Comparisons of Packet Scheduling Algorithms for Fair Service among Connections on the Internet

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1 Comparsons of Packet Schedulng Algorthms for Far Servce among Connectons on the Internet Go Hasegawa, Takahro Matsuo, Masayuk Murata and Hdeo Myahara Department of Infomatcs and Mathematcal Scence Graduate School of Engneerng Scence, Osaka Unversty -3, Machkaneyama, Toyonaka, Osaka , Japan Phone: , Fax: E-mal: Abstract We nvestgate the performance of TCP under three representatves of packet schedulng algorthms at the router. Our man focus s to nvestgate how far servce can be provded for elastc applcatons sharng the lnk. Packet schedulng algorthms that we consder are FIFO (Frst In Frst Out), RED (Random Early Detecton), and DRR (Defct Round Robn). Through smulaton and analyss results, we dscuss the degree of acheved farness n those schedulng algorthms. Furthermore, we propose a new algorthm whch combnes RED and DRR algorthms n order to prevent the unfarness property of the orgnal DRR algorthm, whch appears n some crcumstances where we want to resolve the scalablty problem of the DRR algorthm. In addton to TCP Reno verson, we consder TCP Vegas to nvestgate ts capablty of provdng the farness. The results show that the prncpleof TCP Vegas conformsto DRR, but t cannot help mprovng the farness among connectons n FIFO and RED cases, whch seems to be a substantal obstacle for the deployment of TCP Vegas. Keywords Farness, FIFO (Frst In Frst Out), RED (Random Early Detecton), DRR (Defct Round Robn), TCP (Transmsson Control Protocol) I. INTRODUCTION The conventonal Internet has only been provdng the best effort servce, and t could not offer throughput and/or delay guarantees. It s also lack of farness guarantees; TCP connectons sometmes receve unfar performance n terms of, e.g., throughput. See, e.g., []. However, we now need to provde commercal network servces by the Internet. That s, a new servce should be avalable wthn the network to support the dfferentated servces among the users []. Along wth the context of dff-serv models, several servce prncples have recently been proposed; for example, a constant throughput may be preferred to some connectons, or QoS support s necessary for real tme applcatons. For example, n [3], the authors have proposed an Explct Capacty framework for allocatng the network capacty to users n a controlled way even durng congeston perods. Another mportant servce that the next generaton Internet should support s far allocaton of the bandwdth, whch s our man subject of ths paper. It s one of most desred features for elastc applcatons, but not supported by the current Internet, and we beleve that t may be more mportant even than network effcency. A one exstng servce found n the lterature s the USD (User Share Dfferentaton) scheme descrbed n [4], where users are provded dfferent servce qualtes from ISPs (Internet Servce Provders) based on the contracts. However, the authors n [4] do not provdea quanttatve evaluaton of USD to show how the users are dfferentated. One promsng way to realze the servce dfferentaton for the elastc applcatons seems to be DRR (Defct Round Robn) presented n [5] where the round robn schedulng s performed among actve connectons. In [5], an extensve evaluaton of the DRR algorthm s provded, but they assume Posson arrvals of packets from each connecton. That s, the authors do not consder the behavor of the upper layer protocol,.e., TCP (Transmsson Control Protocol). In ths paper, we focus on the degree of farness provded to TCP connectons by comparng three packet schedulng algorthms at the router. The frst one s FIFO (Frst In Frst Out, or Drop Tal), whch s wdely used n the current Internet routers because of ts smplcty. The second s RED (Random Early Detecton) [6], whch drops ncomng packets at a certan probablty. Whle the orgnal dea of the RED algorthm s to avod consecutve droppng of packets belongng to the same connecton, t also has a capablty of achevng a far servce among connectons by spreadng packet losses. The last one s DRR, whch s a more aggressve one n the sense that t actvely mantans per flow queueng for establshng far servce. For TCP, we consder the Reno verson, whch has wdely been used n the current Internet. The Vegas verson [7], adoptng a dfferent congeston control mechansm from TCP Reno for larger performance gan, s also consdered. In ths paper, for reference purposes, we wll frst show smulaton results that FIFO cannot provde farness among connectons at all because of a bursty nature of packet losses (see Subsecton III-A). It s next shown that RED offers better farness than FIFO to TCP Reno connectons, but t cannot keep a good farness when the capacty of shared lnk becomes small compared wth the total nput lnk capacty (Subsecton III-B). In TCP Vegas, on the other hand, RED offers less farness than FIFO because of the essental ncompatblty of TCP Vegas to the RED algorthm (Secton IV). The packet schedulng algorthms and TCP versons that we wll use n ths paper are not new. Our man contrbutons n the current paper s that the propertes mentoned above are also shown through analytcal results. Whle the model used n the analyss s very smple, the basc features of the above schedulng algorthms can be well explaned. From the analyss results, we further propose the enhanced verson of RED algorthm, where we set each connecton s packet droppng probablty dependently on ts nput lnk capacty, to avod the unfarness property of the orgnal RED algorthm. Another enhancement method of RED can be found n [8], where the flow state are mantaned for some degree of farness enhancements.

2 The above method can be used to resolve an nherent problem of the DRR algorthm. DRR can provde almost perfect farness among connectons n both cases of TCP Reno (Subsecton III-C) and Vegas (Subsecton IV-C), but DRR requres per flow queueng. Snce we manly consder the ISP model, we may not need to consder the stateless far queueng mechansm such as the one found n [?]. However, DRR has a scalablty problem n that as the number of subscrbers grows, the larger number of queues becomes necessary. One possble soluton s flow aggregaton whch treats several connectons as a sngle flow of DRR. However, t results n that the farness property of DRR becomes lost when multple TCP connectons are assgned to the same queue. Based on our analytcal results, we last apply the RED mechansm to each queue of DRR (called DRR+) for farness enhancement. We show that our DRR+ can provde a reasonably good farness even compared wth DRR through the smulaton results (Subsecton III-D). For the dscussons above, we use the network model where the uplnk of the access lne of ISP s shared by the subscrbers wth dfferent capactes. The effect of the reverse traffc s also consdered by the model where the downlnk s shared by the subscrbers. Although we wll not show the results due to space lmtaton, we have found that our analyss results n ths paper can be appled to the reverse traffc model wthout any modfcaton. The smlar model s treated n [9], but we consder RED and DRR as the packet schedulng algorthm n addton to the FIFO algorthm employed n [9]. Further, we devote the farness aspects of packet schedulng algorthms whch are not consdered n [9]. Ths paper s organzed as follows. In Secton II, we descrbe the model treated n Secton III and IV. The packet schedulng algorthms s frst summarzed n Subsecton II-A. We wll also explan the congeston control algorthm of TCP Reno and TCP Vegas by focusng on those congeston avodance mechansms n Subsecton II-B. In Subsecton II-C, we explan the network model we wll use n analyss and smulaton, and ntroduce the farness measure consdered n ths paper n Subsecton II-D. In Secton III, we evaluate the packet schedulng algorthms descrbed n Secton II-A n the case of TCP Reno through the smulaton and the analyss, and propose DRR+ for farness mprovement. We next consder the case of TCP Vegas n Secton III. Fnally, we present some concludng remarks and future works n Secton V. II. THE MODEL A. Packet Schedulng Algorthms In what follows, we brefly summarze the three packet schedulng algorthms, FIFO, RED and DRR for the current paper to be self contaned. A FIFO algorthm s wdely used n the current Internet routers because of ts smple mplementaton. The ncomng packets are accepted n order of arrvals. When the buffer at the router becomes full, arrvng packets are dropped. Therefore, packets belongng to a partcular connecton can sometmes suffer from bursty packet losses. Then, fast retransmt [] mplemented n TCP does not work effectvely. It s also lkely to ntroduce bursty transmsson of packets [6], whch often results n further packet losses. The problem mentoned above s solved by RED [6]. The RED algorthm s desgned to cooperate wth congeston control mechansms provded n TCP. In RED, the router observes the avarage queue sze (buffer occupancy), and the packets arrvng at the router are dropped wth a certan probablty. The DRR algorthm [5] s an extenson of the round robn algorthm to be sutable to treat the varable szed packets. The buffer at the router s logcally dvded nto multple queues. The arrvng packets of each connecton are stored n the pre-assgned queue by usng a hash functon, and those are served n a round robn fashon. A dfference from the pure round robn algorthm s that the packets wth varable length can be allowed to keep the farness among connectons. In DRR, the bandwdth not used n the round s preserved to be used n the next round f the packet s too large to be served n the current round. B. Congeston Control Mechansms of TCP In ths paper, we consder two versons of TCP; Reno and Vegas. TCP Reno s wdely used n the current Internet. TCP Vegas s a recently proposed one n [7]. In TCP Reno, the wndow sze cwnd (congeston wndow sze) s cyclcally changed. cwnd contnues to be ncreased untl segment loss occurs. TCP Reno has two phases n ncreasng cwnd; Slow Start Phase and Congeston Avodance Phase. When an ACK segment s receved by TCP at the server sde at tme t + t A [sec], cwnd(t +t A ) s updated from cwnd(t) as follows (see, e.g., []); cwnd(t + t A ) = cwnd(t) +, f cwnd(t) < ssth; cwnd(t) + cwnd(t), f cwnd(t) ssth; () where ssth [segments] s the threshold value at whch TCP changes ts phase from Slow Start Phase to Congeston Avodance Phase. When segment loss s detected by tmeout or fast retransmsson algorthm [], cwnd(t) and ssth are updated as ssth = cwnd(t)/; cwnd(t) = ssth In TCP Reno (and the older verson Tahoe), the wndow sze, cwnd, contnues to be ncreased untl segment loss occurs due to congeston. Then, the wndow sze s throttled, whch leads to the throughput degradaton of the connecton. However, t cannot be avoded because of an essental nature of the congeston control mechansm adopted n TCP Reno. That s, t can detect network congeston only by segment loss. However, throttlng the wndow sze s not adequate when the TCP connecton tself causes the congeston because of ts too large wndow sze. If cwnd s approprately controlled such that the segment loss does not occur n the network, the throughput degradaton due to the throttled wndow can be avoded. Ths s the reason that TCP Vegas was ntroduced. TCP Vegas employs another mechansm, n whch t controls cwnd by observng changes of RTTs (Round Trp Tme) of segments that the connecton has sent before. If observed RTTs become large, TCP Vegas recognzes that the network begns to be congested, and throttles cwnd down. If RTTs become small, on the other hand, TCP Vegas determnes that the network s

3 Source Source Source N bw bw bw N FIFO/RED/DRR queue τ BW Destnaton We note that other defntons of the farness can be consdered. A more natural defnton may be the functon of subscrpton fees, whch may be determned by (but not be proportonal to) the nput lnk capacty n the ISP model. We wll not treat such a case for smplcty of presentaton, but t s not dffcult to ncorporate t. For example, the weght factor s allowed to be arbtrary n the DRR case. The RED case can also be treated n ths context by utlzng our analyss presented later. Fg.. Network model releved from the congeston, and ncreases cwnd agan. Then, cwnd n an deal stuaton becomes converged to the approprate value. In Congeston Avodance Phase, the wndow sze s updated as; cwnd(t + t A ) = α cwnd(t) +, f dff < base rtt α cwnd(t), f base rtt dff β base rtt () β cwnd(t), f base rtt < dff dff = cwnd(t)/base rtt cwnd(t)/rtt where rtt [sec] s an observed round trp tme, base rtt [sec] s the smallest value of observed RTTs, and α and β are some constant values. Note that Eq. () used n TCP Vegas ndcates that f RTTs of the segments are stable, the wndow sze remans unchanged. C. Network Model Recallng that our man purpose of the current paper s to nvestgate the farness aspect of packet schedulng algorthms, we wll use a smple network model as depcted n Fgure. There are the number N of connectons between N sources (SES, SES,..., SES N ) and one destnaton (DES). N connectons share the bottleneck output lnk of the router. The capacty of the nput lnk between the sources and the router are defned as bw, bw,..., bw N Kbps, and that of the output lnk between the router and destnaton s BW Kbps. We assume bw bw... bw N. By the above model, we ntend to consder the uplnk of the access lne of the ISP, whch s shared by the subscrbers wth dfferent capactes. In the followng numercal examples throughoutthe paper, the propagaton delay between SES and DES, τ, s dentcally set to be msec. The buffer sze of the router s 6 Kbytes. A TCP packet sze s fxed at Kbytes. Every sender s assumed to be a greedy source, that s, t has nfnte packets to transmt. We also assume that n the case of DRR, the connecton can be dentfed by the router so that the packets from the connecton can be approprately queued at the per flow buffer at the router. D. Defnton of Farness We defne the far servce by takng account of the nput lnk capacty. Its smplest form s that the throughput s gven n proporton to ts nput lnk capacty under the condton that the output lnk capacty s smaller than total of the nput lnk capactes. That s, we say that a good farness s acheved f the throughput of connecton, ρ, s gven as ρ = BW bw j bw j III. THE CASE OF TCP RENO In ths secton, we consder TCP Reno to nvestgate the farness property of three packet schedulng algorthms. In addton to the smulaton results, we develop the analyss result for the RED schedulng algorthm. The analyss results supports observatons on the farness property of the RED algorthm obtaned from the smulaton results. We then nvestgate DRR to demonstrate ts effectveness through smulaton experments. In what follows, we set four TCP connectons whch have dfferent capactes of 64, 8, 56 and. The output lnk capacty s vared from 4 Kbps to 96 Kbps to nvestgate the effect of the output lnk capacty on farness. In the smulaton results, we smulated 5, sec n each experment to obtan the result, whch approxmately corresponds to 3, packet generaton. A. FIFO Case We frst show the FIFO case n terms of the average throughput durng the smulaton run (Fgure (a)), the relatve throughput (Fgure (b)), and packet loss rate (Fgure (c)) for all connectons as a functon of the output lnk capacty. Relatve throughput means the rato of the average throughput aganst the nput lnk capacty. When all connectons have dentcal relatve throughput, t s sad that the router perfectly provdes far servce among connectons n our defnton. In Fgure (a), the sold lne labelled total shows the total throughput of four connectons. From Fgures (a) and (b), t s clear that farness cannot be kept at all. In some regon where the output lnk capacty s small, the throughputof the connecton wth smaller nput lnk capacty s larger even than that of the connecton wth larger nput lnk capacty. It can be explaned as follows. In the FIFO algorthm, packet loss occurs ndependently of the packet arrval rate as shown n Fgure (c), and the packet loss becomes bursty. Snce the connecton wth larger nput lnk capacty experences a hgher degree of burstness of packet losses, ts performance degradaton becomes larger. B. RED Case B. Smulaton Results We next nvestgate the RED case. Recallng that the buffer sze of the router s set to be 6 Kbyte, we set th mn = Kbytes, th max = 3 Kbytes and p =. n smulaton. p shows the packet droppng probablty defned n RED, wth whch ncomng packets are dropped when the avarage queue length s over the threshold th mn. Fgure 3 shows smulaton results of the RED algorthm n that case. By comparng the total lne n Fgures 3(a) and (a), t can be observed that the RED algorthm can attan hgher total throughput than that of the FIFO algorthm because RED can avod bursty packet losses by droppng

4 Throughput [Kbps] (a) Average throughput Relatve Throughput Optmal (b) Relatve throughput Packet Loss Rate (%) (c) Packet loss rate Fg.. FIFO case wth TCP Reno Throughput [Kbps] Relatve Throughput Optmal Packet Loss Rate (%) (a) Average throughput (b) Relatve throughput (c) Packet loss rate Fg. 3. RED case wth TCP Reno arrvng packets wth probablty p, whch results n that TCP s fast retransmt algorthm works effectvely. However, f we focus on the farness, t s clear that an mprovement s very lmted. It s especally true when the output lnk capacty s small; the throughput of all connectons becomes almost dentcal (Fgure 3(a)). Also, the packet loss rates of all connectons are almost equal as shown n Fgure 3(c). Of course, ths s one of key features that the RED algorthm ntends; the number of the lost packets of each connecton can be kept n proporton to ts nput lnk capacty by ts mechansm. The problem s that t leads to the unfarness treatment of connectons wth dfferent capactes. The above result s just one example. Also, t s questonable whether smulaton tme of 3, packets generaton s adequate or not for examnng the farness degree. To examne ts generalty, we next show the analyss of the RED algorthm. Through analyss, t s proven that the unfarness observed n smulaton s nherent n the RED algorthm. B. Analyss Results and Dscussons We assume n the followng analyss that there are N connectons n the network (Fgure ) wth the nput lnk capactes of bw, bw,..., bw N [packets/sec], where bw bw,..., bw N. We denote the packet droppng probablty of the RED algorthm by p, and the propagaton delay between sources and the destnaton by τ. We also assume that the average queue length s always larger than th mn, that s, all arrvng packets are dropped wth probablty p. For analyss, we focus on TCP s typcal cycle of the wndow sze as shown n Fgure 4; the cycle begns at the tme when the prevous packet loss occurs, and termnates when the next packet loss occurs. We consder that the cycle begns at tme t = [sec]. We do not take account of the slow start phase [] snce the objectve of the RED algorthm s essentally Wndow Sze Wmax W a Wmax/ cwnd (t) /RTT cycle T Fg. 4. TCP s cyclcally change of the wndow sze to avod fallng nto that phase. tme for connecton Snce all arrvng packets are dropped at the router wth probablty p by our assumpton, the connecton can send /p packets n one cycle (between the events of packet losses). We defne the number of packets transmtted durng one cycle as N p, that s, N p = /p. Durng the cycle, the wndow sze of connecton, cwnd (t) [packets], s ncreased lnearly snce we only consder the congeston avodance phase []. The wndow sze s halved when packet loss detected by fast retransmt, and therefore cwnd (t) s gven as cwnd (t) = W max + RTT t, N, (3) where RTT [sec] s an average round trp tme of packets for connecton, and W max [packets] s the value of the wndow sze at the tme when packet loss occurs. Then, the followng equaton for the total number of the packets n one cycle should be

5 Connecton ID W, W, W, W, W,N [segments], bw [sec] W,N [segments], bw [sec] W,N W,N W,N W,N [segments], bw [sec] Input Lnk Bandwdth bw bw bw BW of connectons whch send the segments smultaneously. For example, snce the number of connectons transmttng ther segments s n phase, the router processes segments of connectons at rate BW [segments/sec]. We denote the number of packets of connecton belongng to phase j by W,j [packets] (, j N). Snce all segments n the phase are dealt at the rate n proporton to ts nput lnk bandwdth, we determne W,N for phase N as follows; N N WN, WN,N [segments], bw [sec] N WN,N [segments], bw [sec] N bw N bw N W N,N = W a W,N = W N,N bw bw N, N. In the same manner, we can obtan all of W,j by solvng the followng equatons; N N Phase satsfed for connecton ; T Fg. 5. Analyss of the RED algorthm cwnd (t)dt = N p, N, (4) where T s the tme duraton of the cycle as shown n Fgure 4. From Eqs.(3) and (4), we can obtan W max [packets], the wndow sze at the tme when the next packet loss occurs, as W max = W max + N p (5) From Eq.(5), we can obtan W max [packets], the average value of W max by equatng W max and W max. That s, W max 8/(3p) (6) As a result, we derve W a [packets], the average wndow sze durng the cycle as; W a = (3/4) W max (7) See Fgure 4. From the equaton above, we can see that the change of the wndow sze does not depend on each connecton s nput lnk capacty, but on the packet droppng probablty of the RED algorthm. For further analyss, we make an assumpton that each connecton s wndow sze s fxed at the average value, W a. We then derve ρ, the throughput of connecton when W a packets of ts wndow are served at the router. To smplfy the analyss, we consder the stuaton where all connectons frst packets of the wndows arrve at the router smultaneously as shown n Fgure 5. In ths fgure, each square shows the burst of connecton s W a segments, and ts length represents the tme duraton bw [sec]. Snce all connectons have dfferent capactes bw on ther lnks, t takes dfferent tme duraton W a /bw for all packets of connecton to arrve at the router as llustrated n Fgure 5. That s, the segment burst of connecton s not served at the same rate, and t depends on the number of the connectons sendng smultaneously ther packets. We dvde all connectons packet burst nto N phases accordng to the number W j,j = W a k=j+ W j,k, j N, W,j = W j,j bw bw j, j N, j. The rate at whch the packets are served at the router n phase j, S j [packets/sec], must depend on the total capacty of the connectons of phase j. Snce, n phase j, all packets belongng to from connecton to connecton j are served at the router, S j s gven as; j BW, f bw k > BW, k= S j = (8) j bw j, otherwse k= Therefore, the throughput of connecton durng phase j, R,j, can be determned as follows; /( ) j W,j k= R,j = W,j j k= W S j = W k,j (9) k,j S j From Eqs.(8) and (9), ρ can be calculated as follows; ρ = k=n + ( ) W,j R,j W a () Although the RED algorthm can elmnate the bursty packet losses leadng to TCP s retransmsson tmeout expraton, tmeout expraton cannot be avoded perfectly []. Even f tmeout expraton rarely happens, the effect of tmeout expraton on throughput s large. Therefore, we next consder the throughput degradaton caused by retransmsson tmeout expraton. We denote the probabltyof occurrng tmeout expraton n the wndow by P to. We determne P to accordng to the followng smple equaton; ( ) P to = p ( p) + () = We assume that RTO [sec], the tmeout duraton for retransmsson, becomes twce RTT, the Round Trp Tme for connecton. RTT can be calculated by consderng the effect of the

6 Throughput [Kbps] Smulaton results 5Kbps 35 Analyss results Kbps 5 8Kbps 5 64Kbps Fg. 6. Accuraces of analyss result n TCP Reno Relatve Throughput K 8K. 56K 5K optmal Output Lnk Bandwdth (Kbps) Fg. 7. The effect of enhanced RED other connectons traffc; RTT = τ + k W a /BW + W a /ρ () From these results, we fnally have ρ, the throughputof connecton, by consderng the effect of TCP s retransmsson tmeouts; ρ = ( P to ) ρ + P to W a /ρ W a /ρ + RTO ρ = ρ W a + ( P to ) ρ RTO W a + ρ RTO (3) Eq. (3) s obtaned as follows. The frst term ( P to ) ρ represents the throughput wthout retransmsson tmeout, and the W second term a/ρ W a/ρ +RT O ρ s that wth retransmsson tmeout. By Eq. (3), we can TCP throughput of each connecton under RED algorthm, whch takes account of the throughput degradaton caused by TCP retransmsson tmeouts. Fgure 6 shows the throughput results from our analyss as a functon of the output lnk capacty. In the fgure, ponts represent the smulaton results (whch correspond to Fgure 3(a)), and the lnes show analyss results. We can observe from ths fgure that our analyss can gve good agreements wth smulaton results, and that the unfarness property of the RED algorthm n the case of small output lnk capacty can be observed. Ths unfarness can be explaned from the analyss result as follows. When the output lnk bandwdth becomes small, the rate at whch the packets are served at the router of phase j becomes BW n almost all the phases. It s clearly shown n Eq. (8). That s, packets arrvng at the router are served at rate BW, whch results n that the throughput of all connectons become equvalent. Furthermore, the connecton whose nput lnk bandwdth s larger can suffer from throughput degradaton caused by TCP retransmsson tmeouts. Ths s also the reason why the throughput of the connecton wth the 5 [Kbyte/sec] nput lnk bandwdth s largely degraded, whch can be explaned by Eq. (3). B.3 Enhancement to RED We last consder the enhancement to the RED algorthm (called enhanced RED) to avod ths unfarness by settng p dependently on each connecton s nput lnk capacty, accordng to the analyss results. We set p, whch s the packet droppng probablty of connecton, such that each connecton s throughput becomes proportonal to ts nput lnk capacty. The approprate values of p s are calculated for all connectons as follows.. Intalze p s.. Calculate ρ from the current p accordng to the analyss results. See Eq.(3). 3. If ρ s proportonal to the nput lnk capacty, set p to the current value. 4. If not, compare ρ wth the deal value, and adjust p of the connecton havng the largest dfference between ρ and the deal value. That s, If ρ s larger than the deal value, change p to a p. If ρ s smaller than the deal value, change p to b p. The values of control parameters a and b that we wll use n the followng smulaton are. and.9. In the enhanced RED algorthm, we calculate p s for all connectons accordng to the above algorthm. Fgure 7 shows the smulaton results on the relatve throughput of the enhanced RED algorthm. Compared wth Fgure 3(b), t s clear that our enhanced verson of the RED algorthm gves much better farness than the orgnal RED algorthm. In smulaton, however, we set the control parameter values of a and b ntutvely. It s a future research topc to seek an approprate method to determne those parameters. C. DRR Case As explaned n Subsecton II-A, the router buffer s logcally dvded nto several queues n DRR and each connecton s assgned ts own queue. We frst consder the case where the large buffer s equpped wth the router so that every connecton s gven a suffcent amount of buffer. In our model depcted Fgure 8, four DRR queues are formed n the router, and DRR parameters are set such that each DRR queue s served n proporton to the nput lnk capacty of the assgned connecton. Fgure (a) shows the smulaton results of relatve throughput. Dfferent from the FIFO (Fgure ) and RED (Fgure 3) algorthms, the DRR algorthm provdes very good farness among connectons even when the output lnk capacty s small. When the output lnk s large, on the other hand, the degree of the farness s slghtly degraded. It s because TCP s retransmsson tmeouts tends to frequently occur due to bursty packet loss at the queue snce the FIFO dscplne s used n each DRR queue. Then, the retransmsson tmeout degrades the performance more serously. Thus the degree of performance degradaton depends on the bandwdth delay product of the connecton. Furthermore, n the DRR algorthm, the capacty not used by a certan queue due to connecton s retransmsson tmeout can be used by other connectons. It ncreases the total throughput, but t s lkely to lead to the unfarness among connectons. Ths s

7 queue queue queue Round Robn Round Robn queue 3 queue queue 4 DRR Router Fg. 8. Suffcent buffer case DRR Router Fg. 9. Insuffcent buffer case Relatve Throughput Optmal (a) Suffcent buffer case Relatve Throughput Fg.. DRR case wth TCP Reno (b) Insuffcent buffer case why farness s degraded n the case of the large output lnk. Whle the DRR algorthm assgns the DRR queues to each connecton, several connectons should be assgned to one DRR queue as the number of connectons grows. It s because the number of DRR queues whch can be prepared must be lmted by the router buffer sze and processng overhead. However, the performance of the DRR algorthm n such a case has not been known. For nvestgatng such an nsuffcent buffer case, we assume that there are two queues and four connectons, and each connecton s assgned to the queue as shown n Fgure 9. The and connectons are assgned to one queue (queue n the fgure) and the and connectons to another queue (queue ). Each queue s assumed to be served n proporton to the total capacty of the assgned connectons. We show the smulaton results n the nsuffcent buffer case n Fgure (b) for the relatve throughput. The buffer szes of two queues are equvalently set to be 3 Kbytes. The lnes labeled total- and total- ndcate total throughput of two queues, queue and queue. Although each queue s served n proporton to the total capacty of the assgned connectons, the two connectons assgned to the same queue show unfar throughput. Ths s because we assumed that the arrvng packets are served accordng to a smple FIFO dscplne wthn the DRR queue. As descrbed n Subsecton III-A, the FIFO algorthm cannot keep farness among connecton at all. In ths subsecton, we have observed that the DRR algorthm gves much better farness than FIFO and RED algorthms, but ts farness property s sometmes lost as each connecton has dfferent capacty or when multple connectons are assgned to one DRR queue. We henceforth consder to mprove the farness property of the DRR algorthm n the next subsecton. D. DRR+ Case In the prevous subsecton, we have shown that the DRR algorthm has some unfarness property. The man reason was that each DRR queue serves packets by the FIFO dscplne. In ths subsecton, we show some smulaton results of DRR+, where the RED algorthm s appled to each DRR queue to prevent unfarness. In smulaton, we consder both suffcent/nsuffcent buffer case. Note that, n the nsuffcent buffer case, we apply the enhanced RED algorthm to two DRR queues depcted n Fgure 9. That s, n each queue, we set the assgned connectons packet droppng probabltes accordng to the enhanced RED algorthm n Subsecton III-B. Fgure shows the smulaton results on the relatve throughput. Our proposed method keeps good farness n the suffcent buffer case (Fgure (a)). Furthermore, when Fgure (b) s compared wth Fgure (b), the farness s sgnfcantly mproved even n the nsuffcent buffer case. IV. TCP VEGAS CASE In ths secton, we change the verson of TCP to TCP Vegas to nvestgate the farness property of three packet schedulng algorthms. TCP vegas conjectures the avalable bandwdth for the connecton, and therefore ts prncple s lkely to be well ft to the DRR algorthm. On the other hand, the RED algorthm does not help mprove the farness when TCP Vegas s employed snce each connecton s wndow sze s not domnated by the packet droppng probablty of the RED algorthm, but by the essental algorthm of TCP Vegas. The purpose of ths secton s to confrm the above observatons.

8 Relatve Throughput (a) Suffcent buffer case Relatve Throughput Fg.. DRR+ case wth TCP Reno 64K 8K 56K 5K optmal (b) Insuffcent buffer case Throughput [Kbps] (a) Throughput Relatve Throughput Optmal (b) Relatve throughput Wndow Sze [segments] e+6 Tme [msec] (c) Change of wndow szes Fg.. FIFO case wth TCP Vegas Throughput [Kbps] Relatve Throughput Optmal Number of Segment Losses (a) Throughput (b) Relatve throughput (c) Number of segment losses Fg. 3. RED case wth TCP Vegas A. FIFO Case Fgure plots smulaton results of the FIFO case usng TCP Vegas. Note that we omt the graph showng the number of packet loss snce no segment loss was observed at the FIFO buffer. Compared wth the TCP Reno case (Fgure ), t s clear that TCP vegas provdes less farness than TCP Reno. Especally, the connecton wth has smaller nput lnk bandwdth acheve almost % throughput (Fgure (b)). Ths unfarness property s caused by the essental characterstc of TCP Vegas. In TCP Vegas, no segment loss occurs at the router buffer f the network s stable, because the wndow sze of all connecton converges to certan values (Fgure (c)). In Fgure (c), t s notceable that the converged wndow sze s ndependent on each connecton s nput lnk bandwdth because base rtt of each connecton s almost equal (See Subsecton II-B). In the current smulaton settng, the converged wndow sze s enough large for connectons havng smaller nput lnk bandwdth to utlze ts bandwdth delay-product,but t s too small for connectons wth larger nput lnk bandwdth. Therefore, whle the result depends on the network envronment, TCP Vegas sometmes fals to acheve farness among connectons due to the essental nature of ts congeston control mechansm. B. The RED Case We next show the smulaton results of the RED case n Fgure. As n the case of TCP Reno (Subsecton III-B), the farness s slghtly mproved when compared wth the FIFO case (Fgure (b)). However, there stll be sgnfcant unfarness among connectons. Ths can be explaned by the throughput analyss presented n the below. In the followng analyss, we use the same notatons as those ntroduced n Subsecton III-B. At the moment, we consder the stuaton where no segment loss occurs at the router, and each connecton s wndowsze converges to a certan value. The packet droppng of the RED wll be consdered later. Let l [segments] be the number of connecton s segments n the router buffer, and L = l + + l N. Assume that each

9 connecton s throughput ρ [segments/sec] s proportonalto the avarage number of ts segments n the router buffer. Ths assumpton s reasonable when the FIFO dscplne s appled at the router buffer. Then, the followng equaton wth respect to ρ s satsfed; ρ = mn (bw, (l /L)BW ) (4) Accordng to the algorthm of TCP Vegas (Eq. ()), we obtan; α base rtt < W base rtt W rtt < β base rtt (5) base rtt = τ + /BW (6) rtt = τ + l /ρ (7) W = τρ + l = rtt ρ (8) where rtt [sec] and W [segments] are the RTT and the wndow sze of the connecton, respectvely. base rtt [sec] corresponds to base rtt of connecton, whch s the mnmum value of RTTs of the connecton. By substtutng Eqs. (6) (8) nto Eq. (5), we obtan the followng equaton; α + ρ /BW < l < β + ρ /BW (9) From Eq. (9), L (= l + + l N ) can be calculated as follows; Nα + Nα + j= j= ρ BW < l + + l N < Nβ + ρ BW < L < Nβ + j= ρ BW j= ρ BW Recallng that bw bw... bw N, Eq. (4) yelds { bw M ρ = (l /L)BW M + N () () Then, from Eqs. (9) (), we obtan ρ for M + N as follows; l M ρ = BW ρ, M + N () M j= L j= l Therefore, W, whch s the converged wndow sze of connecton, can be obtaned by substtutng Eq. (9) and Eq. () to Eq. (8). In the above dervaton, however, we do not take account of random segment losses adopted n the RED algorthm. We next consder the effect of throughput degradaton caused by probablstc segment loss of the RED algorthm. Although each connecton s wndow sze s controlled to be converged to a certan value n TCP Vegas, t s sometmes decreased by segment loss by the RED algorthm. We assume that the segment loss can be detected by the fast retransmt algorthm. Then, f the segment loss occurs after the wndow sze reaches W, the wndow sze s halved to W /. That s, f W / < τρ, the throughput s degraded untl the wndow sze reaches τρ. In Fgure 4, we defne one cycle to be the tme duraton between two segment losses caused by RED. One cycle s dvded nto three phases; phase, phase, and phase 3 as n Fgure 4. In phase, the wndow sze s ncreasng accordng to the TCP Vegas s algorthm, but the wndow sze s less than τρ. That s, the throughput s degraded by the segment loss durng phase. In phase, the wndow sze contnues to ncrease as n phase, but the wndow sze s larger than τρ and there s no throughput degradaton. In phase 3, the wndow sze reaches the converged value, whch s obtaned from Eq. (8). It remans unchanged untl the packet loss occurs at the end of ths phase. Let T [sec] and A [segments] be the tme duraton of phase, and the number of transmtted segments n phase, respectvely. Furthermore, we ntroduce ρ,j [segments/sec] as the avarage throughput of connecton durng phase j. In phase and phase, the rato of wndow sze ncreasng s /rtt [segments/sec] because the wndow sze s ncreased accordng to TCP Vegas s congeston avodance algorthm formulated by Eq. (). Therefore, ρ, s; ρ, = ( W + τρ )/ ( τ + ) ρ (3) Because there s no throughput degradaton n phase and phase 3, ρ, and ρ,3 are dentcal to ρ,.e., ρ, = ρ,3 = ρ (4) Snce the ncreased rate of wndow sze s /rtt [segments/sec], T and T can be calculated as follows; T = ( τρ W ) rtt (5) T = (W τρ ) rtt (6) A and A can also be calculated as follows; A = ( τρ + W ) ( τρ W ) (7) A = (W + τρ )(W τρ ) (8) In phase 3, the wndow sze s converged to W, and segment loss occurs at the router caused by the RED algorthm at the end of ths phase. Snce the avarage number of transmtted segments durng cycle s (/p), A 3 and T 3 can be obtaned as; A 3 = /p A A (9) T 3 = (A 3 /W ) rtt (3) Fnally, we can obtan ˆρ, the throughput of connecton from Eqs. (3) (6), (3) as follows; ˆρ = T ρ, + T ρ, + T 3 ρ,3 T + T + T 3 (3) Fgure 5 shows the result of the analyss as a functon of the output lnk capacty. Compare wth Fgure 6. Our analyss agan gves good agreements wth smulaton results, and t confrms the unfarness property of TCP Vegas when appled to the

10 Wndow Sze (segments) W τρ W/ phase Segment Loss phase Throughput Degradaton T T T3 Cycle phase 3 Tme (sec) Throughput [Kbps] 5 45 Smulaton results 4 35 Analyss results 5Kbps Kbps 8Kbps 5 64Kbps Relatve Throughput Optmal Fg. 4. Throughput degradaton wth RED segment loss Fg. 5. Accuraces of analyss result n TCP Vegas Fg. 6. DRR case wth TCP Vegas RED algorthm. In TCP Reno (Subsecton III-B), we could mprove the farness by settng p (the packet droppng probablty) dependently on each connecton s nput lnk capacty accordng to the analyss results. In TCP Vegas, however, we cannot apply t because the converged wndow sze s ndependent on p as shown n Eqs. (8). That s, we cannot control each connecton s throughput by p. Therefore, f we want to remove the unfarness property n the RED algorthm wth TCP Vegas, we may have to gve some modfcatons to the algorthm of TCP Vegas tself. Otherwse, we need to use the DRR algorthm as wll be presented n the next subsecton. C. The DRR Case Fgure 6 shows the case of DRR. It can be observed from the fgure that farness among connectons s farly good (Fgure 6), and better than TCP Reno case (Fgure (a)). Wth TCP Reno, some connectons could not utlze all amount of bandwdth assgned by the DRR mechansm due to segment loss. Wth TCP Vegas, on the other hand, no segment loss occurs at the router buffer, and then each connecton can completely utlze the bandwdth assgned by the DRR mechansm. However, as the number of connectons becomes large, the scalablty problem s ntroduced as havng been explaned n Subsecton III-C. In Subsecton III-D, we have succeeded to avod the unfarness by applyng the RED mechansm to each DRR queue. In the current case, however, we cannot apply t because of the essental ncompatblty of TCP Vegas to the RED algorthm as explaned n Subsecton IV-B. We need further nvestgaton on ths problem. V. CONCLUDING REMARKS In ths paper, we have evaluated the performance of the router packet schedulng algorthms for far servce among connectons through the smulaton and analyss. We have obtaned the followng results on TCP Reno verson; the FIFO algorthm cannot keep farness among connectons at all. The RED algorthm can mprove farness to some degree, but t fals to keep farness n the dfferent capacty case. The DRR algorthm offers better farness than the FIFO algorthm and the RED algorthm, but ts farness property s lost when each connecton has dfferent capacty and/or when multple connectons are assgned to one DRR queue. Accordngly, we have proposed the DRR+ algorthm, where the RED algorthm s appled to each DRR queue to prevent unfarness, and show that t can mprove farness among connectons n the dfferent capacty case. We have also nvestgated the effect of TCP Vegas, whch s expected to get hgher throughput than TCP Reno, and have made clear through the smulaton and analyss results that TCP Vegas cannot help mprovng the farness among connectons n FIFO and RED cases. TCP Vegas has a good feature to attan the better performance than TCP Reno, as dscussed n Secton IV. However, t fals to keep the good farness among connectons wth dfferent nput (and output) lne capactes. For TCP Vegas to be ntroduced n the future Internet where the RED algorthm s wdely deployed, the algorthm of TCP Vegas should be modfed to mprove the farness among connectons, whch s a future research topc. ACKNOWLEDGEMENTS Ths work was partly supported by Research for the Future Program of Japan Socety for the Promoton of Scence under the Project Integrated Network Archtecture for Advanced Multmeda Applcaton Systems. REFERENCES [] Go Hasegawa, Masayuk Murata, and Hdeo Myahara, Farness and stablty of the congeston control mechansm of TCP, Proceedngs of IEEE INFOCOM 99, March 999. [] Dffserv Home Page,,, [3] Davd D. Clark and Wenja Fang, Explct allocaton of best effort packet delvery servce, avalable at [4] Zheng ng, Toward scalable bandwdth allocaton on the nternet, On The Internet, pp. 4 3, May/June 998. [5] M. Shreedhar and George Varghese, Effcent far queung usng defct round robn, IEEE/ACM Transactons on Networkng, vol. 4, no. 3, pp , June 996. [6] Sally Floyd and Van Jacobson, Random early detecton gateways for congeston avodance, IEEE/ACM Transactons on Networkng, vol., no. 4, pp , August 993. [7] Lawrence S. Brakmo and Larry L. Peterson, TCP Vegas: End to end congeston avodance on a global nternet, IEEE Jounal on Selected Areas n Communcatons, vol. 3, no. 8, pp , October 995. [8] D. Ln and R. Morrs, Dynamcs of random early detecton, Proceedngs of SIGCOMM 97, pp. 7 37, October 997. [9] L. NedhardtD. P. Heyman, T. V. Lakshman, A new method for analyzng feedback based protocolswth applcatons to engneerng web traffcover the nternet, Proceedngs of IEEE SIGMETRICS 97, pp. 4 38, February 997. [] W. Rchard Stevens, TCP/IP Illustrated, Volume : The Protocols, Addson-Wesley, Readng, Massachusetts, 994. [] K. Fall and S. Floyd, Smulaton based comparsons of Tahoe, Reno, and SACK TCP, ACM SIGCOMM Computer Communcaton Revew, vol. 6, no., pp. 5, July 996.

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