Mo deling TCP Throughput: A Simple Mo del and its Empirical Validation Jitendra Padhye Victor Firoiu Don Towsley Jim Kurose f jitu, v roiu, towsley, [email protected] Department of Computer Science University of Massachusetts Amherst, MA 01003 USA Abstract In this pap er we develop a simple analytic characteriza- tion of the steady state throughput of a bulk transfer TCP In this pap er we develop a simple analytic characterization ow i.e., a ow with a large amount of data to send, such of the steady state throughput, as a function of loss rate as FTP transfers as a function of loss rate and round trip and round trip time for a bulk transfer TCP ow, i.e., a time. Unlike the recentwork of [6 , 7, 10 ], our mo del captures ow with an unlimited amount of data to send. Unlike the not only the b ehavior of TCP's fast retransmit mechanism mo dels in [6 , 7, 10 ], our mo del captures not only the be- which is also considered in [6 , 7, 10 ] but also the e ect havior of TCP's fast retransmit mechanism whichis also of TCP's timeout mechanism on throughput. The measure- considered in [6 , 7, 10] but also the e ect of TCP's timeout ments we present in Section 3 indicate that this latter b ehav- mechanism on throughput. Our measurements suggest that ior is imp ortant from a mo deling p ersp ective, as we observe this latter b ehavior is imp ortant from a mo deling p ersp ec- more timeout events than fast retransmit events in almost tive, as almost all of our TCP traces contained more time- all of our TCP traces. Another imp ortant di erence b etween out events than fast retransmit events. Our measurements ours and previous work is the ability of our mo del to accu- demonstrate that our mo del is able to more accurately pre- rately predict throughput over a signi cantly wider range dict TCP throughput and is accurate over a wider range of of loss rates than b efore; measurements presented in [7 ] as loss rates. well the measurements presented in this pap er, indicate that this to o is imp ortant. We also explicitly mo del the e ects of small receiver-side windows. By comparing our mo del's 1 Intro duction predictions with a numb er of TCP measurements made b e- tween various Internet hosts, we demonstrate that our mo del A signi cant amount of to day's Internet trac, including is able to more accurately predict TCP throughput and is WWW HTTP, le transfer FTP, email SMTP, and re- able to do so over a wider range of loss rates. mote access Telnet trac, is carried by the TCP transp ort The remainder of the pap er is organized as follows. In proto col [18 ]. TCP together with UDP form the very core Section 2 we describ e our mo del of TCP congestion control of to day's Internet transp ort layer. Traditionally, simula- in detail and derive a new analytic characterization of TCP tion and implementation/measurementhave b een the to ols throughput as a function of loss rate and average round trip of choice for examining the p erformance of various asp ects of time. In Section 3 we compare the predictions of our mo del TCP. Recently,however, several e orts have b een directed with a set of measured TCP ows over the Internet, having at analytically characterizing the throughput of TCP's con- as their endp oints sites in b oth United States and Europ e. gestion control mechanism, as a function of packet loss and Section 4 discusses the assumptions underlying the mo del round trip delay [6, 10 , 7]. One reason for this recent in- and a number of related issues in more detail. Section 5 terest is that a simple quantitativecharacterization of TCP concludes the pap er. throughput under given op erating conditions o ers the p os- sibility of de ning a \fair share" or \TCP-friendly" [6 ] through- put for a non-TCP ow that interacts with a TCP connec- 2 A Mo del for TCP Congestion Control tion. Indeed, this notion has already b een adopted in the design and development of several multicast congestion con- In this section we develop a sto chastic mo del of TCP conges- trol proto cols [19 , 20 ]. tion control that yields a relatively simple analytic expres- sion for the throughput of a saturated TCP sender, i.e., a This material is based up on work supp orted by the National ow with an unlimited amount of data to send, as a function Science Foundation under grants NCR-95-08274, NCR-95-23807 and of loss rate and average round trip time RTT. CDA-95-02639. Any opinions, ndings, and conclusions or recommen- dations expressed in this material are those of the authors and do not TCP is a proto col that can exhibit complex b ehavior, necessarily re ect the views of the National Science Foundation. esp ecially when considered in the context of the current In- ternet, where the trac conditions themselves can b e quite complicated and subtle [14 ]. In this pap er, we fo cus our at- tention on the congestion avoidance b ehavior of TCP and its impact on throughput, taking into account the dep en- dence of congestion avoidance on ACK b ehavior, the manner in which packet loss is inferred e.g., whether by duplicate ACK detection and fast retransmit, or by timeout, limited advertised window Section 2.3. We note that wedonot receiver window size, and average round trip time RTT. mo del certain asp ects of TCP's b ehavior e.g., fast recov- Our mo del is based on the Reno avor of TCP, asitisby ery but b elievewehave captured the essential elements of far the most p opular implementation in the Internet to day TCP b ehavior, as indicated by the generally very go o d ts [13 , 12]. We assume that the reader is familiar with TCP between mo del predictions and measurements made on nu- Reno congestion control see for example [4 , 17 , 16 ] and we merous commercial TCP implementations, as discussed in adopt most of our terminology from [4 , 17 , 16 ]. Section 3. A more detailed discussion of mo del assumptions Our mo del fo cuses on TCP's congestion avoidance mech- and related issues is presented in Section 4. Also note that anism, where TCP's congestion control window size, W; is in the following, we measure throughput in terms of packets increased by 1=W each time an ACK is received. Con- p er unit of time, instead of bytes p er unit of time. versely, the window is decreased whenever a lost packet is detected, with the amount of the decrease dep ending on whether packet loss is detected by duplicate ACKs or by 2.1 Loss indications are exclusively \triple-duplicate" ACKs timeout, as discussed shortly. In this section we assume that loss indications are exclu- We model TCP's congestion avoidance b ehavior in terms sively of typ e \triple-duplicate" ACK TD, and that the of \rounds." A round starts with the back-to-back transmis- window size is not limited by the receiver's advertised ow sion of W packets, where W is the current size of the TCP control window. We consider a TCP ow starting at time congestion window. Once all packets falling within the con- t = 0, where the sender always has data to send. For any gestion windowhave b een sent in this back-to-back manner, given time t> 0, we de ne N to b e the numb er of pack- t no other packets are sentuntil the rst ACK is received for ets transmitted in the interval [0;t], and B = N =t, the t t one of these W packets. This ACK reception marks the end throughput on that interval. Note that B is the number of t packets sent p er unit of time regardless of their eventual fate of the current round and the b eginning of the next round. i.e., whether they are received or not. Thus, B represents t In this mo del, the duration of a round is equal to the round the throughput of the connection, rather than its go o dput. trip time and is assumed to b e indep endent of the window We de ne the long-term steady-state TCP throughput B to size, an assumption also adopted either implicitly or ex- be plicitly in [6, 7 , 10 ]. Note that wehave also assumed here N t B = lim B = lim t that the time needed to send all the packets in a windowis t!1 t!1 t smaller than the round trip time; this b ehavior can b e seen Wehave assumed that if a packet is lost in a round, all re- in observations rep orted in [2, 12 ]. maining packets transmitted until the end of the round are 0 At the b eginning of the next round, a group of W new also lost. Therefore we de ne p to b e the probability that 0 packets will b e sent, where W is the new size of the con- a packet is lost, given that either it is the rst packet in its gestion control window. Let b be the number of packets round or the preceding packet in its round is not lost.