oft rvic guarant in trm of ytm powr. Fig. 7. Optimal rourc allocation φ (top) and powr Π (bottom) with and without rvic guarant for multicat ur. REFERENCES [] Ericon, MBMS for E-UTRA, R , 3GPP TSG-RAN Working Group. [2] W. Zhu and M. Song, Intgration of Unicat and Multicat Schduling in Input-Quud Packt Switch, Computr Ntwork, vol. 50, no. 5, pp , April [3] C. Minknbrg, Intgrating Unicat and Multicat Traffic Schduling in a Combind Input- and Output-Quud Packt-Switching Sytm, Proc. Int. Conf. Computr Communication and Ntwork (ICCCN), pp , La Vga, NV, Oct [4] L. Mhamdi and S. Vailiadi, Intgrating Uni- and Multicat Schduling in Buffrd Crobar Switch, Proc. IEEE Workhop on High Prformanc Switching and Routing (HPSR), pp , Poznan, Poland, Jun [5] F. Filali and W. Dabbou, Fair Bandwidth Sharing Btwn Unicat and Multicat Flow in Bt-Effort Ntwork, Computr Communication, vol. 27, no. 4, pp , March [6] G. Miao and Z. Niu, Bandwidth Managmnt for Mixd Unicat and Multicat Multimdia Flow with Prcption Bad QoS Diffrntiation, Proc. IEEE Int. Conf. Communication (ICC), vol. 2, pp , Itanbul, Turky, Jun 2006.

8 [7] IST B-Bon Projct: (Acd: Oct. 2, 2006). [8] A. Corria, HSDPA Dlivring MBMS Vido Straming, Proc. Int. Symp. Wirl Pronal Multimdia Communication (WPMC), vol., pp , Aalborg, Dnmark, Sp [9] Motorola and Nokia, Rvid HSDPA CQI Propoal, R , 3GPP TSG-RAN Working Group 4. [0] T. Bonald, S.C. Bort, and A. Proutir, How Mobility Impact th Flow-Lvl Prformanc of Wirl Data Sytm, Proc. IEEE Infocom, vol. 3, pp , Hong ong, March [] V. Rodriguz, D.J. Goodman, and Y. Wang, Optimal Coding Rat and Powr Allocation for th Straming of Scalably Encodd Vido Ovr a Wirl Link, Proc. IEEE Int. Conf. Acoutic, Spch, and Signal Procing (ICASSP), vol.5, pp , Montral, May [2] F. Baktt..M. Chandy, R.R. Muntz and F.G. Palacio, Opn, Clod and Mixd Ntwork with Diffrnt Cla of Cutomr, Journal of th ACM, vol. 22, no. 2, pp , Apr [3] S. Liu and J. Virtamo, Prformanc Analyi of Wirl Data Sytm with a Finit Population of Mobil Ur, Proc. 9th Intrnational Tltraffic Congr (ITC), pp , Bijing, Aug [4] P. Schwitzr. Approximat analyi of multicla clod ntwork of quu, Proc. Int. Conf. Stochatic Control and Optimization, pp , Amtrdam, 979.

Chapter 10 Time-Domain Analysis and Design of Control Systems

Chapter 10 Time-Domain Analysis and Design of Control Systems ME 43 Sytm Dynamic & Control Sction 0-5: Stady Stat Error and Sytm Typ Chaptr 0 Tim-Domain Analyi and Dign of Control Sytm 0.5 STEADY STATE ERRORS AND SYSTEM TYPES A. Bazoun Stady-tat rror contitut an