EWFQ: Enhanced Weghted Fa Queung Scheme ensung accuate nte-packets spacng Mudass TUFAIL and Benad COUSIN IRISA, Campus de Beauleu 35042 Rennes Cedex, Fance. fmtufal, bcousng@sa.f tel: (33) 2 99 84 71 00 fax: (33) 2 99 84 71 71 1 Intoducton Thee s a vaety of dstbuted applcatons (e.g. audo and vdeo confeencng, multmeda nfomaton eteval, ftp, telnet, WWW, etc.) wth a wde ange of Qualty of Sevce (QoS) equements. A netwok meets these equements pmaly by appopately schedulng ts esouces. All netwok swtches eque an ntellgent schedulng algothm to select a packet fom a desevng queue, among those pesent at an output pot, at each packet slot tme, whee a slot s a tme nteval long enough to tansmt one packet. The Genealzed Pocesso Shang (GP S) scheme s a geneal fom of the head-of-lne pocesso shang sevce dscplnes. Dung any tme nteval, GP S scheme seves, n paallel, all the non-empty queues 1 n popoton to the sevce shaes of the coespondng sessons. Obvously, GP S scheme cannot be appled to the actual packet-based taffc scenaos, whee only one sesson can eceve sevce at a tme, and whee an ente packet, must be seved befoe anothe packet s pcked up fo the sevce. GP S scheme s a theoetcal model so thee ae many popostons of queung dscplnes whch emulate GP S scheme. The pogess of schemes emulatng GP S scheme can be pesented n the followng ode: A queue scheme s expected to povde guaanteed bounded delay sevces. It has been demonstated n [?,?] that employng GP S seves at the swtches, end-to-end delay can be guaanteed to a sesson povded ts taffc s leaky bucket constaned at the souce. Paekh [?] poposed Packet-by-Packet Genealzed Pocesso Shang (PGPS) whch emulates the GP S seve and s dentcal to the weghted veson of Fa Queung (WFQ). He also establshed seveal mpotant elatonshps between a GP S scheme and ts coespondng packet W F Q scheme: 1. A packet wll fnsh sevce n a WFQ scheme late than n the coespondng GP S scheme by no moe than the tansmsson tme of one maxmum sze packet. It measues how fas WFQ scheme fom GP S one n tems of delay. 2. As fa as the amount of wok, a sesson gets, s concened, a WFQscheme does not fall behnd a coespondng GP S scheme by moe than one maxmum sze packet. Once the schemes pogessed well n satsfyng the end-to-end delay bounds to sessons then the feedback based netwoks expected them to povde a homogeneous and unfom sevce tend to sessons. In most feedback based congeston contol algothms, souce peodcally samples the netwok state usng feedback fom the eceve o fom the netwok, and tes to detect the symptoms of netwok congeston. In case of congeston, the souce usually lowes the tansmsson ate to allevate the congeston. WFQ scheme povdes each sesson wth the guaanteed ate but sesson packets ae seved back to back befoe packets on othe sessons can be tansmtted. Ths yelds the ON(bust) and OFF(slence) zones n a sesson packet tansmsson patten. Obvously, wth moe sessons, the length of peods between bustng and slence can be lage. Such oscllaton s undesable fo feedback based congeston contol 1 Thee s a sepaate FIFO queue fo each sesson. It s possble to have sngle queue fo all sessons wth smla QoS equements. 1
a k d k s b k s W s (t 1 t 2 ) Q s ( ) L k L max B s ( ) ^ aval tme of the k th packet on sesson depatue tme of the k th packet on sesson n the s scheme sevce stat tme of the k th packet on sesson n the s scheme the amount of wok eceved by the sesson dung the tme nteval [t 1 t 2 ] n the s scheme the queue sze of the sesson at tme n the s scheme sze of the k th packet on sesson n numbe of bts the maxmum packet sze n numbe of bts the set of backlogged sessons at the tme n the s scheme lnk speed guaanteed ate fo sesson any notaton wth^as ovehead epesents ts vtual value Table 1: Notatons used n ths pape algothms as the feedback eceved by the souce entely depends upon an nteval of netwok obsevaton whch s hghly pobable to dffen the vey next nteval. Jon C.R. Benett and Hu Zhang poposed Wost-case Fa Weghted Fa Queung [?] n whch the seve does not seve the sesson packets back to back athe the sevce to a sesson s dstbuted packet by packet dung the seve cycle. The sesson, stll, gets ts guaanteed ate and the wok eceved by the sesson does not fall behnd that n coespondng GP S scheme by moe than one maxmum packet sze. Fo each sesson thee ae no moe ON/OFF tansmsson zones and the feedback eceved by the souce s moe elable whch was nteval dependent n pevous methods of GP S scheme emulaton. Contbuton: The technology pogess eques netwoks to seve the packets, belongng to an applcaton whethe uncast o multcast, wth an assuance of QoS equed. Ths QoS s not assued by esevng the souces statcally to the applcaton athe the applcaton s thoughput s thottled up and down by feedback messages fom the netwok. Moe pecse s the feedback nfomaton, bette the netwok can assue QoS to an applcaton. Moeove multcast applcatons ae moe demandng fo a pecse feedback nfomaton as t affects the esouce allocaton to the packets (whch ultmately changes the allocaton to packets of othe applcatons) on all the eplcated multcast banches. In ode to have pecse feedback nfomaton, t s necessay to mantan the nte-packets spacng close to that n GP S scheme. WF 2 Q scheme elmnates the ON/OFF peods fo a sesson but does not have the capacty fo mantanng a unfom nte-packet spacng. Addtonally the wok consevng popety of WF 2 Q scheme depends upon the status of backlogged 2 sessons (unde/ove-utlzaton of guaanteed esouces). We move ahead n the context of feedback based congeston/taffc contolled netwoks and popose a packet schedulng scheme named as Enhanced Weghted Fa Queung (EWFQ) whch has the same complexty as that of WF 2 Q scheme but an addtonal capacty of mantanng nte-packets spacng close to that n GP S scheme wth lesse numbe of opeatons. The wok consevng popety of EWFQs ndependent of sesson s status. 2 Enhanced Weghted Fa Queung scheme In Enhanced Weghted Fa Queung (EWFQ) scheme, we develop a sesson ode and a sevce ode fo all the sessons, whethe backlogged o not, whch ae guaanteed a non-zeo bandwdth shae. The sesson odes epesented by n whch ndcates the poston of sesson, n the deceasng ode of sevce shaes, among all sessons whch ae supposed to shae the avalable bandwdth. It means that among N sessons, sesson attbuted wth sesson ode n = 1 has the lagest sevce shae whee as one wth n = N has the mnmum sevce shae. Algothm 2 A sesson s backlogged f t has one o moe packets n the queue at the gven nstant. 2
^p 1 4 p 1 4 t=0 t=0 vtual (a) Packet avals eal (c) Real packets n WF 2 Q 0 1 2 3 4 5 6 7 8 9 10 (tme) 0 1 2 3 4 5 6 7 8 9 10 (tme) (b) Vtual packets n GP S (d) Real packets n EWFQ Fgue 1: An example of EWFQ 1. Calculate ^b k GP S fo all vtual packets as: ^b k GP S = ( k;1 ^b GP S + ^L k 0 : k =0 : k>0 2. Ceatng sesson ode: Aange sessons n deceasng ode of the sevce shae and attbute them n such that f k n =1gf k n =2g:::f k n = N g. 3. Stamp each vtual packet as: stamp k = ^b k GP S +(n ; 1) (1) 4. Ceatng sevce ode: Aange packets ae n nceasng ode of the stamp values. If two o moe packets have the same stamp value, aange them n deceasng ode of the espectve sesson s n value. The sevce odes the ode wth whch the sessons ae seved by EWFQ seve. In ode to constuct the sevce ode, we consde a vtually assumed scenao of packets aval (fg.??,a) n whch and all the sessons, n competton, have enough packets, efeed as vtual packets heeafte, n the espectve queues (egadless of the numbe of packets actually pesent n the queue) so that the sesson gets ts guaanteed shae n one seve cycle wth all the vtual packets fully tansmtted. All the vtual packets have unt sze.e. ^L k =1 whch means that thee wll be as many packet slots n the sevce ode as total numbe of vtual packets n all the sessons. Fo allocatng the slots of the sevce ode among the sessons, we stat wth the sesson attbuted wth n =1(.e. havng the lagest bandwdth shae) and allocate ts vtual packet ^p k a slot n the sevce ode bounded by: k;1 ^b EW F Q k;1 ^L + ^b 1 GP S ^b 1 EW F Q < ^L 1 ; 2 < ^b k EW F Q + 1 < ^b k;1 EW F Q k;1 ^L + + 2 (2) fo k>1 (3) The above elatons specfy the bounds fo EWFQ seve to look fo the appopate slot fo ^p k among the unallocated ones n the sevce ode, thus educe the sotng computatons. The unallocated slot whch s the most closest to ^b k GP S and falls 3
wthn the bounds specfed by (??,??) s fnally allocated to ^p k. Afte havng allocated slots to all the vtual packets of sesson, the next sesson attbuted wth n =2s pcked up and ts vtual packets ae allocated slots n the sevce oden smla fashon. The pocess s epeated tll the sesson wth n = N s allocated slots n the sevce ode. The sevce ode has the followng chaactestcs: It s ndependent of the fact that one o moe sessons s slent at the gven nstant. The sevce ode once calculated stays vald unless thee s a change n any sesson s bandwdth shae o the set of sessons shang the bandwdth s alteed. The sevce odes ndependent of the nstant at whch t s beng consulted. It epeats tself afte evey seve cycle. The sevce ode avods schedulng all the packets pesent at the gven nstant (WFQand WF 2 Q schemes do so) athet helps the schedule to select the packet fo sevce among those pesent at the gven nstant. At t =0, a pontes placed on the fst slot of the sevce ode. The slot epesented by the pontendcates the sesson whose packet (pesent at the head of sesson s queue) s to be seved at t =0. The pontes, then, moved fowad to the next slot n the sevce ode whch, when consulted at the next packet slot tme, ndcates the sesson to be seved. If at a gven nstant the sesson ndcated by the ponte of the sevce odes not backlogged then pontes moved fowad tll t ponts to a slot of the sevce ode epesentng a backlogged sesson at the gven nstant. Example: Consde the example shown n fgue??. Thee ae sx sessons shang the bandwdth of lnk seve and the espectve shae values ae =1 2 2 1 2 2. The seve speed s =10. Fst the sessons ae aanged n the deceasng ode of the espectve sevce shae.e. S 2 S 3 S 5 S 6 S 1 S 4, whch makes the espectve sesson ode n values as: 1 2 3 4 5 6. Followng the EWFQpncples, we get the sevce ode as shown n fg(??). The EWFQ seve consults 0 1 2 3 4 5 6 7 8 9 10 Ponte at =0 Fgue 2: The sevce ode. the sevce ode at evey packet slot tme and tansmts the packet pesent at the head of queue of the sesson ndcated by the sevce ode. Refe to fg(??,d) fo the packets pogess n EWFQ scheme. Note that the scheme WF 2 Q (efe to fg(??,c)) s no moe wok consevng n ths case. 3 Concluson We popose EWFQscheme whch, n addton to povdng the guaanteed bounded delay sevce, has the followng mpotant popetes. Inte-packets spacng: We defne the nte-packets spacng fo a sesson, seved by seve of scheme S, as the dffeence between the sevce stat tmes of two consecutve packets of the sesson. Fo a packet p k, the nte-packet spacng, dst k S, s gven as: dst k S = bk S ; bk;1 S (4) In GP S scheme, b k GP S = max(ak dk;1 ). GP S bk GP S = dk;1 fo packet GP S pk of a sesson whch s backlogged at the gven nstant, then dst k fo GP S pk s gven as: dst k GP S = bk GP S ; bk;1 GP S = Lk;1 (5) 4
We defne a paamete Delta k, fo a packet S pk, whch measues that how much the nte-packet spacng n the scheme S dffe fom that n GP S system. It s calculated as: Delta k S = dstk S ; dstk GP S (6) Delta k can be postve o negatve. Lesses the absolute S Deltak S value, bette the scheme S emulates the GP S scheme. Inte-packet spacng n WFQsystem: In a WFQsystem, when the seve chooses the next packet fo tansmsson at tme, t selects. among all the packets that ae backlogged at, the fst packet that would complete sevce n the coespondng GP S system. In othe wods packets ae seved n the nceasng ode of espectve d k values. A GP S packet can leave much ealen a WFQ system than n a GP S system. The ealest possble sevce stat tme of a packet p k n WFQsystem s gven by bk GP S ; ((1 ; ) ; Lk ) whee as a packet should get stat of sevce no late than b k GP S + Lk ; Lk. Thus we have: max k (dst k W F Q ) = (bk GP S + Lk = Lk;1 + Lk ; Lk ) ; (bk;1 + 1 (Lk;1 GP S ; ((1 ; Lk;1 ) ; )) (7) ; L k ; (1 ; ) (8) max k (Delta k W F Q ) = Lk + 1 (Lk;1 ; L k ; (1 ; ) (9) Inte-packet spacng n WF 2 Q system: In WF 2 Q system, when the seves eady to tansmt the next packet at tme, the seve only consdes the set of packets that have stated (and possbly fnshed) ecevng sevce n the coespondng GP S system at tme and pcks up the packet among them that would complete sevce fst n the coespondng GP S system. So a packet p k may be seved as late as at bk GP S + Lk ; Lk and as ealy as at bk GP S and stll espects the WF 2 Q scheme pncples. Thus we have: max k (dst k W F 2 Q ) = (bk GP S + Lk = L k ( 1 ; 1 max k (Delta k W F 2 Q ) = (Lk ( 1 ; 1 )+Lk;1 ; Lk ) ; bk;1 GP S (10) Lk;1 )+ (11) ) ; Lk;1 (12) = L k ( 1 ; 1 ) (13) Wheeas fo EWFQ scheme, the same value fo packet p k s bounded as: max k (Delta k EW F Q )= 1 (L k ; Lk;1 )+ 1 (L max ; L k ) (14) The esults (??,??) shows that EWFQscheme mantans a bettente-packets spacng than the WF 2 Q scheme. Complexty: In the EWFQ scheme, we constuct a sesson ode attbutng n to each sesson whch epesents ts poston n the deceasng ode of the sevce shaes of sessons. The nheted complexty of sotng a lst of N sessons s O(log N). The calculatons, equed to geneate the sevce ode, do not eque any lst sotng and each slot n the sevce odes attbuted to a sesson ndependently hence O(1) be the complexty of ths opeaton. The EWFQ scheme has, globally, a complexty of O(log N) whch s the same as n WF 2 Q. Snce the pobablty of change n the sevce ode at each packet aval s vey low, so most of the tme the EWFQ scheme does not need to constuct the sevce ode at each packet slot thus educng the numbe of opeatons consdeably. Note that n WF 2 Q, smla opeatons ae caed out at each packet slot. 5
Wok consevng: The wok consevng popety of EWFQ scheme s ndependent of the status of backlogged sessons whch s also manfested by the WFQ scheme [?]. The WF 2 Q scheme does not hold ths popety when thee s a backlogged sesson whch s unde-utlzng the esouces guaanteed to t. The EWFQscheme ensues an accuate nte-packets spacng (.e. close to that n GP S scheme) whch helps the netwok to geneate pecse feedback nfomaton fo souce. Moeove, sesson s packets get dstbuted moe accuately wth no addtonal cost, athe the EWFQ scheme s hghly pobable to pefom lesse numbe of opeatons than othe schemes (e.g. WFQ, WF 2 Q) whle ensung bette packet s schedulng. Refeences [1] Jon C.R. Bennett, Hu Zhang. WF 2 Q: Wost-case Fa Weghted Fa Queung. IEEE INFOCOM, Ma-96, pp. 120-128. [2] S. Jamaloddn Golestan. A Self-Clocked Fa Queung Scheme fo Boadband Applcatons. IEEE INFOCOM 94, Toonto, CA, June 1994, pp. 636-646. [3] A. Paekh. A Genealzed Pocesso Shang Appoach to Flow Contol n Integated Sevces Netwoks. Ph.D. dsseton, Massachusetts Insttute of Technology, Febuay 1992. [4] S. Keshav. A contol-theoetc appoach to flow contol. Poceedngs of ACM SIGCOMM 91, pages 3-15, Zuch, Swtzeland, Septembe 1991. [5] L. Klenock. Queung Systems, Vol 1, Compute Applcatons. Wley, 1974. [6] S. Shenke. Makng geed wok n netwoks: A game theoetcal analyss of swtch sevce dscplne. Poceedngs of ACM SIGCOMM 94. pg 47-57, London, UK, August 1994. 6