Retransmission-Based Partially Reliable Transport Service: An Analytic Model *

Transcription

1 Retransmsson-Based Partally Relable Transport Servce: An Analytc Model * Rahm Marasl Paul D. Amer Phllp T. Conrad Computer and nformaton Scence Department Unversty of Delaware, Newark, DE USA Emal: { marasl,amer,pconrad}@cs.udel.edu Abstract Ths paper analytcally studes retransmsson-based partally relable transport servce. Results show that partally relable transport servce provdes ncreasngly hgher throughput and lower delay than relable transport servce as an applcaton s loss tolerance ncreases and as the underlyng network servce gets more lossy. Also, to some degree, partally relable transport servce eases the negatve effects of ack losses on throughput. Three cost functons assocated wth the relablty level that a system can support are ntroduced. These cost functons help demonstrate the penalty when a transport servce does not support the deal relablty level for an applcaton. Results show that the use of relable transport servce when an applcataon only needs a partally relable transport servce can cause consderable throughput drops and delay ncreases n lossy networks. On the other hand, at hgh loss rates, unrelable transport servce s unable to respect an applcaton s loss tolerance. Thus, n lossy envronments, partally relable transport servce s necessary to avod the extra cost of relable transport servce, and, at the same tme, to guarantee the mnmal relablty that an applcaton requres. 1 ntroducton Many applcatons such as vdeo and audo can tolerate loss. When the network layer provdes a best-effort servce such as on the nternet, the loss rate of the underlyng network servce may be hgher than an applcaton s tolerance for loss. n ths case, the transport layer becomes responsble for enhancng the level of relablty provded to the applcaton. Ths enhancement comes at the expense of other Qualty of Servce (QoS) parameters. For example, TCP enhances P servce to full relablty at the cost of ncreased delay and reduced throughput. UDP, on the other hand, ntroduces vrtually no ncrease n delay or reducton n throughput, but provdes no relablty guarantees. Ths paper nvestgates partally relable transport layer protocols that fll the gap between relable and unrelable transport servce by *Ths work supported, n part, by the Natonal Scence Foundaton (NCR ), the US Army Communcaton Electroncs Command (CECOM), Ft. Monmouth, and the US Army Research Offce (DAAH04-94-G-0093, DAAL03-92-G-0070). enhancng an unrelable network servce just enough to allow applcatons to specfy controlled levels of loss. Snce partally relable transport servce does not nsst on delverng all of the data, t can provde hgher throughput and lower delay than relable transport servce, and, at the same tme, t respects the loss tolerance of the applcaton. We study the partal relablty guarantees provded through retransmssons by the transport layer. Bascally, the transport protocol makes enough retransmssons to provde an expected relablty guarantee to the applcaton. n provdng partally relable servce, the transport layer must frst detect the lost packet and then decde whether or not to recover t. Dependng on the transport entty (.e., the sender or the recever) that detects and decdes to recover the lost data, two basc technques n provdng partally relable transport servce are possble: Sender-based loss detecton and recovery: The sender has the responsblty of detectng and decdng to recover the lost data. Lost data detecton s done manly through tmers and occasonally wth negatve acks. Once a lost packet s detected, the sender decdes whether or not to retransmt t based on the loss tolerance of the applcaton. Recever-based loss detecton and recovery: The recevng transport entty detects the lost data through gap-detecton and loss-tmers [4]. Once a lost packet s detected and the recovery decson s made, the recever requests the retransmsson of the lost packet by sendng negatve acks to the sender. n the lterature, dfferent partally relable servces provded by recever-based technques have been studed. Applcaton-Orented Error Control (AOEC) [4] has the objectve of satsfyng an applcaton s error tolerance wth mnmum retransmsson overhead. n [3], Partally Error- Controlled Connectons (PECC) and Slack ARQ are ntroduced to enable lmted recovery of packet losses for streambased communcatons n whch data completeness must be traded off for low delay servce. n AOEC, the lost data s recovered whenever necessary, whereas n PECC and Slack ARQ, the retransmsson of the lost data s requested n the transport layer only f t does not delay the applc% ton. Although wdely rejected, the retransmsson of contnuous meda (e.g., audo) s shown to be feasble by Dempsey n [3] through Slack ARQ. The results of Dempsey are encouragng n terms of provdng partally relable transport W96 $ EEE 5c

2 servce through retransmssons for multmeda applcatons. Dempsey manly uses ncreased control tme to allow tmely retransmssons of the lost data. n ths paper, we analytcally study partally relable transport servce provded by sender-based loss detecton and recovery. Then, we dentfy the cost of not usng the deal relablty servce for an app1catoa2 Ths nvestgaton uses a sender-based approach snce t provdes better performance than a recever-based approach [S. The analytc study bascally serves the followng purposes: To show the performance gans of partally relable transport servce over relable transport servce for applcatons that can tolerate a certan level of loss, and thus, to motvate the use of partally relable servce aganst relable servce. To determne the cost of usng ether more or less relablty than an applcaton needs. These results help show transport servce users what penalty they pay by not usng the deal relablty servce for ther applcatons. Through these results, the use of partally relable servce aganst unrelable servce s also motvated. The paper s organzed as follows: Secton 2 ntroduces an analytc model and dscusses computatonal results. The cost of not usng deal relablty servce for an applcaton s nvestgated n Secton 3. Secton 4 summarzes the man results. 2 Analytc Model We present an analytc model for provdng partally relable transport servce usng sender-based loss detecton and recovery. Ths analytc model s smlar to the one presented n [5] to study the protocol Partal Order Connecton (POC).3 ts major dfference s that, n ths model, t s unnecessary for all of the objects that are transmtted to eventually be communcated. n [5], no such partal relablty s consdered. The results show that partally relable transport servce provdes ncreasngly better throughput and delay than relable transport servce as the underlyng network servce gets more lossy and as the applcaton s loss tolerance ncreases. Later n Secton 3 we nvestgate the penalty pad when there s a msmatch between the applcaton s desred level of relablty and the transport layer s provded level of relablty. 2.1 ntroducton to Model To abstract partally relable transport servce s usage, we use a three layer archtecture whch ncludes only the network layer, the transport layer, and the user applcaton layer (see Control tme s the tme that the frst packet n a contnuous meda (e.g., audo) stream s artfcally delayed at the recever n order to buffer suffcent packets to provde for contnuous playback n the presence of jtter [3]. 2The deal relablty servce for an applcaton s defned n Secton ~~~ s a new transport-layer computer communcatons protocol that provdes partally ordered and partally relable servce to ts users. POC promses to fll the gap between ordered and relable (e.g., TCP) and unordered and unrelable (e.g., UDP) servces [l, 21. Fgure 1). The network layer (called Unrelable NET) s assumed to provde an unrelable servce. n Unrelable NET, the loss of a packet or an ack s characterzed by a Bernoul process, and a constant end-to-end network delay s assumed. The transport layer enhances the network s unrelable servce nto a partally relable servce by usng sender-based loss detecton and recovery. By assumpton, the relablty level of an user layer packet s defned by kxmt relablty as follows: kxmt Relablty: A packet wth kxmt relablty can be transmtted (orgnal plus retransmssons) at most k tmes. f Transport Sender s stll watng for the ack of a packet after the kth transmsson tmeout, that packet wll be released from Transport Sender s buffers. Releasng a packet from the sender s buffers wthout recevng an ack for t s called declarng that packet lost at Transport Sender. The transport layer provdes partally relable servce as follows: Transport Sender takes a packet from User Sender, transmts the packet over the network, then sets a tmer and buffers the packet. f the correspondng ack does not arrve wthn ts tmeout perod, Transport Sender retransmts the packet f t has not already been transmtted k tmes. Otherwse, the packet s declared lost. By assumpton, there s no problem wth runnng out of buffer space at Transport Recever. t s assumed that User Sender submts constant sze packets to Transport Sender. t s also assumed that there are nfntely many packets watng to be communcated at User Sender. User tecever just accepts packets from Transport Recever. The system varables are gven n Table 1, and the assumptons about the varables and the system n general are organzed n Table 2. We wll refer to ths system as NET. Hence NET = (tpackttdeloy,rt,tout,p,q, Bufqf,,BufR,psucc,A), where tpack through psucc represent system varables, and A stands for the assumptons n Table 2. All subsequent values and computatons n ths paper wll refer to ths gven NET unless otherwse stated. The deal relablty servce for an applcaton s defned as the relablty level that acheves the best tradeoff between relablty and other QoS parameters to satsfy a gven applcaton. Determnaton of ths deal level of relablty s the responsblty of each specfc applcaton (or the user of that applcaton). 2.2 Defntons of Target Values We analyze the throughput and the delay characterstcs of partally relable transport servce and determne the cost of not usng deal relablty servce for an applcaton. The throughput and the delay analyss wll be done n Secton 2.3 by computng the set of target values defned n Table 3. Later n Secton 3, the cost functons wll be ntroduced and computed based on the results of Secton 2.3. Fgure 2 shows the general model of our system. Xus 622 5c.4.2

3 User Sender User Recever Transport Sender Transport Recever System Varables Unrelable NET Fgure 1: Archtecture Defntons Table 1: System varables and XUR represent the admsson rate at the sender and the throughput at the recever, respectvely. For relable servce (.e., nothng s permtted to be lost), we have the followng equalty: Xus = XUR = XReloble. n [5], t s shown that XRe1,oble = e. n further sectons, we wll use ths result when comparng partally relable servce wth relable servce. The packet loss rate by transport layer (.e., Xloss = Xus - A, ) depends on the loss probabltes (.e., p and q) and the levels of relablty that the packets have. 'Bansport layer delay, Delay, s the expected tme for a packet to arrve to Transport Recever, once t s gven to Transport Sender. Ths delay does not nclude the expected bufferng tme at Transport Recever. Through Delay, we nvestgate the delay characterstcs of partally relable servce. Transport Sender Declared Loss Rate, TSDLR, represents the rate at whch packets are declared lost at the sender. t s vtal to realze that a packet that s delvered at the recever stll mght be declared lost at Transport Sender. Such a stuaton can happen when the ack(s) of the delvered packet s lost. Therefore, we have the followng relatonshp: XUR + TSDLR 2 Xus (.e., the rate of packets that are declared lost at Transport Sender s hgher than the rate of the packets that are actually lost by transport layer). For relable servce, both Xloss and TSDLR are zero. 2.3 Computaton of Target Values We wll show the performance gans of partally relable servce over relable servce. The results of ths secton s the bass of Secton 3's computatons for cost functons. The analyss of ths secton wll proceed as follows: (1) The delvery probablty (.e., PLD) s computed. (2) The computa- ton of admsson rate (.e., A,) s done by Lttle's theorem. (3) The throughput (.e., XUR) s computed as the product of Xus and PLD. (4) Transport Sender Declared Loss Rate, TSDLR, and Transport layer delay, Delay, are computed Delvery Probablty: PLD Delvery probablty, PLD, s the probablty that a packet s delvered to ts destnaton by the transport layer. PLD czwz also be seen as the probablstc delvery guarantee provded by partally relable servce. Thus, the relablty guarantee of the transport layer s determned by ths pr~bablty.~ PLD = 1-*b (1) t s noteworthy that PLD s ndependent of the ack loss rate (.e., q). Whether we lose none or all of the acks, delvery probablty does not change. Thus, expresson (1) shows that kxmt can provde relablty guarantees regardless of ack loss level. ntutvely, ths s because Transport Sender detects and recovers the lost packets wthout relyng on the responses from Transport Recever. As expected, PLD = 1 - p for unrelable servce (.e., k = 1) and PLD = 1 for relable servce (.e., k = CO). Thus, delvery probablty cannot be smaller than the packet success rate (.e., 1 -p). PLD s vrtually one when k 2 5 for all the practcal loss levels (e.g., PLD lo-' when k 2 5 and p 5 0.1). Thus, partally relable servce occurs only when 1 < k < 5 for all the practcal cases.5 Expresson (1) also shows that allowng few retransmssons (e.g., k = 3) s suffcent to have hgh delvery guarantees (e.g., greater than ) at practcal loss levels. 4The computatonal detals can be found n (61. 'The same concluson can be made through other target values. 5c

4 ASSUMPTONS Table 2: Assumptons Delvery Probablty (PLD) Throughput of Relable Servce (XRelable) Transport Sender Declared Loss Rate ( TSDLR) P(de1verng a packet to User Recever) Average number of packets that are delvered per unt tme at Transport Recever when nothng s permtted to be lost Average number of packets that are declared lost per unt tme Table 3: Target Values Throughput: XUR Throughput, XUR, s the rate at whch the recevng applcaton (.e., User Recever) gets data packets. Some applcatons may requre specfc throughput QoS guarantees. Ths secton nvestgates the condtons for ncreasng throughput. Let TS-Tme be the expected tme that a packet spends at Transport Sender. Wth assumptons 2, 3, 4, 5, 6, and 8, the number of packets at Transport Sender s always Buf S. Then by usng Lttle's theorem and the expresson for TS-Tme, X us can be computed. X UR s the product of X us and PLD: 1 - (1 - Ps"ce)k TS-Tame = *tout P.UW n expresson (4), XUR > XReloble snce p < ( -psucc) as long as q # 0. Ths expresson shows that partally relable servce provdes throughput mprovements over relable servce as long as there are ack losses n the network layer (.e., p < (1-psucc)). ntutvely, ths can be explaned as follows: snce each packet can be transmtted at most k tmes, after the kth transmsson, the unnecessary retransmssons of the packets due to ack losses are avoded. For relable servce XUR = e and for unrelable servce XUR = s. Therefore, the maxmal throughput mprovement by any partally relable servce s bounded by 0*9. For 10% network loss tpacb level (.e., p = q = 0.1) and 1% applcaton loss tolerance (.e., k = 2), the throughput mprovement of partally relable ser- (2) vce over relable servce can be as hgh as 3%. Fgure 3.A shows the relatonshp between XUR and kxmt values. n the fgure, the correspondng relable servce throughput s also gven. As shown n the graph, XUR decreases exponentally as k ncreases and converges to XRelable. The relatonshp between X UR and loss probabltes s nvestgated n Fgure 3.B. Ths fgure llustrates "XUR vs p and q" as well as correspondng relable servce throughput. Packet and ack losses have dfferent effects on throughput. n general, XUR decreases as both p and q ncrease, but the decrease n XUR s slower wth ncreasng q than wth ncreasng p. Thus, ack losses are not as detrmental to throughput as packet losses n partally relable servce. As Fgure 3.B shows, the gan n throughput over relable servce s small wth ncreasng packet losses. On the other hand, ncreasng ack loss rate provdes more sgnfcant throughput advantages over relable servce. Thus, a key result s that partally relable servce manly provdes throughput mprovement over relable servce when the network loses acks. One can also make ths observaton through Fgure 3.A. Ths fgure llustrates "XUR vs k" for p = O.l,q = 0.2 and p = 0.2, q = 0.1. The correspondng relable servce throughput s 0.72 packets/unt tme for both cases, whle the throughput of partally relable servce s hgher n the case of hgher ack loss rate than n the case of hgher packet loss rate. To some degree, partally relable servce overcomes the negatve effects of ack losses on the throughput. Based on these observatons, one can say that f network loses packets and acks, and f the applcaton has a hgh loss tolerance, then one can use partally relable transport servce and have consderable throughput mprovement over relable 624 5c.4.4

5 User Sender User Recever Admsson Rate Actual Loss Rate T Throughput Transport Sender Transport Recever 1 A TS DLR packet flow ack flow Fgure 2: Packet flow rate among dfferent layers Throughput tpack = Throughput 1 tpack = 1;= A _ l.l.blrslnc , 5 6 k Fgure 3: Effects of k-xmt values and loss probabltes on XUR transport servce Transport Sender Declared Loss Rate: TSDLR We now nvestgate TSDLR, Transport Sender Declared LOSS Rate. TSDLR s the rate at whch packets are declared lost at Transport Sender. Recall that packets that are declared lost are not necessarly the ones undelvered to User Recever. The nvestgaton of TSDLR s helpful n understandng the overall analytc model. X ~ S Let PL be the probablty of declarng a packet lost at Transport Sender. PL = (1- psllcc)k. TSDLR can be computed as the product of PL and Xus: * (1- P,"c,)h TSDLR = (5) tpllck 1 - (1- P m c P Expresson (5) shows that TSDLR s nonzero for pallcc < 1. Hence, as long as the network layer loses packets or acks, there wll be packets that are declared lost at Transport Sender. Ths s because, f pallcc < 1, the probablty of not recevng an ack n each of frst k transmssons s nonzero, and thus, the probablty of not declarng a packet lost s not zero. As an nterestng specal case, we have the followng equalty when one assumes acks are never lost (.e., Hence, when q = 0, X~oss = TSDLR (.e., the packets that are declared lost at Transport Sender are precsely the ones that are not delvered to User Recever). Thus, XUS = X ~ + R TSDLR for q = 0. Ths can be explaned as follows: the packets that are delvered at Transport Recever wll receve ther acks snce q = 0. Hence, t s mpossble for a delvered packet to be declared lost at Transport Sender. For q > 0, we have q = 0): Xloss = TSDLR = e * 6. > XUR + TSDLR. Ths s because, there wll be some packets whch do arrve at Transport Recever (and User Recever) but are declared lost at Transport Sender because of ack losses. TSDLR = 0 for relable servce and TSDLR = l;p:cy for unrelable servce. For k 2 5 and p,q 5 0.1, TSDLR * ARelnble (.e., TSDLR s small as compared to XRelable when k 2 5 for almost all Practcal loss levels). When P (Or Q) s 1, every packet that s gven to Transport Sender wll be declared lost snce no ack wll arrve. Thus, when P = 1 or = 1, Xus = TSDLR = -. 5c

6 2.3.4 Transport Layer Delay: Delay Transport layer delay, Delay, s the expected tme for a packet to arrve at Transport Recever once t s gven to Transport Sender by User Sender. Applcatons may requre specfc delay &OS guarantees. For many applcatons such as real tme audo and vdeo, lower delay s even more mportant than hgher throughput. Delay does not nclude the bufferng tme of the packet at Transport Recever; t only accounts for the expected tme to reach to Transport Recever for a packet. Once a packet s receved, t may reman buffered at Transport Recever for some tme. Generally, lower Delay also wll cause lower overall delay. Notce that Delay s only computed for the packets that are successfully receved by Transport Recever snce the recevng applcaton (.e., User Recever) wll only experence the delays of such packets. Thus, f a packet s lost k consecutve tmes, then the transport layer delay for that packet s not ncluded. For 5 k - 1, let P(s) be the probablty that a packet succeeds at ( + l)th try gven that the packet s successfully receved by Transport Recever. Then: P(s) = P(packet succeeds at ( + l)*h try packet P * (1 - P succeeds wthn k tres) = 1 -p k-1 =O As expected, Delay = &lay for unrelable servce and Delay = td&y + 6 * tout for relable servce. Thus, potentally, partally relable servce can provde delay mprovements as hgh as &*tout. Fgure 4.A shows the relatonshp between Delay and kxmt values. The correspondng relable servce Delay curve also s provded. As the graph shows, partally relable servce provdes potkntally valuable delay mprovement over relable servce even at the practcal loss levels. For example, for p = 0.1, tout = 2 * td&y and about 1% applcaton loss tolerance (.e., k = 2), Delay can be as much as 3.3% lower usng partally relable servce. Delay ncreases wth ncreasng k and converges to the delay value of relable servce. Fgure 4.B llustrates Delay vs p for both relable and partally relable servce. As seen n the graph, the delay gan of partally relable servce over relable servce ncreases wth ncreasng packet losses. 3 Cost of Not Wng deal Relablty Servce Tradtonal computer networks offer ether relable (e.g., TCP) or unrelable (e.g., UDP) transport servce. For many applcatons such as multmeda, nether of these servces s deal because unrelable servce lacks any relablty guarantee, whle relable servce wastes resources by provdng too much relablty. Relable servce does not allow any loss, and thus, the communcaton system cannot take advantage of an applcaton s loss tolerance. Ths wll result n hgher delay and lower throughput than what would have been achevable wth deal relablty servce. On the other hand, unrelable servce s unable to support the mnmal loss guarantees of some applcatons. Thus, by havng to choose ether (1) relable or (2) unrelable servce, applcatons pay a prce n the form of ether hgher delay and lower throughput, or a hgher loss rate, respectvely. n ths secton, we nvestgate the cost of usng a transport servce that provdes ether less or more relablty than an applcaton requres. The notaton used n the computaton of cost functons s ntroduced n Table 4. n an deal case, the applcaton uses a communcaton system that perfectly supports ts desred level of relablty (.e., knet = kdeal). There s no relablty cost (.e., penalty) assocated wth such a case. A cost (or penalty) occurs when knet # kd&: the communcaton system provdes ether more or less relablty than the applcaton needs. n Secton 2.3, we have shown that wth ncreasng relablty level, throughput decreases and the delay ncreases. Thus, f a system NETprovdes more relablty than an applcaton needs, such a relablty msmatch wll result n lower throughput and hgher delay than wth the deal relablty level. n such a case, the applcaton s penalzed by lower throughput and hgher delay. On the other hand, Secton 2.3 s results also show that f the communcaton system lacks relablty guarantees that an applcaton needs, then the applcaton wll be penalzed by a hgher loss level than t could tolerate. Thus, from the results of Secton 2.3, we dentfy three cost functons: (1) throughput, and (2) delay costs of more relablty, and (3) loss cost of less relablty. These cost functons are formally defned n Table Costs ncurred by Usng More Relablty than Needed The cost of usng more relablty than an applcaton needs s defned n terms of two worsenng performance metrcs: throughput and delay (see Table 5). These two cost values show the percentage worsenng n the correspondng performance metrc due to excess relablty provded by the communcaton system. Snce these cost functons are defned when the transport layer provdes hgher relablty than the deal case, they are always greater than or equal to 0. For knet > k;deal, they have no practcal nterpretaton. f any of these cost values s equal to k, ths cost should be nterpreted as 100* c % worsenng n the correspondng performance metrc because of more relablty provded by the transport layer. For example, llx~~cost = 0.1 means 10% decrease n the throughput, whle Delaycost = 0.2 means 20% ncrease n delay, due to more relablty. The throughput cost,6 X U R ~ of ~ more ~ ~, relablty can easly be computed by usng expresson (4): 61n [6], t s shown that the-throughput cost s equvalent to the bandwdth cost n system NET. The bandwdth cost of usng more relablty than needed s defned as the extra bandwdth needed to acheve the throughput of deal relablty servce c.4.6

7 ~ t-ouf~8. ~ Delay Delay tdelay4, k=2 /R.l&l. t;.ms. 16. B p-0)., tdelay4 tout=8.j ParCally R.l.bl. A. B. Fgure 4: Effects of k-xmt values and loss probabltes on Delay r Notaton Defnton Table 4: Notaton The maxmal throughput cost that can occur s q snce ths s the throughput cost of relable servce over unrelable servce (.e., k,deal = 1, knet = 00). For q = 0.1, ths corresponds to a throughput cost of 0.1 (.e., 10% decrease n throughput due to unnecessary relablty). Thus, the use of more relablty (e.g., relable servce) can be very costly n terms of throughput. t s worth notng that f ack loss probablty s zero, then there s no throughput cost of usng more relablty. X U R of ~ relable ~ ~ ~ servce over partally relable servce (Le., ~NET = 00 and k,deal s fnte) -pruec)kdeal -pkdeal s. As expected, for practcal loss lev-pkdeal els and kdeal 2 5, ths cost s neglgble. The relatonshp between XURCost and k-xmt s llustrated n Fgure 5.A. X U R ncreases ~ ~ ~ ~ and converges to q as the relablty level of the system ncreases. Fgure 5.B plots X U R vs ~ p ~ ~ and ~ L X~~COst vs q. The throughput cost changes only slghtly wth ncreasng packet losses. On the other hand, wth ncreasng ack losses, URCost ncreases steadly and converges to 1 - as q + 1. Thus, the throughput cost can be NET consderably large at hgh ack loss rates. The results of ths secton show that f s network loses acks and the applcaton can tolerate loss, then usng more relablty (e.g., relable servce) can result n severe throughput drops. On the other hand, f ack loss probablty s low, then there s lttle throughput penalty n not usng the deal relablty servce for the applcaton Delay Cost: Delraycost Delaycost of relable servce over unrelable servce s (*). For tort = 2 * &lay and p = q = 0.1, ths cor- tdelay responds to a delay cost of (.e., 22.2% ncrease n delay due to extra relablty). Under the same condtons, the throughput cost s 0.1. Thus, the negatve effects of extra relablty (e.g., relable servce) are even worse on delay than on throughput. DelayCost vs knet s gven n Fgure 6.A. The delay cost ncreases as the unnecessary relablty level of the transport layer (.e., knet) ncreases. Delaycost VS p n Fgure 6.B shows that Delaycost ncreases wth ncreasng packet losses. Thus, the delay cost of usng more relablty can potentally be arbtrarly large n lossy networks. The results of Secton show that the throughput penalty of relable servce ncreases manly wth ncreasng ack losses. On the other hand, the results of ths secton show that unlke X U R ~ the ~ ~ delay ~, cost of relable servce ncreases wth packet losses. Thus, n lossy networks where both packets and acks can be lost, the use of relable transport servce when an applcaton only needs partally relable transport servce can be very costly n terms of both throughput and delay. The applcatons that can tolerate loss such as audo and vdeo also requre certan delay and through- put QoS guarantees. Thus, manly because of hgh delay and throughput costs of relable servce (e.g., TCP), such applcatons often are forced to use unrelable servce (e.g., UDP). The Of usng more DelayCOSt, be n the next secton we consder the nverse problem: the cost computed by usng expresson (7) as follows: 5c

8 ~ Cost Functon Defnton Throughput Cost ( A u R ~ ~ ~ ~ Cost ) of usng more relablty n terms of decreased Throughput, defned as 1 - where knet 2 kdeal Delay Cost (Delaycost) n terms of ncreased Transport Layer Delay, Table 5: Cost functons Throughput Cost Throughput Cost A. B. Fgure 5: Effects of kxmt dues and loss probabltes on X U R ~ ~ ~ ~ of usng less relablty than an applcaton needs (e.g., unrelable servce). 3.2 Loss Cost of Less Relablty n Sectons 3.1, we quantfed the cost when applcatons must choose to use more relablty (e.g., relable servce) than they need. Due to such costs of relable servce and unavalablty of partally relable servce, applcatons may choose to use unrelable servce. n such a stuaton, the applcaton uses less relablty at the expense of losng more packets than t really wants to tolerate. n ths secton, we nvestgate the cost of usng less relablty. The results of Secton 2.3 show that as the relablty level of the transport layer decreases, percentage loss (PLS) ncreases. Thus, we wll characterze the cost of usng less relablty as the ncrease n percentage loss (.e., PLScost = PLS(kNET) - PLS(kdeal)). PLScost s defned only when the system NET provdes less relablty than the deal case (.e., knet 5 kdear). Thus, ths cost value s always greater than or equal to 0. For knet > k,deal, PLScost has no practcal nterpretaton. PLScost = c should be nterpreted as 100 * c% more loss than the applcaton can tolerate Percentage Loss Cost: PLScost The percentage loss cost of less relablty, PLScoSt, can be computed by usng expresson (1) as follows: P L S ~ = ~ pknet ~ ~ - p deol (10) The percentage loss cost of unrelable servce over relable servce (.e., knet = 1,.kldeal = 00) s p. Thus, 0 5 PLSco,t 5 p. As expected, f packet loss rate of the network layer s neglgble, then PLScost wll also be neglgble. PLScost VS k,dej s gven n Fgure 7.A. PLSCost ncreases as the relablty need of the applcaton (.e., kdeal) ncreases. Smlarly, PLSCost vs p n Fgure 7.B shows that the loss cost of less relablty frst ncreases, then starts decreasng and goes to 0 wth ncreasng p. Thus, n lossy networks ths cost can be large. These results show that the loss cost of usng less relablty (e.g., unrelable servce) only depends on packet loss rate, and ths cost cannot be greater than p. n general, f the overall loss tolerance level of an applcaton s hgher than the overall packet loss level of the network layer, then such an applcaton can use unrelable servce. On the other hand, even though the average loss level of a network s smaller than the overall loss tolerance level of the applcaton, there can be tmes where the network loses large amounts of data that the applcaton cannot tolerate. Ths s especally the case wth packet-swtched networks where the losses manly occur n bursts due to buffer overflows. Notce that our analytc model assumes random (.e., Bernoull) losses, and thus, the cost of burst losses s not studed. The results of Secton 3.1 show that f the transport layer provdes hgher relablty than needed, ths can result n severe throughput drops and delay ncreases n lossy networks. On the other hand, ths secton shows that at hgh loss rates, unrelable servce cannot respect the loss tolerance of applcatons. Thus, n lossy envronments, partally relable servce s necessary to avod the prce of relable servce, and at the same tme, to provde the relablty guarantees for applca c.4.8

9 Delay cost A. B. Fgure 6: Effects of kxmt values and loss probabltes on Delaycost Percentage Loss Cost Percentage Loss Cos& 0.11 k-net= 1.pmO.l (.la t 0.6 CNET-2, CdUl-O A. B. Fgure 7 Effects of k-xmt values and loss probabltes on PLScost tons. 4 Summary of Man Results Ths paper studes partally relable transport servce va an analytc model. We nvestgate the effects of packet and ack losses, as well as varous levels of applcaton loss tolerance on the system performance. The results show that partally relable transport servce provdes consderable throughput, admsson rate, and delay mprovements over relable transport servce when the underlyng network servce s lossy and an applcaton has a hgh loss tolerance. t s also shown that, to some degree, partally relable transport servce eases the negatve effects of ack losses on throughput. Three cost functons assocated wth the level of relablty that the communcaton system can support are also ntroduced. The three cost functons are (1) throughput, and (2) delay costs of usng more relablty, and (3) loss cost of usng less relablty. These functons show the cost of not usng deal relablty servce for an applcaton n terms of three worsenng performance metrcs. The results show that the use of relable transport servce nstead of partally relable transport servce can result n consderable throughput drops and delay ncreases n lossy networks. On the other hand, at hgh loss levels, unrelable transport servce s unable to support an applcaton s mnmal loss guarantee. Thus, n lossy envronments, partally relable transport servce s necessary to avod the prce of relable transport servce, and at the same tme, to provde relablty guarantees for applcatons. References [l] Paul D. Amer, C. Chassot, Thomas J. Connolly, Phllp T. Conrad, and M. Daz. Partal order transport servce for multmeda and other applcatons. EEE/ACM Trans on Networkng, 2(5), , Oct [2] Thomas J. Connolly, Paul D. Amer, and Phllp T. Conrad. RFC- 1693, An Extenson to TCP: Partal Order Servce. [3] Bert J. Dempsey. Retransmsson-Based Error Control For Contrnuous Meda Traflc n Packet-Swthced Networks. PhD Dssertaton, Unversty of Vrgna, [4] F. Gong and G. Parulkar, An Applcaton-Orented Error Control Scheme for Hgh-speed Networks. Tech Report WUCS-92-37, Department of Computer Scence, Washngton Unversty n St. Lous, November [5] R. Marssl, P. D. Amer, P. T. Conrad, and G. Burch. Partal Order Transport Servce: An Analytc Model. n gth Annual EEE Workshop on Computer Communcatons, Marathon, Florda, October EEE. [6] Rahm Marasl. Partally Ordered and Partally Relzable Transport Protocols: Performance Analyss. PhD Dssertaton, Unversty of Delaware, (n progress) 5c