A Simple Throughput Model for TCP Veno

Transcription

1 A Simle Throughut Model for TCP Veno Bin Zhou, Cheng Peng Fu, Dah-Ming Chiu, Chiew Tong Lau, and Lek Heng Ngoh School of Comuter Engineering, Nanyang Technological University, Singaore {zhou00, ascfu, Deartment of Information Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong Networking Deartment, Institute for Infocomm Research, Singaore Abstract TCP Veno was roosed to eliminate TCP erformance suffering from wireless links Real network measurements and live Internet results have validated TCP Veno s significant throughut imrovement in wireless networks and its harmonious co-existence with TCP Reno connections in wired networks In this aer, we develo a simle analytic aroach to characterize TCP Veno behavior in both wire and wireless situations Being different from the equation of TCP Reno, a more general close formula is derived, taking into account of the refined multilicative decrease algorithm in Veno, to model the throughut for a bulk transfer of TCP Veno flow Our simulation and exerimental results demonstrate that such an equation is able to accurately redict TCP Veno throughut over different network scenarios, ranging from very low lossy links to very heavy lossy links I INTRODUCTION TCP Reno [1] is the dominating version of TCP Over last decade, many efforts have been made to model its throughut in a bulk transfer TCP flow Among those work, a equation derived by [] hereinafter, called Reno equation has been widely used today, eg, in the TCP-Friendly Rate Control TFRC rotocol [3] Recently, wireless communication technology has been making significant rogress and will be laying a more and more imortant role in the future Such evolution brings new challenges to TCP Reno For examle, Reno assumes acket loss is always induced by congestion, which can lead to significant erformance degradation in wireless networks, where random loss is ramant due to environmental noise To deal with random loss effectively, a novel end-to-end congestion control mechanism called TCP Veno [4][7][9][1][13] was roosed The key innovation in Veno is the enhancement of Reno congestion control algorithm by making use of the estimated state of a connection based on Vegas [5] This scheme significantly reduces blind reduction of TCP window regardless of the cause of acket loss Thus Veno is suitable for any heterogeneous networks, articularly when wireless links form art of such networks [6][8][][11] In this aer, we develo a simle analytic aroach to characterize TCP Veno behavior in both wire and wireless situations Being different from the equation of TCP Reno, a more general closed form equation hereinafter, called Veno equation is derived, taking into account of the refined multilicative decrease algorithm in Veno, to model the throughut for a bulk transfer of TCP Veno flow The remainder of the aer is organized as follows In Section, we describe TCP Veno mechanism in detail Then Section 3 gives the derivation of Veno equation A validation of this equation on NS- [14] simulation and wireless LAN exeriments is resented in Section 4 Finally, Section 5 concludes our work and gives the future directions II BASIC MECHANISM OF VENO TCP Veno makes use of the state distinguishing scheme from TCP Vegas, and integrates it into congestion window evolution scheme of TCP Reno In Vegas, the sender measures the so-called Exected and Actual rates: Exected = BaseRTT Actual = where, is the current congestion window size, BaseRTT is the minimum of measured round-tri time, and is the smoothed round-tri time measured The difference of the rate is: Diff = Exected Actual When > Base, there is a bottleneck link where the ackets of the connection accumulate Let the backlog at the queue be denoted by N Wehave: = BaseRTT N Actual That is, we attribute the extra delay to the bottleneck link in the second term of the right side above Rearranging, we have: N = Actual BaseRTT = Diff BaseRTT = BaseRTT BaseRTT The main idea of Veno is to use the measurement of N as an indication of whether the network is in congestive state or non-congestive state At any time, if N β, Veno deduces the link is in congestive state and considers the acket loss is congestion loss Otherwise if N<β, the link

2 is in non-congestive state and the acket loss is random loss Here β is normally set to be 3 Based on the differentiated state, Veno alies different algorithms to Reno s additive increase AI and multilicative decrease MD hases, thus makes congestion window evolution more efficient: In AI hase, IF N <β THEN set = 1 for every new ACK ELSE IF N β THEN set = 1 for every other new ACK In MD hase, 1Retransmit the missing acket, and IF N <β THEN set ssthresh = 4 5 ELSE IF N β THEN set ssthresh = 1, and set = ssthresh 3 Each time another du ACK arrives, increment by one acket 3When the next ACK acknowledging new data arrives, set to ssthresh value in ste 1 Note that, Veno only refines the AIMD mechanism of Reno All other arts of Reno, including initial slow start, fast retransmit, fast recovery, comutation of the retransmission timeout, and the backoff algorithm remain intact III DERIVATION OF VENO EQUATION From the mathematical view, we simlify the above AIMD mechanism as follows: in AI hase, { 1 =, for every new ACK N<β 1, for every other new ACK N β and in MD hase, { 4 = 5 N<β 1 N β As shown in Figure 1, although new AI hase in Veno brings certain imrovement in throughut, the most enhancement of Veno is contributed by the MD hases at random losses ie, cutting down 1 5 rather than 1 of To simlify the roblem, we ignore the different AI hases of Veno and Reno in the following derivation As a result, Veno acts quite similarly as Reno, and the only difference between Veno and Reno is how much value should be cut down when losses occur: Reno always cuts down 1 and, while Veno sometimes cuts down 1 congestion loss, and sometimes cuts down 1 5 random loss In this case, we introduce a random variable λ to reresent the roortion of value after cut down, instead of a 1 constant Hereλ can be 1 or 4 5 with certain robability This is a new arameter introduced by Veno s MD hase characteristic The following derivation is divided into three stes: firstly we only consider the situation where acket losses W Fig 1 1/ 1/5 Congestion Loss Random Loss Random Loss X 1 X X 3 1/5 X 4 Veno Reno Congestion window evolution of Veno and Reno No of rounds is indicated by the trile dulicated ACKs We call these losses trile-dulicated TD losses; then we include acket losses indicated by time outs, which are called time-out TO losses; finally we extend our model to include the imact of advertisement window limitation A Veno Equation for Only TD Losses According to equation 7 in [] we have: W i = λ i W i 1 X i 1 b where, W i 1, W i are value before the revious TD loss and the next TD loss resectively, X i is the number of round between these two losses, and b is the number of ackets that are acknowledged by a received ACK Note that all these arameters have the same meanings as those in [] In addition, λ i is the roortion of value 1 or 4 5 after the revious TD loss Then the ackets transmitted between these two TD losses are: Y i = X i/b 1 k=0 λ i W i 1 kb β i = λ i W i 1 X i X i X i b 1 β i = X i λ iw i 1 W i 1 1 β i using1 where β i is the number of ackets sent in the last round, as seen in [] As same in [], β i is considered as a uniformly distributed variable between 1 and W i From above equation 1, and equation 5 in aer [], we have: 1 1 E[λ]E[W ]= E[X] b 3 E[W ]= E[X] 1 E[λ]E[W ] 1 E[β] 4 where, E[β] = E[W ], and is the robability that a acket is lost, given that either it is the first acket in its round or the receding acket in its round is not lost Note that includes both congestion and random losses

3 Let γ = E[λ], and from 3 and 4 we can get: b1 γ1 b1 γ1 E[W ]= b1 γ 1 b1 γ b 1 γ 5 Then from above equation 3 and equation 6 in aer [], it follows: E[X] = b1 γ1 1 γ and, E[A] = b1 γ1 1γ b1 γ1 1 γ b1 γ 1γ b1 γ1 1 γ 6 b1 γ1 1γ 1 7 Finally, substitute E[A] and E[W ] into equation 1 and 5 in aer [] we have: B = = E[W ] E[A] b1 γ1 b1 γ b1 γ1 1γ b1 γ1 b1 γ b 1 γ b1 γ1 b1 γ 1γ 1γ 1 8 For small values of, it can be aroximated by: B 1 1 γ 9 b1 γ B Veno Equation for Both TD and TO Losses So far equation 9 gives Veno equation when only TD losses occur Actually there are many TO losses over real communications, and they must be included in the model According to equation 1 in [], with TO losses the throughut can be written as follows: E[Y ]Q E[R] B = E[A]Q E[Z TO ] where, E[Y ] and E[A] have been derived in the revious section Q is the robability that a loss indication ending a TD eriod is a TO, E[R] is the mean number of ackets sent during TO eriods, and E[Z TO ] denotes the mean duration of TO eriods As we have ointed out before, Veno does not change Reno s algorithms on dealing with TO losses, such as the comutation of the timeout, and the backoff algorithm We can easily derive the equation following the same routine described in [], because the exressions of Q, E[R], and E[Z TO ] are same in both Veno and Reno Therefore, we have: B = E[W ] ˆQE[W ] 1 E[X]1 ˆQE[W ]T 0 f 11 where, E[W ] and E[X] have been given in the revious section Note that, both E[W ] and E[X] now include a new arameter γ here T 0 denotes the eriod the sender will wait for to retransmit non-acknowledged acket, ˆQw = min1, w w 1 and, f = For small values of, equation 11 can be aroximated by: B 1 b1 γ T 1γ 0 min 1,3 b1 γ 13 C Veno Equation with Imact of window limitation 14 Finally, we consider the Veno equation with the imact of the advertisement window limitation In such scenario, the congestion window will start increase after the revious loss, and will kee constant when it reaches the advertisement window limitation Let W max denote the advertisement window limitation, U i denote the number of rounds where the congestion window increases, and V i denote the number of rounds where the congestion window kees constant Due to the new MD hase in Veno, W max has following equation, according to []: W max = λ i W max U i 15 b where, λ i is the roortion of value after the revious TD loss 1 or 4 5, as defined in Section A We assume E[U] = bw max, same as that in [] Then considering the number of ackets sent in the ith TD eriod, we have: and then, Y i = U i λ iw max W max V i W max 16 E[Y ] = 1γ W max E[U]W max E[V ] b1 γ = Wmax W max E[V ] 17 4 After getting E[Y ], we can easily derive the final throughut equation when the advertisement window is limited, following the stes of []: B = W max ˆQW max 1 b1 γ 4 W max W max ˆQW max T 0 f 18 Combine equation 11 and 18 we can get the final aroximated result for small values of, according to equation 31 in aer []: B min Wmax, 1 b1 γ T 1γ 0 min 1,3 b1 γ 13 19

4 D Exression of γ Now we need to determine the value of γ From our definition: γ = E[λ] = 4 5 P N <β1 P N β = 4 5 P N <β1 1 P N <β = 1 03 P N <β 0 Recall: N = W BaseRTT W BaseRTT BaseRTT = W 1 For simlicity, we assume the value of congestion window at losses including congestion and random losses, W, is uniformly distributed between 0 and W max, where W max is the maximum congestion window size during the transmission Then we have: P N <β = P W <β BaseRTT β = min 1, BaseRTT W max From 0 and we have: 4 γ = min 5, 1 03 β BaseRTT W max 3 Equation 19 with 3 is the derived Veno equation E Discussion Being different from the Reno equation, the Veno equation uses a variable γ [ 1, 4 5 ] to relace the original constant 1 Here we call it Veno arameter To verify the boundary of this arameter, consider two extreme scenarios: 1 if all losses are estimated to be congestion losses during transmission, then Veno erforms same as Reno by halving the congestion window every time, and the result leads to γ = 1 in the equation; if all losses are estimated to be random losses, then Veno erforms as suer Reno by cutting down only 1 5 of the congestion window every time The result leads to γ = 4 5 in the equation Because Veno equation is a none-decreasing function of γ, for a normal Veno flow γ should be a value between 1 and 4 5 To determine an accurate exression for γ is still an ongoing work We assumes W value is uniformly distributed The validation on NS- simulation and wireless LAN exeriments shows that, our assumtion can aroximate the exeriment results quite well Moreover, we assume that the refined AI hase in Veno has negligible imrovement in TCP throughut as comared to the refined MD hase This has been illustrated at the beginning of this section Some other simlifying assumtions have also been made during our derivation: 1 our model does not include the slow start and fast recovery algorithm of Veno We believe the imacts of both hases are small, and can be ignored in the model; we assume that acket losses within a round are correlated This is caused by the dro-tail olicy of intermediate routers: if one acket is droed by the full buffer, it is likely the following ackets in the round will be droed too; 3 we assume losses in one round are indeendent of losses in another round, because acket in different rounds are searated by one RTT and more, and thus they are likely to encounter different buffer states; 4 we assume the round tri time is indeendent of the window size Note that, all the above assumtions are the same as those in [] IV VALIDATION OF VENO EQUATION The validation of Veno equation is divided into two arts: the simulation results on NS- and the exerimental results on a wireless LAN A Simulation Results The toology of our exeriment on NS- [14] is shown in Figure N connections TCP Veno Fig W l = Mbs Delay l = 1 ms Packet W b Delay b W l = Mbs Delay l = 1 ms Toology of NS- exeriments TCP Sink The left side network has wired links with bandwidth of Mbs, delay of 1ms and acket buffer size of 50 The right side network has wireless links with bandwidth of Mbs, delay of 1ms and acket buffer size of 50 Random losses in wireless links follow exonential distribution and the acket loss rate ranges from to 01 The bottleneck link between these two networks is a wired link Its bandwidth W b and delay Delay b will be changed during our exeriments Its acket buffer size is set to be 0 TCP ackets are transferred from the wired network to the wireless network Packet size is Byte 1 Single Flow: At first a single TCP Veno connection is established The bandwidth of the bottleneck link is set to be Mbs and the delay is 80ms Figure 3 shows the validation result under different acket loss rates from to 01 We also lot the minimum and maximum boundaries curves when γ = 1 and γ = 4 5 resectively Note that during exeriments, we collect the dynamic values of and BaseRTT at every TD loss, to calculate the Veno arameter γ i using equation 3 Finally we use the average of γ i to calculate the throughut using equation 19 As shown in Figure 3, most exeriment results fall between the maximum and minimum boundaries, and they can be accurately redicted by our Veno equation At the same time, we study whether the

5 Throughut acket/s Maximum Exeriment Minimum Value of Veno Parameter Exeriment Fig 3 Single flow, W b =Mbs, Delay b =80ms Fig 4 Single flow, comarison of γ and γ e Throughut acket/s 40ms Exeriment40ms 80ms Exeriment80ms 160ms Exeriment160ms 30ms Exeriment30ms Throughut acket/s 50K Exeriment50K 500K Exeriment500K 750K Exeriment750K 1M Exeriment1M Fig 5 Single flow, validation under different bottleneck link delays Delay b Fig Single flow, validation under different background traffic Throughut acket/s 4 Exeriment4 8 Exeriment8 16 Exeriment16 3 Exeriment3 Throughut acket/s 4 Exeriment4 8 Exeriment8 16 Exeriment16 3 Exeriment3 Fig Multile flows, W b =1Mbs, Delay b =80ms Fig Mix flows of Veno and Sack, W b =1Mbs, Delay b =80ms Veno arameter γ estimated by equation 3 can accurately redict the real one The real Veno arameter γ e can be calculated in the exeriments as follows: γ e = N 4 5 M 1 4 N M where, N and M are the times of congestion window being cut down 1 5 or 1 resectively during transmission Figure 4 shows these two values are close, regardless of different acket loss rates Figure 5 demonstrates the validation under different bottleneck link delays from 40ms to 30ms, and Figure 6 is the result under different bottleneck link background traffic Noted that, to simulate the background traffic, we set u two UDP connections with areto distribution [15] over the bottleneck link The acket size of UDP is 51Byte The burst time and idle time are both ms The rate of each connection is set to be from 50Kbs to 1Mbs As we see in these figures, the theoretical results and the simulation results match quite well, regardless of different loss rates Multile Flows: To further verify the correction of Veno equation in comlicated scenarios, we test multile TCP connections ranging from 4 connections to 3 connections Firstly, we let all connections are TCP Veno flows, and thereafter, we relace half of them with TCP Sack flows The bandwidth of the bottleneck link is changed to be 1Mbs and the delay is 80ms The results are observed in Figure 7 and 8 resectively Seeing these two figures, our equation continues to kee high match with the simulation results either for multile connections or for mix connections B Wireless LAN Exeriments Figure 9 deicts the environments of our wireless LAN exeriments In wireless side, the client is a Comaq lato

6 with W00D wireless card The wireless Access Point is Cisco Linksys WRT54G They are searately laced at two corners and the distance between them is about 8m The bandwidth of the wireless network is 11Mbs and the frequency is 4GHz In the wired side, the server is a PC with FreeBSD 43, where TCP Veno is imlemented The gateway between wireless and wired networks is installed with FreeBSD 49 Number of Packets 1e09 1e08 1e07 1e06 Normal case Maximum Exeriment Minimum x x a Comaq lato with W00D wireless card Fig 9 Cisco Linksys WRT54G Gateway & NAT Dummynet FreeBSD 49 Toology of the wireless LAN TCP Veno FreeBSD 43 To verify our Veno equation, we use the method similar to that in [] One object Veno flow runs from the server to the client for 1hr The other four Veno flows run in the same direction for 800s, 000s, s, and 400s sequentially, which are regarded as the background traffic The 1hr flow trace is divided into 36 consecutive s intervals, and we count the number of ackets transmitted,, BaseRTT, and the acket loss rate in every interval Note that is given as the total number of loss indications TD and TO divided by the number of ackets transmitted Then, we ut the average values of and BaseRTT into the Veno equation to calculate the theoretical result Note that the acket size transmitted is 51Byte Two scenarios are studied here: 1 with Dummynet [16] configured at the gateway; without Dummynet configured at the gateway When Dummynet is set, it shaes the wired link bandwidth to Mbs, the delay to 80ms and the buffer to 0 ackets Because the general trends of the results in each exeriment are similar, we only give one samle in each case for the length limitation In each figure, three curves reresent the maximum boundary when γ = 4 5, the minimum boundary when γ = 1, and the actual results of Veno equation resectively, and the oints reresent the exeriment results As shown in Figure, the Veno equation can model TCP Veno s throughuts fairly well in each case V CONCLUSION AND FUTURE WORK In this aer, a simle throughut equation for TCP Veno is derived We introduce a Veno arameter γ into revious work on Reno [] Such arameter accurately characterizes the refined MD hase of Veno Our extensive exeriments on both simulation and wireless LAN have validated the correctness of the equation In the future work, further efforts are needed to refine the simle assumtion about the uniformly distributed W in the deduction, and a more accurate exression of the Veno arameter γ will be studied Furthermore, we will aly such derived closed form equation of TCP Veno into TFRC rotocol Number of Packets 1e09 1e08 1e07 1e06 Dummynet case Maximum Exeriment Minimum b Fig Exeriment results on the wireless LAN in a normal case and b Dummynet case REFERENCES [1] Van Jacobson Congestion Avoidance and Control SIGCOMM 88, ACM, Aug 1988 [] J Padhye, V Firoiu, D Towsley, and J Kurose Modeling TCP Throughut: A Simle Model and its Emirical Validation SIGCOMM 98, ACM, 1998 [3] Sally Floyd, Mark Handley, Jitendra Padhye, and Joerg Widmer Equation-Based Congestion Control for Unicast Alications SIG- COMM 000, ACM, August 000 [4] Cheng Peng Fu, Soung C Liew TCP Veno: TCP Enhancement for Transmission over Wireless Access Networks IEEE Journal of Selected Areas in Communications, Feb 003 [5] L Brakmo, S O Malley, and L Peterson TCP Vegas: New techniques for congestion detection and avoidance SIGCOMM 94, ACM, 1994 [6] C L Zhang, CPFu, MTYa, CHFoh et al Dynamics Comarison of TCP Reno and Veno IEEE Globecom, 004 [7] C P Fu, W Lu, B S Lee TCP Veno Revisited IEEE Globecom, 003 [8] Q X Pan, S C Liew, C P Fu, W Wang Performance Study of TCP Veno over wireless LAN and RED router IEEE Globecom, 003 [9] Z X Zou, C P Fu et al A Modification for Imroving TCP Veno Performance with Bursty Congestion IEEE Globecom, 005 [] Z X Zou, B S Lee, C P Fu Packet Loss and Congestion State in TCP Veno IEEE ICON, 004 [11] C B Fu, J L Wang, C P Fu, K Zhang Performance Study of TCP Veno in Wireless/Asymmetric Links International conference on cyberworlds, Jaan 004 [1] Ling-chi Chung, C P Fu, Song C Liew Imrovements Achieved by SAK Emloying TCP Veno Equilibrium-Oriented Mechanism over Lossy Networks IEEE EUROCOM, 001 [13] Y Liu, C P Fu et al An Enhancement of Multicast Congestion Control over Hybrid Wired/Wireless Networks IEEE WCNC, 004 [14] S Bajij, L Breslau, D Estrin, K Fall et al Imroving simulation for network research Univ Southern California, Los Angeles, Tech Re 99-70b, 1999 [15] htt://wwwisiedu/nsnam/ns/doc/ns docdf [16] htt://infoietuniiit/ luigi/i dummynet