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2 13 Introducton to Packet Schedulng Algorthms for Communcaton Networks Tsung-Yu Tsa 1, Yao-Lang Chung 2 and Zsehong Tsa 2 1 Insttute for Informaton Industry 2 Graduate Insttute of Communcaton Engneerng, Natonal Tawan Unversty 1,2 Tape, Tawan, R.O.C. 1. Introducton As mpled by the word packet schedulng, the shared transmsson resource should be ntentonally assgned to some users at a gven tme. The process of assgnng users packets to approprate shared resource to acheve some performance guarantee s so-called packet schedulng. It s antcpated that packetzed transmssons over lnks va proper packet schedulng algorthms wll possbly make hgher resource utlzaton through statstcal multplexng of packets compared to conventonal crcut-based communcatons. A packet-swtched and ntegrated servce envronment s therefore prevalent n most practcal systems nowadays. However, t wll possbly lead to crucal problems when multple packets assocated to dfferent knds of Qualty of Servce (QoS) (e.g. requred throughput, tolerated delay, jtter, etc) or packet lengths competng for the fnte common transmsson resource. That s, when the traffc load s relatvely heavy, the frst-come-frst-serve dscplne may no longer be an effcent way to utlze the avalable transmsson resource to satsfy the QoS requrements of each user. In such case, approprate packet-level schedulng algorthms, whch are desgned to schedule the order of packet transmsson under the consderaton of dfferent QoS requrements of ndvdual users or other crtera, such as farness, can alter the servce performance and ncrease the system capacty. As a result, packet schedulng algorthms have been one of the most crucal functons n many practcal wred and wreless communcaton network systems. In ths chapter, we wll focus on such topc drecton for complete nvestgaton. Tll now, many packet schedulng algorthms for wred and wreless communcaton network systems have been successfully presented. Generally speakng, n the most parts of researches, the man goal of packet schedulng algorthms s to maxmze the system capacty whle satsfyng the QoS of users and achevng certan level of farness. To be more specfc, most of packet schedulng algorthm proposed are ntended to acheve the followng desred propertes: 1. Effcency: The basc functon of packet schedulng algorthms s schedulng the transmsson order of packets queued n the system based on the avalable shared resource n a way that satsfes the set of QoS requrements of each user. A packet schedulng algorthm s generally sad to Source: Communcatons and Networkng, Book edted by: Jun Peng, ISBN , pp. 434, September 2010, Scyo, Croata, downloaded from SCIYO.COM

3 264 Communcatons and Networkng be more effcent than others f t can provde larger capacty regon. That s, t can meet the same QoS guarantee under a heaver traffc load or more served users. 2. Protecton: Besdes the guarantees of QoS, another desred property of a packet schedulng algorthm to treat the flows lke provdng ndvdual vrtual channels, such that the traffc characterstc of one flow wll have as small effect to the servce qualty of other flows as possble. Ths property s sometmes refered as flow solaton n many schedulng contexts. Here, we smply defne the term flow be a data connecton of certan user. A more formal defnton wll be gven n the next secton. Flow solaton can greatly facltate the system to provde flow-by-flow QoS guarantees whch are ndependent of the traffc demand of other flows. It s benefcal n several aspects, such as the per-flow QoS guarantee can be avoded to be degraded by some llbehavor users whch send packet wth a hgher rate than they declared. On the other hands, a more flexble performance guarantee servce scheme can also be allowed by logcally dvdng the users whch are assocated to a wde range of QoS requrements and traffc characterstc whle provdng protecton from affectng each other. 3. Flexblty: A packet schedulng algorthm shall be able to support users wth wdely dfferent QoS requrements. Provdng applcatons wth vast dversty of traffc characterstc and performance requrements s a typcal case n most practcal ntegrated system nowadays. 4. Low complexty: A packet schedulng algorthm should have reasonable computatonal complexty to be mplemented. Due to the fast growng of bandwdth and transmsson rate n today s communcaton system, the processng speed of packets becomes more and more crtcal. Thus, the complexty of the packet schedulng algorthm s also of mportant concern. Due to the evoluton process of the communcaton technology, many packet schedulng algorthms for wreless systems n lteratures are based on the rch results from the packet schedulng algorthms for wred systems, ether n the desgn phlosophy or the mathematcal models. However, because of the fundamental dfferences of the physcal characterstcs and transmsson technologes used between wred and wreless channels, t also leads to some dfference between the consderatons of the packet schedulng for wred and wreless communcaton systems. Hence, we suggest separate the exstng packet schedulng algorthms nto two parts, namely, wred ones and wreless ones, and llustrate the packet schedulng algorthms for wred systems frst to buld several basc backgrounds frst and then go to that for the wreless systems. The rest of the chapter s outlned as follows. In Secton 2, we wll start by ntroducng some prelmnary defnton for preparaton. Secton 3 wll make a overvew for packet schedulng algorthms n wred communcaton systems. Comprehensve surveys for packet schedulng n wreless communcaton systems wll then ncluded n Secton 4. In Secton 5, we wll employ two case studes for desgnng packet schedulng mechansms n OFDMA-based systems. In Secton 6, summary and some open ssues of nterest for packet schedulng wll be addressed. Fnally, references wll be provded n the end of ths chapter. 2. Prelmnary defntons The revew of the packet schedulng algorthms throughout ths chapter consders a packetswtched sngle server. The server has an outgong lnk wth transmsson rate C. The man

4 Introducton to Packet Schedulng Algorthms for Communcaton Networks 265 task of the server s dealng wth the packets nput to t and forwardng them nto the outgong lnk. A packet schedulng algorthm s employed by the server to schedule the approprate forwardng order to the outgong lnk to meet a varety of QoS requrements assocated to each packet. For wrelne systems, the physcal medum s n general regarded as stable and robust. Thus the packet error rate (PER) s usually gnored and C can be smply consdered as a constant wth unt bts/sec. Ths knd of model s usually referred as errorfree channel n lteratures. On the other hands, for wreless systems, the stuaton can become much more complcate. Whether n wreless networks wth short transmsson range (about tens of meters) such as WLAN and femtocell or that wth long transmsson range (about hundreds of meters or even several klometers) such as the macrocell envronments based on WCDMA, WMAX and LTE, the packet transmsson n wreless medum suffers locaton-dependent path loss, shadowng, and fadng. These mparment make the PER be no longer gnorable and the lnk capacty C may also become varyng (when adaptve modulaton and codng s adopted). Ths knd of model s usually referred as error-prone channel n lteratures. Each nput packet s assocated to a flow. Flow s a logcal unt whch represents a sequence of nput packets. In practce, packets assocated to the same flows often share the same or smlar qualty of servce (QoS) requrement. There should be a classfer n the server to map each nput packets to approprate flows. The QoS requrement of a flow s usually characterzed by a set of QoS parameters. In practce, the QoS parameters may nclude tolerant delay or tolerant jtter of each packet, or data rate requrement such as the mnmum requred throughput. The choce of QoS parameters mght defer flow by flow, accordng to the specfc requrement of dfferent servces. For example, n IEEE e [47], each data connecton s assocated to a servce type. There are totally fve servce types to be defned. That s, unsolcted grant servce (UGS), real-tme pollng servce (rtps), extended real-tme pollng servce (ertps), non-real-tme pollng servce (nrtps), and best effort (BE). Among these, rtps s generally for streamng audo or vdeo servces, and the QoS parameters contans the mnmum reserved rate, maxmum sustaned rate, and maxmum latency tolerant. On the other hands, UGS s desgned for IP telephony servces wthout slence suppresson (.e. voce servces wth constant bt rate). The QoS parameters of UGS connectons contans all the parameters of rtps connectons and addtonally, t also contans a parameter, jtter tolerance, snce the servce experment of IP telephony s more senstve to the smoothness of traffc. Moreover, for nrtps, whch s manly desgned for non-real-tme data transmsson servce such as FTP, the QoS parameters contans mnmum reserved data rate and maxmum sustaned data rate. Unlke rtps and UGS, whch requred the latency of each packet to be below certan level, nrtps s somewhat less senstve to the packet latency. It allows some packets to be postponed wthout degradng the servce experment mmedately, however, an average data rate should stll be guaranteed, snce throughput s of the most concern for data transmsson servces. The server can be further dvded nto two categores, accordng to the elgble tme of the nput packets. Elgble tme of a packet s defned as the earlest tme that the packet begns beng transmtted. Addtonally, a packet s called elgble when t s avalable to be transmtted by the server. If all packets mmedately become elgble for transmsson upon arrval, the system s called work-conservng, otherwse, t s called nonwork-conservng. A drect consequence of a system beng work-conservng s that the server s never dle whenever there are packets queued n the server. It always forwards the packets when the queues are not empty.

5 266 Communcatons and Networkng 3. Packet schedulng algorthms n wrelne systems In ths secton, we wll ntroduce several representatve packet schedulng algorthms of wrelne systems. Ther merts and expense wll be examned respectvely. 3.1 Frst Come Frst Serve (FCFS) FCFS may be the smplest way for a scheduler to schedule the packets. In fact, FCFS does not consder the QoS parameters of each packets, t just sends the packets accordng to the order of ther arrval tme. Thus, the QoS guarantee provded by FCFS s n general weak and hghly depends on the traffc characterstc of flows. For example, f there are some flows whch have very bursty traffc, under the dscplne of FCFS, a packet wll very lkely be blocked for a long tme by packets burst whch arrves before t. In the worst case, the unfarness between dfferent flows cannot be bounded, and the QoS cannot be no longer guaranteed. However, snce FCFS has the advantage of smple to mplement, t s stll adopted n many communcaton networks, especally the networks provdng best effort servces. If some level of QoS s requred, then more sophstcated schedulng algorthm s needed. 3.2 Round Robn Round Robn (RR) scheme s a choce to compensate the drawbacks of FCFS whch also has low mplementaton complexty. Specfcally speakng, newly arrval packets queue up by flow such that each flow has ts respectve queue. The scheduler polls each flow queue n a cyclc order and serves a packet from any-empty buffer encountered; therefore, the RR scheme s also called flow-based RR scheme. RR schedulng s one of the oldest, smplest, farest and most wdely used schedulng algorthms, desgned especally for tme-sharng systems. They do offer greater farness and better bandwdth utlzaton, and are of great nterest when consderng other scenaros than the hgh-speed pont-to-pont scenaro. However, snce RR s an attempt to treat all flows equally, t wll lead to the lack of flexblty whch s essental f certan flows are supported to be treated better than other ones. 3.3 Strct prorty Strct prorty s another classcal servce dscplne whch assgns classes to each flow. Dfferent classes may be assocated to dfferent QoS level and have dfferent prorty. The elgble packets assocated to the flow wth hgher-prorty classes are send ahead of the elgble packets assocated to the flow wth lower-prorty classes. The sendng order of packets under strct prorty dscplne only depends on the classes of the packets. Ths s why t called strct snce the elgble packets wth lower-prorty classes wll never be sent before the elgble packets wth hgher-prorty classes. Strct prorty suffers from the same problem as that of FCFS, snce a packet may also wat arbtrarly long tme to be sent. Especally for the packets wth lower-prorty classes, they may be even starved by the packets wth hgher-prorty classes. 3.4 Earlest Deadlne Frst (EDF) For networks provdng real-tme servces such as multmeda applcatons, earlest deadlne frst (EDF) [5][6] s one of the most well-known schedulng algorthms. Under EDF dscplne, each flow s assgned a tolerant delay bound d ; a packet j of flow arrvng at tme a j s naturally assgned a deadlne a j + d. Each elgble packet s sent accordng to the

6 Introducton to Packet Schedulng Algorthms for Communcaton Networks 267 ncreasng order of ther deadlnes. The concept behnd EDF s straghtforward. It essentally schedules the packets n a greedy manner whch always pcks the packets wth the closest deadlne. Compare wth strct prorty dscplne, we can regard EDF as a schedulng algorthm whch provdes tme-dependent prorty [8] to each elgble packet. Actually, the prorty of an elgble packet under EDF s an ncreasng functon of tme snce the sendng order n EDF s accordng to the closeness of packets deadlnes. Ths fact allows the guarantee of QoS f the traffc characterstc of each flow obeys some specfc constrant (e.g. the ncomng traffc n a tme nterval s upper bounded by some amount).defne the traffc envelope A (t) s the amount of flow traffc enterng the server n any nterval of length t. The authors n [9] and [13] proved that n a work-conservng system, the necessary and suffcent condton for the served flows are schedulable (.e. each packet are guaranteed to be sent before ts deadlne expres), whch s expressed by A( t d) + lmax I{ dmn t dmax } Ct (3.1) where C s the outgong lnk capacty as descrbed n secton 2, l max s the maxmum possble packet sze among all flows, d mn = mn {d }, d max = max {d }, I {event} s the ndcator functon of event E. An mportant result of EDF s that t has been known to be the optmal schedulng polcy n the sense that t has the largest schedulable regon [9]. More specfcally, gven N flows wth traffc envelopes A (t) ( = 1,2,..., N), and gven a vector of delay bounds d = (d 1, d 2,... d N ), where d s the to delay bound that flow can tolerate. It can be proved that f d s schedulable under a schedulng algorthm π, then d wll also be schedulable under EDF. Although EDF has optmal schedulable regon, t encounters the same drawback as that of FCFS and strct prorty dscplnes. That s, the lack of protecton between flows whch ntroduces weak flow solaton (see secton 1). For example, f some flows do not have bounded traffc envelope, that s, A (t) can be arbtrary large (or at least, very large) for some, then the condton n (3.1) can t no longer be guaranteed to be satsfed, and no QoS guarantee can be provded to any flows beng served. In the next secton, we wll ntroduce generalzed processor sharng (GPS) dscplne, whch can provde deal flow solaton property. The lack of flow solaton of EDF s often compensated by adoptng traffc shapers to each flow to shape the traffc envelopes and bound the worst-case amount of ncomng traffc of per flow. There are also some modfed versons of EDF proposed to provde more protecton among flows, such as [7] [10]. 3.5 Generalzed Processor Sharng (GPS) Generalzed processor sharng (GPS) s an deal servce dscplne whch provdes perfect flow solaton. It assumes that the traffc s nfntely dvsble, and the server can serve multple flows smultaneously wth rates proportonal to the weghtng factors assocated to each flow. More formally, assume there are N flows, and each flow s characterzed by a weghtng factor w. Let S(τ,t) be the amount of flow traffc served n an nterval (τ,t) and a flow s backlogged at tme t f a postve amount of that flow s traffc s queued at tme t. Then, a GPS server s defned as one servce dscplne for whch S( τ, t) w, j = 1,2,..., N S ( τ, t) w j j (3.2)

7 268 Communcatons and Networkng For any flow that s contnuously backlogged n the nterval (τ,t). Summng over all flow j, we can obtan: S ( τ, t) w ( t τ) Cw j j that s, when flow s backlogged, t s guaranteed a mnmum rate of g = w In fact, GPS s more lke an dealzed model rather than a schedulng algorthm, snce t assumes a flud traffc model n whch all the packets s nfntely dvsble. The assumptons make GPS not practcal to be realzed n a packet-swtched system. However, GPS s stll worth to remark for the followng reasons: 1. It provdes followng attractve deal propertes and can be a benchmark for other schedulng algorthms. a. Ideal resource dvson and servce rate guarantee GPS assumes that a server can serve all backlogged flows smultaneously and the outgong lnk capacty C can be perfectly dvded accordng to the weght factor assocated to each backlogged flow. It leads to deal flow solaton n whch each flow can be guaranteed a mnmum servce rate ndependent of the demands of the other flows. Thus, the delay of an arrvng bt of a flow can be bounded as a functon of the flow s queue length, whch s ndependent of the queue lengths and arrvals of the other flows. Accordng to ths fact, one can see that f the traffc envelope of a flow obeys some constrant (e.g. leaky buckets) and s bounded, then the traffc delay of a flow can be guaranteed. Schemes such as FCFS and strct prorty do not have ths property. Compare to EDF, snce the delay bound provded by GPS s not affected by the traffc characterstc or queue status of other flows, whch makes the system more controllable and be able to provde QoS guarantee n per-flow bass. b. Ideal flexblty By varyng the weght factors, we can enjoy the flexblty of treatng the flows n a varety of dfferent ways and provdng wdely dfferent performance guarantees. 2. A packet-by-packet schedulng algorthm whch can provde excellent approxmaton to GPS has been proposed [1]. Ths schedulng algorthm s known as packet-by-packet GPS (PGPS) or weghted far queueng (WFQ). In the later secton, we wll dscuss the operaton and several mportant propertes of PGPS n more detal. j w j C 3.6 Packet-by-packet Generalzed Processor Sharng (PGPS) PGPS s a schedulng algorthm whch can provde excellent approxmaton to the deal propertes of GPS and s practcal enough to be realzed n a packet-swtched system. The concept of PGPS s frst proposed n [4] under the name Weghted Far Queueng (WFQ). However, a great generalzaton and nsghtful analyss was done by Parekh and Gallager n the remarkable paper [1] and [2]. The basc dea of PGPS s smulatng the transmsson order of GPS system. More specfc, let F p be the tme at whch packet p wll depart (fnsh servce) under GPS system, then the basc dea of PGPS s to approxmate GPS by servng

8 Introducton to Packet Schedulng Algorthms for Communcaton Networks 269 the packets n ncreasng order of F p. However, sometmes there s no way for a workconservng system to serve all the arrval packets n the exactly the same order as that of correspondng GPS system. To explan t, we make the followng observatons: 1. The busy perod (the tme duraton that a server contnuously sends packets) of GPS and PSPS s dentcal, snce GPS and PGPS are all work-conservng system, the server wll never dle and send packets wth rate C when there are unfnshed packets queued n the system. 2. When the PGPS server s avalable for sendng the next packet at tme τ, the next packet to depart under GPS may not have arrved at tme τ. It s essentally due to the fact that a packet may depart earler than the packets whch arrve earler than t under GPS. A packet may arrve too late to be send n PGPS system, at ths tme, f the system s work-conservng, the server should pck another backlogged packet to send, and ths would conflct the sendng order under GPS system. Snce we do not have addtonal assumpton to the arrval pattern of packets here, there s no way for the server to be both work-conservng and to always serve the packet n ncreasng order of F p. To preserve the property of work-conservng, the PGPS server pcks the frst packet that would complete servce n the GPS smulaton. In other words, f PGPS schedules a packet p at tme τ before another packet p that s also backlogged at tme τ, then packet p cannot leave later than packet p n the smulated GPS system. We have known the basc operaton of PGPS, now a natural queston arses: how well does PGPS approxmate GPS? To answer ths queston, we may attempt to fnd the worst-case performance under PGPS compared to that of GPS. So we ask another queston: how much later packets may depart the system under PGPS relatve to GPS? In fact, t can be proved that let the G p be the tme at whch packet p departs under PGPS, then G p L Fp C where L max s the maxmum packet length. That s, the depart tme of a packet under PGPS system s not later than that under GPS system by more than the tme of transmttng one packet. To verfy ths result, we frst present a useful property: Lemma 1 Let p and p be packets n a GPS system at tme τ and suppose that packet p complete servce before packet p f there are no arrvals after tme τ. Then packet p wll also complete servce before packet p for any pattern of arrvals after tme τ Proof. The flows to whch packet p and p belong are backlogged at tme τ. By (3.2), the rato of the servce receved by these flows s ndependent of future arrvals. Now we have prepared to prove the worst-case delay of PGPS system. Theorem 1 For all packet p, let G p and F p be the departure tme of packet p under PGPS and GPS systems, respectvely. Then G p max L Fp C where L max s the maxmum packet length, and C s the outgong lnk capacty. Proof. As observed above, the busy perods of GPS and PGPS concde, that s, the GPS server s n a busy perod f and only f the PGPS server s n a busy perod. Hence t suffces to prove max

9 270 Communcatons and Networkng the theorem by consderng one busy perod. Let p k be the k-th packet n the busy perod to depart under PGPS and let ts length be L k. Also let t k be the tme that p k depart under PGPS and u k be the tme that p k departs under GPS. Fnally, let a k be the tme that p k arrves. It should be frst noted that, f the sendng order n a busy perod under PGPS s the same as that under GPS, then t can be easly verfed the departure tme of the packets under PGPS system are earler or equal to those under GPS system. However, snce the busy perods of GPS and PGPS systems concde, there are only two possble cases: 1. The departure tmes of all the packets under PGPS system n a busy perod are all the same as those of correspondng GPS system. 2. If the departure tmes of some packets under PGPS system n a busy perod are earler than that of GPS, then there are also some packets wth whch the departure tme are later than those of correspondng GPS system. The second case mples that f there s a packet wth whch the departure tme under PGPS system s later than the departure tme of the correspondng GPS system, then the sendng orders are not the same n the two systems n the busy perod. Accordng to the operaton of PGPS, the dfference of sendng orders s only caused by some packets arrve too late to be transmtted n ther order n GPS system. Thus, after these packets arrve, they may wat for the packets whch should be sent later than them n GPS system to be served. Then, the addtonal delay caused. Now we are clear that the only packets that have later departure tme under PGPS system than under GPS system are those that arrve too late to be send n the order of correspondng GPS system. Based on ths fact, we now show that: t k L uk + C For k = 1,2, Let p m be the packet wth the largest ndex that has earler departure tme than p k under PGPS system but has later depart tme under GPS system. That s, m satsfes 0< m k 1 max u > u u for m< < k m k So packet pm s send before packets p m+1,, p k under PGPS, but after all these packets under GPS. If no such m exsts then set m = 0. For the case m = 0, t drect lead to case 1 above, and u k > t k. For the case m > 0, packet pm begns transmsson at t m L m /C, so from Lemma 1: Lm mn{ am+ 1,..., ak} > tm C That s, p m+1,, p k-1 arrve and are served under GPS system after tm-lm/c. Thus Moreover, snce 1 L ( ) m uk Lk + Lk+ + + Lm+ + tm C C 1 ( L + L L ) + t = t C k k 1 m+ 1 m k

10 Introducton to Packet Schedulng Algorthms for Communcaton Networks 271 we obtan the nequalty Lm L uk tk tk C C whch drectly lead to the desred result. It s worth to note that the guarantee of delay n PGPS system n Theorem 1 leads to the guarantee of per-flow throughput. Theorem 2 For all tmes τ and flows S (0, τ) S' (0, τ) L where S (a,b) and S (a,b) are the amount of flow traffc served n the nterval [a,b], respectvely. Prove. max max ( a) Lmax max S (0, τ ) L S (0, τ ) S' (0, τ) C relaton (a) comes from the fact that all the flow packets transmtted before τ-l max /C under GPS system wll always be transmtted before τ under PGPS system, whch s the drect consequence of Theorem 1. Let Q (τ) and Q (τ) be the flow backlog at tme τ under GPS and PGPS system, respectvely. Then t mmedately follows from Theorem 2 that Corollary 2.1 For all tme τ and flow Q'( τ) Q ( τ) L From the above results, we can see that PGPS provdes quet close approxmaton to GPS wth the servce curve never falls behnd more than one packet length. Ths allows us to relate results for GPS to the packet-swtched system n a precse manner. For more extensve analyss of PGPS, readers can refer to [1], [2], and [3]. max 4. Wreless packet schedulng algorthms Recently, as varous wreless technologes and systems are rapdly developed, the desgn of packet schedulng algorthms n such wreless envronments for effcent packet transmssons has been a crucal research drecton. Tll now, a lot of wreless packet schedulng algorthms have been studed n many research papers. In the secton, we wll select four much more representatve ones for llustratons n detal. 4.1 Idealzed Wreless Far Queueng (IWFQ) algorthm The Idealzed Wreless Far Queueng (IWFQ) algorthm, proposed by Lu, Bharghavan, and Srkant [14] s one of the earlest representatve packet schedulng algorthms for wreless access networks and to handle the characterstc of locaton-dependent burst error n wreless lnks. IWFQ takes an error-free WFQ servce system as ts reference system, where a channel predctor s ncluded n the system to montor the wreless lnk statuses of each flow

11 272 Communcatons and Networkng and determnes the lnks are n ether good or bad states. The dfference between IWFQ and WFQ s that when a pcked packet s predcted n a bad lnk state, t wll not be transmt and the packet wth the next smallest vrtual fnsh tme wll be pcked. The process wll repeat untl the scheduler fnds a packet wth a good state. A flow s sad to be laggng, leadng, or n sync when the queue sze s smaller than, larger than, or equal to the queue sze n the reference system. When a laggng flow recovered from a bad lnk state, t must have packets wth smaller vrtual fnsh tmes, compare to other error-free flows packets. Thus, t wll have precedence to be pcked to transmt. So the compensaton s guaranteed [15]. Addtonally, to avod unbounded amount of compensaton starve other flows n good lnk state, the total lag that wll be compensated among all laggng flows s bounded by B bts. Smlarly, a flow cannot lead more than l bts. However, IWFQ does not consder the delay/jtter requrements n real-tme applcatons. It makes no dfference for dfferent knd of applcatons, but n fact, non-real-tme and delaysenstve real-tme applcatons have fundamental dfference n QoS requrement, so always treat them dentcally may not be a reasonable soluton. In addton, the choce of the parameter B reflects a conflct between the worst-case delay and throughput propertes. Hence, the guarantees for throughput and delay are tghtly coupled. In many scenaros, especally for real-tme applcatons, decouplng of delay from bandwdth mght be a more attractve approach [16]. Moreover, snce the absolute prorty s gven to packets wth the smallest vrtual fnsh tme, so a laggng flow may be compensated n a rate ndependent of ts allocated servce rate, volatng the semantcs that a larger guaranteed rate mples better QoS, whch may be not desrable. 4.2 Channel-condton Independent packet Far Queueng (CIF-Q) algorthm The Channel-condton Independent packet Far Queueng (CIF-Q) algorthm [17], proposed by Ng, Stoca, and Zhang. CIF-Q also uses an error free far queueng algorthm as a reference system. In [17], Start-tme Far Queueng (SFQ) s chosen to be the core of CIF-Q. Smlar to IWFQ, a flow s also classfed to be laggng, leadng, or satsfed accordng to the dfference of the amount of servce t have receved to that of the correspondng reference system. The major dfference between CIF-Q and IWFQ s that n CIF-Q the leadng flows are allowed to contnue to receve servce at an average rate ar, where r s the servce rate allocated to flow and a s a confgurable parameter. And nstead of always choosng the packet wth smallest vrtual servce tag lke IWFQ, the compensaton n CIF-Q s dstrbuted among the laggng flows n proporton to ther allocated servce rates. Compared wth IWFQ, CIF-Q has better schedulng farness and also has good propertes of guaranteeng delay and throughput for error-free flows lke IWFQ. However, the requrement of decouplng of delay from bandwdth s stll not acheved by CIF-Q. 4.3 Improved Channel State Dependent Packet Schedulng (I-CSDPS) algorthm A wreless schedulng algorthm employng a modfed verson of Defct Round Robn (DRR) scheduler s called Improved Channel State Dependent Packet Schedulng (I-CSDPS), whch s proposed by J. Gomez, A. T. Campbell, and H. Morkawa [18]. In DRR, each flow has ts own queue, and the queues are served n a round robn fashon. Each queue mantans two parameters: Defct Counter (DC) and Quantum Sze (QS). DC can be regarded as the total credt (n bts or bytes) that a flow has to transmt packets. And

12 Introducton to Packet Schedulng Algorthms for Communcaton Networks 273 QS determnes how much credt s gven to a flow n each round. For each flow at the begnnng of each round, a credt of sze QS s added to DC. When the scheduler serves a queue, t transmts the frst N packets n the queue, where N s the largest nteger such that N l = 1 decreased by DC, where l s the sze of the th packet n the queue. After transmsson DC s N l = 1. If the scheduler serves a queue and fnds that there are no packets n queue, ts DC s reset to zero. To allow flows to receve compensaton for ther lost servce due to lnk errors, I-CSDPS adds a compensaton counter (CC) to each flow. CC to keep track of the amount of lost servce for each flow. If the scheduler defers transmsson of a packet because of lnk errors, the correspondng DC s decreased by the QS of the flow and the CC s ncreased by the QS. At the begnnng of each round, α CC amount of credt s added to DC, and CC s decreased by the same amount, where 0 < α 1. Also, to avod problems caused by unbounded compensaton, the credt accumulated n a DC cannot exceed a certan value DC max. Smlar to the parameter B n IWFQ, the choce of DC max also lead to the tradeoff between delay bound and the compensaton for a flow lost ts servce. However, ths bound s very loose and s n proporton to on the number of all actve flows. 4.4 Proportonal Far (PF) algorthm In the recent years, the two most well-known packet schedulng schemes for future wreless cellular networks are the maxmum carrer-to-nterference rato (Max CIR) [26] and the proportonal far (PF) [27] schemes. Max CIR tends to maxmze the system s capacty by servng the connectons wth the best channel qualty condton at the expense of farness snce those connectons wth bad channel qualty condtons may not get served. PF tres to ncrease the degree of farness among connectons by selectng those wth the largest relatve channel qualty where the relatve channel qualty s the rato between the connecton s current supportable data rate (whch depends on ts channel qualty condtons) and ts average throughput. However, a recent study shows that the PF scheme gves more prorty to connectons wth hgh varance n ther channel condtons [28]. Therefore, we pay our attenton focusng on the PF scheme for llustraton here. In another pont of vew, n wreless communcaton systems, the optmal desgn of forward lnk gets more attenton because of the asymmetrc nature of multmeda traffc, such as vdeo streamng, e-mal, http and Web surfng. For the effcent utlzaton of scarce rado resources under massve downlnk traffc, opportunstc schedulng n wreless networks has recently been consdered mportant. The PF was orgnally proposed n the network schedulng context by Kelly et al. n [45] as an alternatve for a max-mn scheduler, a PF schedulng promses an attractve trade-off between the maxmum average throughput and user farness. The standard PF scheme n packet schedulng was formally defned n [45]. Defnton: A schedulng P s proportonal far f and only f, for any feasble schedulng S, t satsfes: U R ( S) ( P) R ( P) R 0

13 274 Communcatons and Networkng where U s the user set and ( S) R s the average rate of user by scheduler S. Also, t s known that a PF allocaton P should maxmze the sum of logarthmc average user rates [21], whch s expressed by ( S) P = arg max log R. S The PF schedulng s mplemented for Qualcomm s HDR system, where the number of transmsson channels s one. Only one user s allocated to transmt at a tme, and the PF s acheved by schedulng a user j accordng to U r j = arg max, R where r s the nstantaneous transmttable data rate at the current slot of user and R s the average data rate at the prevous slot of user. Consder a model where there are N actve users sharng a wreless channel wth the channel condton seen by each user varyng ndependently. Better channel condtons translate nto hgher data rate and vce versa. Each user contnuously sends ts measured channel condton back to the centralzed PF scheduler whch resdes at the base staton. If the channel measurement feedback delay s relatvely small compared to the channel rate varaton, the scheduler has a good enough estmate of all the users channel condton when t schedules a packet to be transmtted to the user. Snce channel condton vares ndependently among dfferent users, PF explots user dversty by selectng the user wth the best condton to transmt durng dfferent tme slots. The PF algorthm was proposed after studyng the unfarness exhbted when ncreasng the capacty of CDMA by means of dfferentatng between dfferent users. Transmsson of plot symbols to the dfferent users yelds channel state nformaton, and by allocatng most resources to the users havng the best channels, the total system capacty of the CDMA scheme could be ncreased. Such allocaton of resources favors the users closest to the transmttng node, resultng n reduced farness between the dfferent users. The PF algorthm seeks to ncrease the farness among the users at the same tme as keepng some of the hgh system throughput characterstcs. The PF schedulng algorthm has receved much attenton due to ts favorable trade-off between total system throughput and farness n throughput between scheduled users [19] [20]. The PF schedulng algorthm can acheve mult-user dversty [20] [21], where the scheduler tracks the channel fluctuatons of the users and only schedules users when ther nstantaneous channel qualty s near the peak. In other words, the PF scheme s a channelstate based schedulng algorthm that reles on the concept of explotng user dversty. PF has extensvely been studed under well-defned propagaton channel condtons, such as flat fadng channels wth Raylegh and/or Rcan type of fadng [22], or the ITU Vehcular and Pedestran channels [24], whch are typcally appled n standardzaton work [23]. In early years, the PF schedulng s wdely consdered n sngle-carrer stuatons. In addton, t s ponted out n [26] that the PF scheme for a sngle antenna system s attractve for non-real tme traffcs, snce t acheves substantally larger system throughput than the Round-Robn (RR) scheme. The PF scheme also provdes the same level of farness as the RR

14 Introducton to Packet Schedulng Algorthms for Communcaton Networks 275 scheme n the average sense [25]. Further descrptons of the PF algorthm can be n [29], [30], [31], [32] and [33], whle a varant whch offers delay constrants s descrbed n [34]. In more recent years, as many modern broadband wreless systems wth mult-carrer transmssons are rapdly developed, mult-carrer schedulng becomes a hot topc. The ssue wll be nvestgated and llustrated n detal n Secton Case study: desgn of packet schedulng schemes for OFDMA-based systems 5.1 Introducton to OFDMA Recently there has been a hgh demand for large volume of multmeda and other applcaton servces. Such a demand n wreless communcaton networks requres hgh transmsson data rates. However, such hgh transmsson data rates would result n frequency selectve fadng and Inter-Symbol Interference (ISI). As a soluton to overcome these ssues, Orthogonal Frequency Dvson Multplexng (OFDM) had been proposed n [35]. Nowadays, the OFDM technology has wdely been used n most of the mult-user wreless systems, whch can be referred to research papers [36-38] for nstance. When such a multple carrer system has mult-user, t can referred to as Orthogonal Frequency Dvson Multple Access (OFDMA) system. In other words, the key dfference between both transmsson methods s that OFDM allows only one user on the channel at any gven tme whereas OFDMA allows multple accesses on the same channel. OFDMA assgns a subset of subcarrers to ndvdual users and ther transmssons are smultaneous. OFDMA functons essentally as OFDM-FDMA. Each OFDMA user transmts symbols usng some subcarrers that reman orthogonal to those of other users. More than one subcarrer can be assgned to one user to support hgh data rate applcatons. Smultaneous transmssons from several users can acheve better spectral effcency. 5.2 Token-based packet schedulng scheme for IEEE [46] Frame by frame operaton scheme Snce IEEE s a dscrete-tme system, tme s dvded nto fxed-length frames, and every MS s mandatory to synchronze wth the BS before enterng the IEEE network [45], our packet scheduler scheme s also a dscrete-tme scheme and schedule packets n a per-frame bass. Addtonally, because we consder downlnk traffc only, all the components and algorthms are all operated n BS. Fgure 5.1 s a smple descrpton of the operaton of our packet schedulng scheme. When a packet arrves at the BS from the upper layer, t s buffered n the BS frst and the system decdes whether t wll be scheduled to be transmtted n the next frame. Ths procedure wll be repeated every frame untl ths packet s transmtted successfully n the downlnk subframe of one of the afterward frame. We assumed that a packet transmtted n the downlnk subframe of a frame wll receve ARQ feedback (ACK or NAK) mmedately from MSs n the uplnk subframe of the same frame. The result of schedulng of the next frame s broadcast va the DL-MAP whch s transmtted at the begnnng of the next frame. 1. System Resource Normalzaton Snce the packets of each flow may be transmtted n dfferent Modulaton and Codng Schemes (MCS), we use slots as a general unt of entre system to descrbe traffc characterstc and system resource. Suppose that the MSC used for a flow s not changed durng the sesson s lfe tme.

15 276 Communcatons and Networkng Fg. 5.1 Smple descrpton of the operaton of packet schedulng scheme For example, we can say a leaky bucket shaper has bucket depth 10 slots and slots/frame. Or we guaranteed a non-real-tme sesson a mnmum throughput of 5.35 slots/frame. In ths study, we assume our system has a total of C slots avalable for downlnk traffc n a frame. We can also say that ths system has a capacty of C slots/frame. 2. System Archtectures Fgure 5.2 s our proposed packet schedulng scheme operated n the BS. It conssts of several components. We descrbe ther functons and algorthms respectvely n ths secton. Classfer and Traffc Profle The classfer s responsble for classfyng packets from upper layers to the approprate servce group. Two servce groups are defned, that s, real-tme group and non-real-tme group, accordng to ther fundamental dfferences of QoS requrement. There are several approaches to dentfy each packet s group. One suggeston s to classfy each packet accordng to the servce type of ts MAC connecton ID. For example, UGS, rtps, and ertps are belong to real-tme group and nrtps and BE are belong to non-real-tme group. We also assume that each flow has a flow profle for descrpton of ts traffc characterstc. Flows of real-tme group and flows of non-real-tme group have dfferent flow profles. We ntroduce them respectvely as follows: Real-tme group: Real-tme flows are delay-senstve traffc. A packet from real-tme sessons s expected to be transmtted successfully n some delay constrant or t s regarded as meanngless and dropped. Although that, some loss rate does not degrade the applcaton layer qualty serously and s tolerable for users. A trple {δ, λ, D} s used to descrbe the traffc characterstc of real-tme flow. Where δ s maxmum burst sze (normalzed to slots), λ s the mnmum sustanable data rate ( normalzed to slots/frame), D s the maxmum tolerable packet delay ( n frame ). Note that when a leaky bucket polcer [46] s used, δ s equvalent to the bucket depth and λ s equvalent to the average rate n the leaky-bucket polcng algorthm.

16 Introducton to Packet Schedulng Algorthms for Communcaton Networks 277 Non-real-tme group: Non-real-tme flows are not senstve to delay and jtter. The QoS matrx of non-real-tme servces s the average throughput. A parameter λ j s used to descrbe the traffc characterstc of non-real-tme sesson j. Where λ j s the mnmum reserved data rate (normalzed to slots/frame). Data packet Classfer RT Group Sesson 1 δ, λ, ) ( 1 1 D1 Sesson 2 δ, λ, ) ( 2 2 D2 Sesson δ, λ, D ) ( NRT Group Sesson +1 λ + 1 Sesson +2 λ + 2 Sesson n λ n n 2 1 WFQ Algorthm Weght Generator 3 VQ-RTRX VQ-NRTRX VQ-TX Token-Based Scheduler Feedback remaned token and retransmsson Token generator Update Token New sesson request CAC accept Add new sesson New Sesson Profle New Sesson Profle reject Fg. 5.2 The system archtecture of our packet scheduler Packet Scheduler and Weght Generator In the followng sectons, we ntroduce the man part of our packet schedulng scheme. Some useful notatons are as follows: S RT : The set of all real-tme flows S NRT : The set of all non-real-tme flows b : The mnmum requred capacty to acheve the QoS requrement of flow (normalzed to slots/frame). For real-tme servces, the QoS marx s the tolerant delay of a packet, and for non-real-tme servces, the QoS matrx s the average throughput w : t : The weghtng factor of flow n the WFQ scheduler The current token value of flow. If a packet of flow s scheduled to transmt n the next frame. It must take the token value equal to the sze of the packet (normalze to slot) away T : The maxmum token value flow can keep α : The protectng factor of flow. A number whch s larger than or equal to 1. The more α s, the more protected capacty for flow. r : The token ncremental rate of flow. At the begnnng of a frame, the token value of flow s updated to max(t +r,t ). r can be regard as the protected capacty for flow. r = b * α. R: The sum of the protected capacty of real-tme flows, R= r S RT

17 278 Communcatons and Networkng N: The sum of the protected capacty of non-real-tme flows, N = N max : The maxmum value of the sum of protected capacty of non-real-tme flows C: The avalable slots for downlnk traffc per frame. Intutvely, C R+ N Our packet schedulng scheme has two stages. The frst stage s a work conservng packet scheduler. When a packet arrves from upper layer, t frst enters the frst stage. The actual condtons n the lower layer such as the channel status or the allocaton of slot are transparent to the frst stage. It always assumes there s an error-free channel wth fxed capacty C n the lower layer. The man purpose of the frst stage packet scheduler s to emulate the transmsson order of a work conservng system n an deal condton and be a reference system to our scheme. The packet order n the reference system s not certanly the actual transmsson order n our packet schedulng scheme. The task of determnng whch packet should be scheduled to transmt n the next frame s executed by the token-based slot scheduler whch s n the second stage of our scheme. The detal of the operaton of the token-based slot scheduler wll be llustrated n the next secton. There s no constrant to the schedulng dscplne adopted n the frst stage packet scheduler. But to acheve a better resource allocaton and solaton among each flow, weghtbased schedulng dscplnes such as WFQ, VC, are suggested. In our packet schedulng scheme, we take WFQ as the reference system. When a packet arrves from the upper layer, t enters the packet scheduler n the frst stage, the packet scheduler then schedules the transmsson order of ths packet wth WFQ algorthm. The packet order scheduled by the packet scheduler s recorded n a vrtual queue. Vrtual queue s not really buffered the packets but store the ponters of packet whch s the nput of the token-based slot scheduler n the second stage. There are three vrtual queues wth strct prortes. They are vrtual queue for real-tme retransmsson (VQ-RTRX), vrtual queue (VQ-NRTRX) for non-real-tme retransmsson, and vrtual queue for frst tme transmsson (VQ-TX) accordng to ther prortes. The packets whch have not been transmtted are recorded ther ponter n the VQ. The real-tme packets whch have transmtted but not receved successfully by the recever, ther ponters are moved from VQ to VQ-RTRX. The non-real-tme packets whch have transmtted but not receved successfully by the recever, ther ponters are moved from VQ to NRTRVQ. The token-based packet scheduler checks the packet ponters from the vrtual queue wth hghest prorty (RTRVQ) to that wth lowest prorty (VQ) and determnes whch packets wll be scheduled to transmt n the next frame. The algorthm determnng whch packets wll be scheduled wll be dscussed n the next secton n detal. Fgure 5.3 s the queueng model of our packet schedulngscheme. To ndcate the resource sharng of the flows, each flow assocates a weghtng factor w. The weghtng factor s an mportant parameter as the weght n packet scheduler n the frst stage and n the debt allocaton procedure n token-based slot scheduler. We wll return to dscuss the procedure of weght allocaton after we ntroduce the token-based slot scheduler and ts algorthm n the next secton. Token-Based Scheduler We use a token-based scheduler to determne whch packet should be scheduled to transmt n the next frame. The fundamental operaton of the token-based slot scheduler s as follows. For convenence of llustraton, we defne some notaton as follows: S NRT r

18 Introducton to Packet Schedulng Algorthms for Communcaton Networks 279 Fg. 5.3 The queueng model of our proposed packet schedulng scheme l : j l : The sze of the packet that s checked by the token-based scheduler The j th packets of flow whch s scheduled n the next frame L : The total length of the scheduled packets of flow. That s, L j j = l remaned _ slots :The remaned slots avalable for schedulng. remaned _ slot = C L Assume that there are C slots avalable for downlnk traffc each frame. Each flow mantans a token value t. The token value of every sesson has a fxed token ncremental rate r, the unt of r s slots/frame. At every begnnng of a frame, the token value of sesson s ncreased by r slots. The task of updatng the token value of each flow at the begnnng of a frame s operated by the token generator. When a packet of flow wth sze l (normalzed to slots) s scheduled to transmt, t must take the token value equal to the amount of the sze of the packet (normalzed to slots) away. And the number of slots avalable for schedulng s also decreased by That s, When a packet of flow wth sze l s scheduled t t -l (5.1) L + = l (5.2) remaned _ slot = C L (5.3) There should be an upper bound of the token value t, where we denote t by T. The settng of T can affect the system performance. We wll dscuss the ssue of the effect of T later. Thus, when a new frame start t max(t +r,t ), for each flow I (5.4) We can regarded r as the protected capacty of flow. The confguraton of r can affect the system performance sgnfcantly. We ntroduce the detaled algorthm of token-based slot scheduler n ths secton. Then we wll return to dscuss the gudelne of the settng of token ncremental rate n the next secton. The basc prncple of schedulng s as follows:

19 280 Communcatons and Networkng 1. The packet whch has suffcent token value to transmt t has the hgher prorty, or t has the lower prorty 2. For the packets wth the same prorty, the schedulng order s accordng to the order n WFQ scheduler (.e. the order of the vrtual fnsh tme n the WFQ) The process of our token-based packet scheduler algorthm can be dvded nto two phases. At the begnnng of schedulng, the token-based packet scheduler enters the frst phase. It checks the packet ponters sequentally n each vrtual queue from hgh prorty to low prorty. We call the frst step packet selecton procedure. If the checked packet has suffcent token value (that s, t l) and there are suffenct slots to transmt t n the next frame (that s, remaned _ slots L + l L ). It s scheduled n the next frame. And the token value of ths flow s decreased by the sze of the packet. Otherwse, the token-based slot scheduler wll skp t, and to keep the packets of the same flow to be transmtted n order, other packets from the same flow whch have not been checked are also skpped n the frst phase. For convenence of dscusson, we say that ths flow s blocked n ths phase. After all the packets are checked, the slot scheduler enters the second phase. Durng the second phase, the slot scheduler contnues to fnd other packets can be transmtted wth the remaned slots n the next frame. The token-based scheduler does t by checkng the packets whch have not been scheduled n the frst phase. Agan, the order of checkng s the same as the frst phase. If there are stll suffcent slots to transmt the checked packet (that s, remaned _ slots L + l L ), the packet s scheduled n the next frame, or the packet s skpped and the flow of ths packet s blocked whch s the same as the frst phase. When the checked packet s scheduled, the token value of the scheduled packet must runs out and become a negatve number, t mples that the sesson of ths packet uses more capacty than ts protected capacty. The addtonal consumed token value exceedng the protected capacty s regarded as the debt draw from other flows. For example, f t =30, now flow has a packet wth sze 50 slots and s scheduled to transmt n the next frame by the scheduler. The debt s 20. If t = -10, a packet wth the same sze s scheduled, the debt s 50. We can represent debt as follows: debt = 1*max( l, t l), l t (5.5) In our algorthm, we prefer to gve real-tme sessons more opportunty to ncrease ts token value, snce f we clean the packets of real-tme sessons as soon as possble, t s more lkely to have more remaned resource to mprove the throughput of non-real-tme traffc n the operaton of our token-based algorthm, thus meet the QoS requrement of both. So the debt s allocated to the token value of all real-tme flows n proporton to ther weght. That s, w t = max( T, t + * debt), for all SRT (5.6) w j S RT We call the second step debt allocaton procedure. For example, there are three flows. Flow 1 and 2 s real-tme flows wth weghtng factor 0.3 and 0.2 respectvely, flow 3 s non-real-tme flows wth weghtng factor 0.5. And ther token value s -10, 40, 20. Now flow 2 has a packet of sze 50 slots be scheduled by the token-based slot scheduler. Snce the packet sze s larger j

20 Introducton to Packet Schedulng Algorthms for Communcaton Networks 281 than the token value of flow 2. We can calculate the debt s 10 and allocate t to the token value of real-tme flows, that s, flow 1 and flow 2. Fnally, the token value of flow 1 s 10 * * = 4, the token value of flow 2 s = 6. The token value of flow 3 s not changed. The debt allocaton procedure s fnshed when all the packets are checked. Then n the slot the scheduler transmts the scheduled packet and receves ARQ from the recevers. The chosen of T can affect system performance sgnfcantly. If the T s set too large, suppose flow s n good channel status for a long tme and t accumulates a large amount of token value from the token generator and the debt of other flows, now t ncurs burst error and the channel s n bad channel for an long nterval of tme. Then flow wll waste a large amount of system resource to transmt error packet because t accumulates too much token value when t s n good channel. Thus s unfavorable. On the other hand, f the maxmum token value s set too small. Then t s hard to dfferentate the flows behave well and gve t more opportunty to be scheduled. Thus s dffcult to show the advantage of our algorthm. Furthermore, the traffc characterstc also should be taken nto consder. Generally, we suggest that the maxmum token value of non-real-tme flows has better larger than that of real-tme flows, because most non-real-tme flow are TCP traffc, whch s composed of several burst. The flow chart of all procedures of the token-based slot scheduler s shown n Fg The checkng procedure and the debt allocaton procedure s the core of our slot scheduler. The pseudo codes of these two procedures are shown n Fg. 5.5 and Fg. 5.6, respectvely. Fg. 5.4 The flow chart of the procedure of the token-based scheduler

21 282 Communcatons and Networkng packet-selecton-procedure(system_capacty){ remaned_slot system_capacty; for(each flow j){ block j =0; } for(each vrtual queue, from hghest prorty to lowest prorty) whle(packets not checked n the vrtual queue){ the flow the packet belong to; l the sze of the checked packet; f( remaned _ slot L + l L and l t and block ==0){ schedule ths packet n the next frame; remaned _ slot = L + l L ; t = l; } else block =1; /* the other packet of flow s also skpped n ths procedure */ } } debt-allocaton-procedure(remaned_slot); } Fg. 5.5 The pseudo code of packet selecton procedure Weght Allocaton and Token Generator In ths secton, we dscuss the functons of token generator, and the relatonshp between. The man tasks of token generator are calculatng the token ncremental rate of each flow, and allocatng token value to all the flows per frame. In ths secton, we address the ssues of the chosen of weghtng factor and token ncremental rate. The dfferent confguraton of the token ncremental rate alters the system performance. We suggest that the token ncremental rate of flow s set to ts mnmum requred capacty b multples a protectng factorα. The mnmum requred capacty of flow s the mnmum capacty need to reserved for flow to satsfy ts QoS requrement. That s, the capacty to make flow s QoS acceptable n the assumpton that no channel error occurs. For real-tme servces, the QoS matrx s the tolerable delay of a packet. A real-tme flow wth traffc δ profle {δ, λ, D}, the mnmum requred capacty s max(, λ ). For non-real-tme servces, the QoS matrx s the average throughput. A non-real-tme flow j wth traffc profle λj, the mnmum requred capacty s λj. Thus, b s calculated as follows: D b δ max(, λ), S = D λ, SNRT RT (5.7) The purpose of protectng factor α s to expand the protected capacty of flow by multplyng the mnmum requred capacty by a number larger than or equal to 1. The larger the protectng

22 Introducton to Packet Schedulng Algorthms for Communcaton Networks 283 debt_allocaton_procedure(remaned_slot){ for(each flow j) block 0; for(each vrtual queue, from the hghest prorty to the lowest prorty){ } } whle(packets not checked and not scheduled n the vrtual queue){ the flow the packet belong to; l the sze of the packet; f( remaned _ slot L + l L and block!=1){ schedule the packet n the next frame; debt -1* max( t l, l) ; t = l; _ = + remaned slot L l L ; for(all real-tme flows k){ wk * debt tk = max( tk +, Tk) ; w j RT j } } else block 1; /* the other packet of flow s also skpped n ths procedure */ } Fg. 5.6 The pseudo code of debt allocaton procedure factor, the larger the protected capacty. It mples that provdng a flow more protecton by gvng t more resource than t requred to compensate the loss due to wreless channel error. The tunng of protectng factors s also mportant and closely relatve to system performance. If the protectng factor of a flow s too large, t may be unfar to other flows and also cause waste of resource, whch wll be harmful to overall system performance. In our scheme, we set the protectng factors of real-tme flows to 1, and set the protectng factors of non-real-tme flows to a number slghtly larger than 1, for example, Snce n our token-based scheduler, we gve real-tme flows more opportunty to ncrease ther token value than that of non-real-tme flows by allocatng all the debt to real-tme flows. So we compensate nonreal-tme flows by regulatng ther protectng factors to be larger than that of real-tme flows. Addtonally, settng the protectng factor of real-tme flows to 1 means the protected capacty of a real-tme flow s the same as ts mnmum requred capacty. It brngs benefts to dfferentate the flows wth good channel status and the flows wth bad channel status. Because when a flow suffers burst error, t wll use more capacty than ts mnmum requred, so t soon runs out of ts token value, and other real-tme flows n good channel status get addtonal token value. It makes the real-tme flows n good channel status has hgher prorty to be transmtted, and mprove the effcency of the use of system resource.

23 284 Communcatons and Networkng In many real stuatons, we may degrade some resource sharng of non-real-tme flows to make the system to accommodate more real-tme flows. That s, satsfy more real-tme users at the cost of some average throughput of non-real-tme servces. We can acheve ths by boundng the sum of the token generatng rate of non-real-tme flows. When the sum of the token generatng rate of all non-real-tme flows exceeds a defned value N max, the token generatng ratse of all non-real-tme flows degrade proportonally to make ther sum not larger than N max. Thus, the sum of the token rate of all non-real-tme flows N can be represented as N = mn( N, ( α * b )) (5.8) max S and the token rate of a non-real-tme flow can be calculated as NRT r = N * b S NRT b (5.9) The weghtng factor s for ndcatng the resource allocaton of the WFQ n the frst stage of our scheme. The WFQ emulates a work-conservng system wth error-free channel. The weghtng factor of flow s proportonal to ts protected capacty dvded by ts protectng factor. That s, w r α = for all flow (5.10) r j α j j 5.3 PF schemes for OFDMA systems Recently, for the hgher rate data transmsson, nterest n wreless communcatons has shfted n the drecton of broadband systems such as multcarrer transmsson systems such lke the OFDMA system. There has been a growng nterest n defnng rado resource allocaton for a physcal layer based on the OFDMA technology for 4G cellular system. Whle throughput optmal schedulng can be acheved by usng the mult user dversty effect, t can generate unfarness as users wth bad channel condtons have a lower probablty to get a resource. Based on the defnton of the standard PF schedulng scheme [45], the theorem of the modfed PF schedulng for mult-carrer transmsson systems was proposed n [40]. Notce that the proof of ths theorem s omtted and can be referred to [40]. Theorem: A schedulng P s proportonal far for a multcarrer transmsson system, f and only f, for any feasble schedulng S, t satsfes: r k, k C P = arg max 1 S +, U ( T 1) R

24 Introducton to Packet Schedulng Algorthms for Communcaton Networks 285 where U s the set of selected users by S, C s the set of carrers allocated to user, r k, s the nstantaneous transmttable data rate of carrer k C at the current slot, R s the average rate of user at the prevous slot, and T s the average wndow sze. Wth OFDMA, there are multple transmsson channels that can be used, where schedulng schemes consderng the PF algorthms have wdely been studed n many papers. See, for example, [ ]. Papers [39] and [42] had proposed heurstc approaches by smply applyng PF of the sngle carrer case n each subcarrer to adapt for the mult carrer case n a suboptmal manner. Addtonal the QoS requrement for each user was consdered n [41]. Furthermore, readers are suggested to refer to [43-44] for more complete nvestgaton of related modfed PF schemes n mult-carrer systems. 6. Summary and the dscusson of open ssues Packet schedulng s one of most mportant rado resource management functons. It s responsble for determnng whch packet s to be transmtted such that the resources are fully utlzed. The desgn of an effcent algorthm to be used for the schedulng of packet transmssons n wreless communcaton networks s a stll a open ssue for research. Ths Chapter has wdely covered the conceptual descrpton of many representatve packet schedulng algorthms deployed n hgh-speed pont-to-pont wrelne and wreless scenaros. Well desgnng algorthms wth low complexty offerng farness among and potentally dfferentaton between dfferent data-flows s mportant n the evoluton of communcaton networks. The rapdly growng demand of network nodes capable of takng nto account the dfferent QoS requrements of dfferent flows to better utlze the avalable resources at the same tme as some degree of farness s mantaned, makes more ntellgent packet schedulng a central topc n future development of communcaton technologes. 7. Acknowledgement The authors wsh to express ther sncere apprecaton for fnancal support from the Natonal Scence Councl of the Republc of Chna under Contract NSC E References [1] A. Parekh, R. G. Gallager, A generalzed processor sharng approach to flow control n ntegrated servces networks: The sngle-node case, IEEE/ACM Trans. on Networkng, Vol. 1, June 1993 [2] A. Parekh, R. G. Gallager, A generalzed processor sharng approach to flow control n ntegrated servces networks: The multple-node case, IEEE/ACM Trans. On Networkng, Vol. 2, Aprl 1994 [3] R. Cruz, Qualty of Servce Guarantees n Vrtual Crcut Swtched Networks, IEEE J. Select. Areas Commun., Specal ssue on Advances n the Fundamentals of Networkng, August, [4] A. Demers, S. Keshav, and S. Shenkar, Analyss and smulaton of a far queueng algorthm, Internet. Res. Amd Exper., vol. 1, 1990 [5] D. Ferarr, Real-tme communcaton n an nternetwork, J. Hgh Speed Networks, vol. 1, no. 1, pp ,

25 286 Communcatons and Networkng [6] D. Ferrar and D. Verma. A scheme for real-tme channel establshment n wde-area networks, IEEE Journal on Selected Areas n Communcatons, 8(3): , Aprl [7] J. R. Pney, S. Sallent, Performance Evaluaton of a Normalzed EDF Servce Dscplne, n Proc. IEEE MELECON 2004, Dubrovnk, Croata, May 2004 [8] S. Chaudhry, and A. Choudhary, Tune dependent prorty schedulng for guaranteed QoS Systems, n Proc. Sxth Internatonal Conference on Computer Communcatons and Networks, pp , Sept [9] L. Georgads, R. Guern, A. Parekh, Optmal multplexng on a sngle lnk: delay and buffer requrements, IEEE Trans. On Informaton Theory, 43(5), pp , Sep [10] K. Za, Y. Zhang, Y. Vnots, Achevng end-to-end delay bounds by EDF schedulng wthout traffc shapng, n Proc. Infocom 01, 2001 [11] V. Svaraman, F. M. Chuss, Maro Gerla, End-to-End Statstcal Delay Servce under GPS and EDF Schedulng: A Comparson Study, n Proc. Infocom 01, 2001 [12] H. Zhang, Servce dscplnes for guaranteed performance servce n packet-swtchng networks, Proceedngs of the IEEE, vol. 83, No. 10, Oct [13] J. Lebeherr, D. Wrege and D. Ferrar, Exact admsson control n networks wth bounded delay servces, IEEE/ACM Trans. Networkng, vol. 4, pp , [14] S. Lu and V. Bharghavan, Far Schedulng n Wreless Packet Networks, IEEE/ACM Trans. Neetworkng, vol. 7, no. 4, pp , [15] Y. Cao, and VICOR O. K. L, Schedulng Algorthms n Broad-Band Wreless Networks, Proceedngs of the IEEE, Vol. 89, No. 1, Jan [16] F. Tsou, H. Chou, and Z. Tsa, WDFQ: An Effcent Traffc Scheduler wth Far Bandwdth Sharng for Wreless Multmeda Servces, IEICE TRANS. COMMUNICATIONS, Vol. E00-A, No. 1, Jan [17] T. S. Eugene Ng, I. Stoca, and H. Zhang, Packet Far Queueng Algorthms for Wreless Networks wth Locaton-Dependent Errors, n Proc. INFOCOM 98, Mar. 1998, pp [18] J. Gomez, A. T. Campbell, and H. Morkawa, The Havana Framework for Supportng Applcaton and Channel Dependent QOS n Wreless Networks, n Proc. Seventh Internatonal Conference on Network Protocols, [19] T. E. Koldng, K. I. Pedersen, J. Wgard, F. Frederksen, and P. E. Mogensen, "Hgh Speed Downlnk Packet Access: WCDMA Evoluton," IEEE Vehcular Technology Socety News, February 2003, pp [20] P. Vswanath, D. Tse, and R. Laroa, Opportunstc beam formng usng dumb antennas, IEEE Transactons on Informaton Theory, vol. 48, no. 6, June [21] D. Tse, Multuser dversty n wreless networks, Wreless Communcaton Semnar, Stanford Unversty, Aprl [22] J. M. Holtzman, Asymptotc analyss of Proportonal Far algorthm, IEEE Proc. Personal Indoor Moble Rado Communcatons (PIMRC), September 2001, pp [23] T. E. Koldng, Lnk and system performance aspects of Proportonal Far schedulng n WCDMA/HSDPA, Proceedngs of 58th IEEE Vehcular Technology Conference (VTC), Florda USA, October 2003, pp [24] "Gudelnes for the evaluaton of rado transmsson technologes for IMT-2000," Recommendaton ITU-R M.1225,

26 Introducton to Packet Schedulng Algorthms for Communcaton Networks 287 [25] A. Jalal, R. Padovan, and R. Pankaj, Data throughput of CDMA-HDR a hgh effcency-hgh data rate personal communcaton wreless system, n Proc. IEEE. Veh. Technol. Conf. Sprng, Tokyo, Japan, May 2000, pp [26] S. Borst, User-level performance of channel-aware schedulng schemes n wreless data networks, IEEE INFOCOM, Mar. 2003, vol. 1, pp [27] A. Jalal, R. Padovan, and R. Pankaj, Data throughput of CDMA-HDR a hgh effcency-hgh date rate personal communcaton wreless system, n Proc. IEEE VTC, May 2000, pp [28] M. Kazm and N. Wberg, Schedulng schemes for HSDSCH n a WCDMA mxed traffc scenaro, n Proc. IEEE Int. Symp. PIMRC, Bejng, Chna, Sep. 2003, pp [29] J. M. Holtzman, "Asymptotc Analyss of Proportonal Far Algorthm", IEEE Internatonal Symposum on Personal, Indoor and Moble Rado Communcatons, Vol. 2, October 2001 [30] L. Erwu, and K. K. Leung, "MAC Proportonal Far Schedulng: Analytcal Insght under Raylegh Fadng Envronment", IEEE Wreless Communcatons and Networkng Conference, Aprl 2008 [31] P. Vswanath, D. N. C. Tse, and R. Laroa, "Opportunstc Beamformng usng Dumb Antennas", IEEE Transactons on Informaton Theory, Vol. 48, Issue 6, June 2002 [32] P. Mueng, W. Ychuan, and W. Wenbo, "Jont an Advanced Proportonally Far Schedulng and Rate Adaptaton for Mult-servces n TDD-CDMA Systems", IEEE 59th Vehcular Technology Conference, Vol. 3, May 2004 [33] K. Kuenyoung, K. Hoon, and H. Youngnam, "A Proportonally Far Schedulng Algorthm wth QoS and Prorty n 1xEV-DO", IEEE Symposum on Personal, Indoor and Moble Rado Communcatons, Vol. 5, September 2002 [34] O. S. Shn, and K. B. Lee, "Packet Schedulng over a Shared Wreless Lnk for Heterogeneous Classes of Traffc", IEEE Internatonal Conference on Communcatons, Vol. 1, June 2004 [35] J. A.C. Bngham, Mult carrer modulaton for data transmsson: an dea whose tme has come, IEEE Communcatons Magazne, pp. 5-14, May [36] J. Jang and K. Lee, Transmt power adaptaton for multuser OFDM systems, IEEE Journal on Selected Areas n Communcatons, 21(2): , Feb [37] Y. J. Zhang and K. B. Letaef, Multuser adaptve subcarrer-and bt allocaton wth adaptve cell selecton for OFDM systems, IEEE Transactons on Wreless Communcatons, 3(4): , Sept [38] Z. Shen, J. G. Andrews, and B. L. Evans, Adaptve resource allocaton for multuser OFDM wth constraned farness, IEEE Transactons on Wreless Communcatons, 4(6): , Nov [39] W. Anchun, X. Lang, Z. Shdong, X. Xbn, and Y. Yan, Dynamc resource management n the fourth generaton wreless systems, n Proc. ICCT, vol. 2, Aprl 2003, pp [40] H. Km and Y. Han, A proportonal far schedulng for multcarrer transmsson systems, IEEE Communcatons Letters, vol. 9, no. 3, pp , March [41] Y. Lu, C. Wang, C. Yn,and G. Yue, Downlnk schedulng and rado resource allocaton n adaptve OFDMA wreless communcaton system for user-ndvdual QoS, Internatonal Journal of Electrcal, Computer, and Systems Engneerng

27 288 Communcatons and Networkng [42] N. Ruangchajatupon and Y. J, Smple proportonal farness schedulng for OFDMA frame-based wreless system, IEEE WCNC 2008 [43] M. Kaneko, P. Popovsk, and J. Dahl, Proportonal farness n mult carrer system wth mult slot frames: upper bound and user multplexng algorthms, IEEE Transactons Wreless Communcatons, vol. 7, no. 1, January 2008 [44] N. Ruangchajatupon and Y. J, Proportonal farness wth mnmum rate guarantee schedulng n a multuser OFDMA wreless network, ACM IWCMC, Lepzg, Germany, 2009 [45] F. P. Kelly, A. K. Maulloo, and D.K.H. Tan., Rate control n communcaton networks: shadow prces, proportonal farness and stablty, J. of the Operatonal Research Socety, vol.49, pp , Aprl [46] T.-Y. Tsa and Z. Tsa, Desgn of a packet schedulng scheme for downlnk channel n IEEE BWA systems, IEEE WCNC [47] IEEE e-2005, IEEE Standard for Local and Metropoltan Area Networks Part 16: Ar Interface for Fxed and Moble Broadband Wreless Access Systems Amendent for Phscal and Medum Access Control Layers for Combned Fxed and Moble Operaton n Lcensed Bands, Dec. 7,

28 Communcatons and Networkng Edted by Jun Peng ISBN Hard cover, 434 pages Publsher Scyo Publshed onlne 28, September, 2010 Publshed n prnt edton September, 2010 Ths book "Communcatons and Networkng" focuses on the ssues at the lowest two layers of communcatons and networkng and provdes recent research results on some of these ssues. In partcular, t frst ntroduces recent research results on many mportant ssues at the physcal layer and data lnk layer of communcatons and networkng and then brefly shows some results on some other mportant topcs such as securty and the applcaton of wreless networks. In summary, ths book covers a wde range of nterestng topcs of communcatons and networkng. The ntroductons, data, and references n ths book wll help the readers know more abut ths topc and help them explore ths exctng and fast-evolvng feld. How to reference In order to correctly reference ths scholarly work, feel free to copy and paste the followng: Tsung-Yu Tsa, Yao-Lang Chung and Zsehong Tsa (2010). Introducton to Packet Schedulng Algorthms for Communcaton Networks, Communcatons and Networkng, Jun Peng (Ed.), ISBN: , InTech, Avalable from: InTech Europe Unversty Campus STeP R Slavka Krautzeka 83/A Rjeka, Croata Phone: +385 (51) Fax: +385 (51) InTech Chna Unt 405, Offce Block, Hotel Equatoral Shangha No.65, Yan An Road (West), Shangha, , Chna Phone: Fax: