Modelling TCP Reno with Spurious Timeouts in Wireless Mobile Environment

Transcription

1 1 Moelling TCP Reno with Spurious Timeouts in Wireless Mobile Environment Shaojian Fu an Mohamme Atiquzzaman Telecommunications an Networks Research Lab School of Computer Science University of Oklahoma, Norman, OK , USA. aresses: Abstract TCP has been foun to perform poorly in the presence of spurious timeouts (ST) cause by elay spikes which are especially more frequent in toay s wireless mobile networks than in traitional wire network. Because ST oes not frequently appear in wire networks an is generally consiere to represent a transient state, previous research in t consier the effects of ST on the steay state performance of TCP. However, ST is more frequent in wireless mobile environments, an must be consiere explicitly to accurately moel the steay state sening rate an throughput of TCP. In this paper, we propose an analytical moel of TCP Reno sening rate an throughput as a function of packet error rate an characteristics of spurious timeouts. The accuracy of the is valiate against results. The effectiveness of the moel is compare with those of previous moels, an has been foun to be more accurate than previous moels in the presence of spurious timeouts. I. INTRODUCTION TCP is the ominant transport layer protocol in the IP protocol suite, which carries most of the Internet traffic such as Web browsing, bulk file transfer an Telnet. TCP was initially esigne for wire networks, an hence performs poorly in the presence of elay spikes which are especially more frequent in toay s wireless mobile networks than in traitional wire network [1], [2], [3], [4], []. A suen increase of the instantaneous roun trip time (RT T ) beyon the sener s retransmission timeout value (RT O) causes retransmission ambiguity [6], [7], resulting in Spurious Timeouts 1 (ST) an Spurious Fast Retransmissions 2 (SFR) which prouce serious en-to-en TCP performance penalty [4], [7]. Causes of elay spikes in a wireless mobile environment inclue [1]: The hanoff of a mobile host between cells requires the base station to o channel allocation before ata can be transmitte from the mobile host. This causes segments at the mobile host to be queue until the completion of the channel allocation, giving rise to suen extra elay (in aition to the normal RT T ). 1 Spurious timeout is efine as a timeout which woul not have happene if the sener waite long enough. It is a timeout resulting in retransmission ue to a segment being elaye (but NOT lost) beyon RT O [7]. 2 Spurious fast retransmission occurs when segments get re-orere beyon the DUPACK-threshol in the network before reaching the receiver [7], i.e. the reorering length is greater than the DUPACK threshol (three for TCP). The physical isconnection of the wireless link uring a har hanoff will also result in a suen increase of the RTT. A Raio Link Control (RLC) layer between the LLC an MAC layers, to carry out retransmission at the link layer (for error recovery) in wireless mobile networks (such as GPRS an CDMA00), may result in elay spikes ue to repeate retransmission attempts uring link outages an perios of high link errors. Higher-priority traffic, such as circuit-switche voice, can preempt (block) the ata traffic temporarily. The uration of this blocking may be very long as compare to TCP s RTT estimate. A number of mechanisms have been propose in the literature to improve the performance of TCP in the presence of ST or SFR. For example, Luwig et.al. [7] uses the TCP timestamp option in the Eifel algorithm to resolve retransmission ambiguity; a retransmit flag, calle rtx, is ae in the TCP heaer [8] also to resolve retransmission ambiguity; Blanton et.al. proposes using the TCP D-SACK option to etect spurious retransmissions [9]; Gurtov et.al. have suggeste conservative management of TCP s retransmission timer []. However, there is no analytical framework to compare the performance an effectiveness of these improvements. During recent years, several papers have reporte analytical moels to preict the throughput of TCP uring bulk file transfers [], [11], [12], [13]. Lakshman et. al. [] analyze the performance of one or more TCP connections that share a bottleneck link in a WAN environment for large banwith-rtt prouct connections. They consiere slow start an congestion avoiance, but not timeouts. The moel by Mathis et. al. [11] i not consier retransmission timeouts, an hence it cannot be applie to non-ranom losses cause by rop-tail queues. Kumar et. al. [12] moelle an compare several TCP versions (TCP Tahoe, Reno, NewReno), where they consiere timeouts, an are therefore, more appropriate for the analysis of local wireless networks. The moel propose by Pahye et. al. [13] improves the one in [11] by consiering the effect of timeouts an limite receiver winow; this moel is more accurate than previous moels for correlate losses an a wie range of packet loss rates. However, none of the above moels consiers the effect of ST on the steay state throughput of TCP. This

2 2 may be ue to the fact that (a) ST oes not occur frequently in wire networks, an (b) ST is consiere to be a transient state in a wire network, an thus cannot prouce much impact on the steay state performance of TCP. However, in wireless mobile environments, STs are more frequent an must be consiere explicitly in orer to accurately moel the steay state throughput of TCP. The objective of this paper is to evelop an analytical moel to enable us to unerstan an preict the performance of TCP uring STs. This paper iffers from previous research in the fact that the moel propose in the paper explicitly takes into account the effect of ST on the steay state performance of TCP. The of TCP will, therefore, enhance further evelopment an evaluation of transport protocols in the area of wireless an mobile networks. Our is base on a stochastic analysis of the steay state sening rate an throughput of TCP Reno as a function of packet error rate, interval between long elays, an uration of long elays. The moel by Pahye et. al. [13] characterizes both the fast retransmit an the time out behavior of TCP Reno, an can accurately preict TCP performance over a wie range of loss rates. We therefore, use the result of Pahye et. al. as a basis of our work. From this point on, we will use PFTK (the initials of the authors) to refer to this moel. The main contributions of this paper can be summarize as follows: we evelope an analytical moel of TCP performance byexplicitly consiering ST effect; we compare the effectiveness of our propose analytical moel with that of, an foun that our propose moel is much more accurate for estimating TCP performance in the presence of frequent long elays. the moel has been valiate against results; The moel propose in this paper is expecte to significantly contribute to future stuies as follows: 1) There is always a funamental trae off between the rapiness of etection of true losses versus the risk of unnecessary retransmissions when esigning a RTO calculation algorithm or setting relate parameters. For example, the TCP parameter RT O min, the lower boun of the RTO value, has a significant impact on the effectiveness of the RTO estimator [14]. There is no existing metho to optimally set RT O min, an the current practice is to set it to twice the clock granularity. Since our consiers the effect of ST, it can assist in etermining an appropriate value of RT O min. 2) There is an increasing research interest to stuy the interaction between TCP an lower layer protocols in wireless environments [4], [1], [2]. The settings of lower layer protocols, such as hanoff schemes in Mobile IP an retransmission schemes at the link layer, have a non-trivial impact on the frequency of TCP spurious timeouts. The moel propose in this paper can facilitate the fine-tuning of these settings in a more coorinate fashion in orer to achieve an optimal performance. 3) When new moifications to TCP are mae to alleviate the effects of ST, our provie a framework for evaluating the impact of the moifications, an to compare the performance of the moifie TCP with previous versions of TCP. This will improve the current situation where the moifications are mainly teste by s, an hence may not be able to cover all possible network scenarios. The rest of the paper is organize as follows. In Sec. II, the assumptions for eveloping our moel are iscusse, followe by the moel in Sec.III. We then valiate the accuracy of the against s using the ns-2 network simulator in Sec. IV. We present the accuracy of our propose moel, an compare the performance of TCP uner ST obtaine from our moel with a previous TCP moel in Sec. V. Finally, we present our concluing remarks in Sec. VI. II. MODELLING ASSUMPTIONS The assumptions we have mae for eveloping our analytical moel of TCP with STs are escribe below. To isolate only the impact of long elays an segment losses on TCP, we assume that the sening rate is not limite by the avertise receiver winow, an the sener always has sufficient ata to sen. This assumption is satisfie easily by setting a large buffer size at the receiver. Possible extension of our moel to limite receiver winow is outline in Sec. VI. Segment losses in a roun are inepenent from losses in other rouns. Here, a roun is efine as the time between the sening of the first segment in a winow to the receipt of the corresponing acknowlegment (ACK). We assume that all other segments which were sent after the first lost segment in a specific roun are also lost (same assumption as in PFTK [13]). This loss moel is similar to the 2-state Markov chain approximation of the loss behavior observe in previous research [16]. The time require to sen a winow of ata is smaller than an RTT. This assumption is justifie by the observations of trace plots of Fall et. al. performe in [17], an was also use in the [13]. Our goal is to moel the effect of elay spikes cause by mobile hanoff, link layer retransmission, or packet rerouting on the performance of TCP. We therefore, o not consier the fluctuation of roun trip time measurements cause by queueing elays. We assume that these measurements compose a stationary ranom process with an expecte value of RT T in the absence of elay spikes. Since our main concern in this paper is to moel the effect of Spurious Timeouts on TCP, we assume that BugFix, propose in RFC82 [18], is enable to prevent Spurious Fast Retransmission. However, note that if BugFix is not enable, a Spurious Fast Retransmission usually follows a Spurious Timeout. This is because the spuriously retransmitte segments prouce a sequence of uplicate acknowlegements at the receiver [7]. III. ANALYTICAL MODEL In this section, our objective is to evelop an analytical moel for sening rate an throughput of TCP as a function of packet error rate an long elay. First, we will etermine the sening rate (Sec. III-D), an then the throughput (Sec. III-E) by subtracting the lost an spuriously retransmitte segments from the sening rate. The sening rate is obtaine by analyzing the ynamics of the sener s winow aroun a long elay (Sec. III-B). We escribe below the notations that will be use in our moel.

3 3 A. Notations The notations use in this paper are given below. Our moel is base on the moelling approach use by. For the sake of consistency an ease of unerstaning by the reaer, we therefore use many of the terminology an notations use in [13]. I interval between long elays. D uration of the long elay. p packet error rate. b number of segments acknowlege by one ACK segment. b = 2 when elaye acknowlegment is use at the receiver. RT T expecte value of roun trip time when there is no long elay. T 0 converge RTO value as efine in Sec. III-B. W TCP sener winow size. B, T steay state sening rate an throughput, respectively, of TCP connection. T DP triple uplicate perio, i.e. the time between two successive triple uplicate loss inications. LDP long elay perio, which consists of one T DP, one long elay, one slow start, an a secon T DP (see Fig. 1). N P normal perio, which consists of n instances of T DP an one instance of timeout perio (see Fig. 3). n number of T DP s in one NP. LDC long elay cycle, which consists of m NP s an one LDP (see Fig. 3). m number of NP s in one LDC. Z T DP, Z NP, Z LDP uration of one T DP, NP, an LDP, respectively, note that A an S is use in [13] instea of Z T DP an Z NP. Z T D uration of n instances of T DP s in one NP (see Fig. 3). Z T O uration of the timeout perio in one NP (see Fig. 3). Y number of segments sent from the sener uring one T DP. M r number of segments sent uring r th NP, r = 1, 2 m. R number of retransmitte segments uring the timeout perio in one NP. R D number of retransmitte segments uring D. SST v K value of slow start threshol at the en of a long elay D. the number of rouns neee to complete the slow start stage after a long elay. number of segments sent uring the slow start stage in an LDP. U, G number of segments sent uring one LDP an one LDC respectively. B. Dynamics of sener winow aroun a long elay Before we evelop a moel for the sener s sening rate in the next section, we analyze the ynamics of the sener s winow aroun a long elay in this section. Fig. 1 shows the evolution of sener s winow size as represente by the number of segments that can be sent. At each roun the winow is Segments Sent W i W i-1 / X i }b }b }b TDP i T 0 LDP ACKe segment elaye segment x lost segment s spuriously retransmitte segment } W i+1 x x x x s R D SSTs s.... s s s...s s s s... Slow b.... }b 2T 0 Start TDP i+1 D Fig. 1. Segments sent uring one Long Delay Perio (LDP ). No. of rouns increase by 1/b. After X i rouns, the long elay (D) begins, when some of the segments in the X i -th roun are elaye (segments marke ). Since the long elay is of a much larger timescale than a roun, any extra segments that were sent in roun X i+1, corresponing to the ACKs of successfully elivere segments of roun X i, are also elaye. After T 0 secons, which is the converge value of RTO when the roun trip time is stable for a relatively long perio of time, the sener will timeout an reuce the winow to one an retransmit the first elaye segment. If it is not acknowlege within 2T 0, the sener will retransmit it again, an so on. The number of retransmissions uring the long elay is enote by R D ; all these retransmitte segments are also elaye. Eventually, when the ACK for the first elaye segments comes back after the long elay has cleare, the sener will enter slow start an spuriously retransmit all the elaye segments (segments marke s ). The sener will exit slow start when the winow hits the slow start threshol (enote SST ). TCP Reno starts fast retransmit after receiving three uplicate ACKs, which are calle triple-uplicate loss inications. Triple Duplicate Perio (TDP) is efine in [13] as a perio between two successive triple-uplicate loss inications. We efine a Long Delay Perio (LDP) as consisting of two consecutive TDPs, one long elay, an one slow start as shown in Fig. 1. Note that even though the first perio, labelle with TDP i in the figure, oes not en with a triple uplicate loss inication, the number of segments sent an the uration of TDP i is the same as other TDPs, so we just use TDP for convenience. The sener s winow was W i 1 at the en of TDP i 1 ; after the fast retransmit, it has been reuce to W i 1 /2, which is the sener s winow at the start of TDP i. C. Statistical moelling of the long elay pattern In this section, we evelop a moel for the long elay pattern, which will be use to moel the sening rate in Sec. III-D. The roun trip times as measure by the sener in the presence of long elays is shown in Fig. 2(a). We use a two-state Markov chain to moel the start an en of a long elay as shown in Fig. 2(b). The two states are: Interval between long elays (S I ) an long Delay (S D ). Here, we assume that the length of the S I an S D states are both exponentially istribute, with an q being the transition probabilities from state S I to state S D an

4 4 Roun trip time RTT I (a) D time 1- SI q (b) Fig. 2. (a) Variation of RTT showing four long elays, an (b) moel of long elays. state S D to state S I, respectively. By solving the Markov chain in Fig. 2(b), the relationship between I an D can be expresse as: = E(I) + q Given a moel for the lower layer events (such as link layer retransmission, mobile hanoff, etc. [19]) that cause long elays, we can obtain the values of E(I),,, an q to be use in Eqn. (1). D. Moelling the TCP sening rate In this section, we consier the sening rate of TCP as a function of p, I, an D. The average sening rate of TCP can be calculate as B(p, I, D) = E(G) me (Z NP ) + E (Z LDP ) where, the numerator enotes the number of segments sent uring one Long Delay Cycle (LDC) (to be erive in Sec. III-D.2) an the enominator is the uration of an LDC. We first look at the macroscopic behavior of one LDP in Sec. III-D.1, which will then be use to etermine the number of segments sent an the uration of an LDC. 1) Analysis of a Long Delay Perio (LDP): The total number of segments sent uring one LDP is the sum of segments sent uring two T DP perios, the timeout perio, an the slow start stage (Fig. 1): SD 1-q (1) E(U) = 2E(Y ) + E(R D ) + E(K) (3) The uration of LDP can be written as the sum of the time uration of the two TDP perios, the long elay, an one slow start stage, minus the overlapping area (2RT T ) between D an TDP i : E(Z LDP ) = 2E(Z T DP ) + + v RT T 2RT T (2) = 2E(Z T DP ) + + (v 2) RT T (4) E(Y ) an E(Z T DP ) in Eqns. (3) an (4) can be etermine from Eqns. (6) an (7), which can be obtaine from the PFTK moel [13] as follows: E(W ) = 8 3bp E(Y ) = 1 p p E(Z T DP ) = + E(W ) = 1 p p + 8 3bp () (6) ( b 2 E(W ) + 1 ) RT T (7) Next, we erive the three unknown variables (E(R D ), v, an E(K)) in Eqns. (3) an (4). Determine E(R D ): Since we assume that D is exponentially istribute (see Sec. III-C) with mean, if the sener experiences a long elay of D, the probability that there is one timeout is: P r (T 0 < D 2T 0 ) = P r(d 2T 0 ) P r(d T 0 ) = e T 0 e 2T 0 (8) The probability that there are two or more timeouts is: P r (D > 2T 0 ) = e 2T 0 (9) Because the sener sens out a segment when a timeout occurs, the number of segments sent uring D is the same as the number of timeouts. since the sener can backoff a maximum of 6 times to get a RT O of 64T 0, the number of segments sent can be expresse as: E(R D ) = 1P r (T 0 < D 2T 0 ) + 2P r (2T 0 < D 3T 0 ) + = + 6P r (32T 0 < D 64T 0 ) ( ) e 2 j T0 e 64T 0 j=0 () Determine v: After the long elay, the SST value will be max(w i /2, 2) if there is only one timeout uring D, otherwise it will be two for two or more timeouts. Therefore, the expecte value of SST after the long elay is: ) E(SST ) = max(w i /2, 2) (e T 0 e 2T 0 + 2e 2T 0 (11) During the slow start, if the receiver aopts elaye acknowlegment, the sener s congestion winow will grow by half of the winow size in the previous roun accoring to the following rule: ( cwnj ) cwn j+1 = cwn j + 2 which can be approximate as: cwn j = with cwn 1 = 1, j = 1, 2, 3 (12) ( ) 3 j j = 1, 2, 3 (13) 2 En of the slow start stage at E(SST ) after v rouns implies that cwn v = E(SST ); the number of rouns neee to complete this stage is approximately expresse as: (E(SST )) v = log 3/ log (E (SST )) (14) Determine E(K): The number of segments sent in each roun of the slow start stage in Fig. 1 is given in Eqn. (13). So the number of segments sent uring slow start can be approximate by the sum of the segments sent uring these v rouns: E(K) = v j=1 ( ) 3 j ( ) log(e(sst )) 3 3 (1) 2 2 By substituting E(R D ), v, an E(K) from Eqns. (), (14), an (1) into Eqns. (3) an (4), we can obtain the number of segments sent an the uration of one LDP.

5 Segments Sent I LDC The total number of segments sent uring one LDC is the sum of segments sent uring m instances of NP perio an an LDP perio: m instances of normal perios E(G) = m M r + E(U) = me(m r) + E(U) (21) r=1 Slow TDP Start Fig. 3. LDP i-1 Y 11 Y 12 Y 13 No. of rouns TDP TDP TDP T Z TD 0 2T Z TO 0 TDP D Slow TDP Start NP1 NP 2...NP r...np m LDP i Sener winow evolution in one Long Delay Cycle (LDC). 2) Analysis of one Long Delay Cycle (LDC): In Eqn. (2), Z NP can be obtaine from [13] as given in Eqn. (16), E(Z LDP ) has alreay been evelope in Sec. III-D.1, an E(G) epens on m, E(U), E(M r ), E(R). E(M r ) an E(R) can be obtaine from [13] as given in Eqns. (16) an (17). ( E(Z NP ) = E(n)E(Z T DP ) + E Z T O) ( ) b = 2 E(W ) + 1 f p E(n)RT T + T 0 1 p 6 where f p = i 1 p i i=1 1 p 8 + p 3bp E(M r ) = E(n)E(Y ) + E(R) = ( ) + 1 min 1, 3 3bp 1 p 8 (16) (17) E(n) an E(R) in Eqns. (16) an (17) can be etermine from Eqns. (18) an (19), which can be obtaine from the PFTK moel [13] as given below. E(n) = E(R) = ( 1 ) 3 min 1, E(W ) (18) 1 1 p (19) E(U) has alreay been evelope in Sec. III-D.1, which leaves us with only etermining m. We efine another term, calle LDC (as shown in Fig. 3), which starts with the en of the previous LDP. An LDC consists of several instances of normal perios (NP) at the beginning an an LDP at the en. Here, the normal perio enotes the time interval with no long elays, which is equal to the sum of Z T D an Z T O ; values of Z T D an Z T O are obtaine from [13] as given in Eqn. (16). Referring to Fig. 3, the interval between long elays (I) consists of a slow start phase following the previous long elay, m instances of NP an a T DP. We can calculate m as: m = E(I) 2E ( Z T DP ) v RT T E (Z NP ) () Since one LDC consists of m instances of NP an ens with one LDP, the uration of one LDC can be obtaine as: me ( Z NP ) + E ( Z LDP ) By substituting E(G) from Eqn. (21) into Eqn. (2), we can obtain the steay state sening rate of the TCP sener. E. Moelling TCP throughput We etermine the TCP throughput by subtracting the spuriously retransmitte an lost segments from the sening rate (erive in Sec. III-D). Referring to Fig. 1, the elaye segments in the X i an X i+1 -th rouns of the first TDP are subsequently spuriously retransmitte uring the slow start stage. Therefore, we nee to subtract one winow of segments (E(W )) from E(Y ). E(Y 1 1 p ) = E(Y ) E(W ) = (22) p In the secon TDP of the LDP perio, the lost segments (marke x ) nee to be subtracte from the sening rate, i.e. on the average, we nee to subtract E(W ) 2. E(Y 2 E(W ) ) = E(Y ) = 1 p + E(W ) 2 p 2 (23) Because the segments retransmitte uring the timeout perio are iscare by the receiver, we can replace E(R) in Eqn. (17) with E(R ) = 1. Similarly, we have E(R D ) = 1. Replacing E(Y ), E(R) an E(R D ) in Eqns. (3) an (17) with E(Y ), E(R ) an E(R D ), we obtain: E(U ) = E(Y 1 D ) + E(K) + E(Y 2 ) (24) E(M r) = E(n)E(Y 2 ) () Therefore, the average TCP throughput uring one LDC can be calculate as the total number of segments elivere to the receiver ivie by the uration of one LDC. The segments elivere can be obtaine by replacing E(U) an E(M r ) in Eqn. (21) with E(U ) an E(M r). Although we subtract the spuriously retransmitte an lost segments from the total number of segments receive at the receiver, the uration of an LDC remains unchange. We can write the throughput of the TCP connection as: T (p, I, D) = me(m r ) + E(U ) me(z NP ) + E(Z LDP ) IV. SIMULATION SETUP (26) In orer to valiate the accuracy of our moel presente in Sec. III, we compare the results obtaine from the analytical moel against results obtaine from the ns-2 [] network simulator in Sec. V. The long elays are simulate using an ns-2 moule calle hiccup [21] which hols all the arriving segments for time D, before releasing them into the link. This hiccup moule enables us to accurately control the start an en of long suen elays. The topology is shown in Fig. 4, where a TCP Reno sener sens FTP traffic to a estination via a link equippe with a hiccup moule an an error moule. The queue size of the link is set to be large enough (800 packets) to remove the possibility of packet rops

6 6 Fig. 4. FTP/Reno S Hiccup moule Error moule ns-2 topology with hiccup an error moules. TABLE I TCPSink SIMULATION PARAMETERS FOR THE TOPOLOGY OF FIG. 4. Protocol TCP Reno Heaer size 40 bytes Payloa size 36 bytes rwn limit 800 segments Initial cwn 1 segment Initial ssthresh 800 segments link banwith 0Mbps link propagation elay 0-0 ms link loss rate link buffer size limit 800 packets D 3 =6 3 Fig.. 3 =8 =12 3 Sening rate estimation for RT T =0ms, E(I)= sec. cause by link queue overflow, thus we can control the packet error rate accurately by the error moule. We insert the hiccup moule to simulate ifferent elay patterns (E(I), ) (see Sec. III-C), an also simulate the packet error rate p using a 2-state Markov error moule. We measure the sening rate (B) an the throughput (T ) of TCP, an compare them with the an our propose analytical moel in Sec. V. Values of relevant parameters are summarize in Table I. Note that we set the rwn limit to a large value of 800 segments to avoiing any effect of avertise receiver winow on sening rate an throughput, an set the link banwith to a large value of 0Mbps to simulate the sener behavior of probing for available network banwith, consequently, the sening rate an throughput are only limite by the p, I, an D settings. We vary the interval between the long elays (I) with an expecte value ranging from to 240 secons, an long elay uration (D) with an expecte value ranging from 2 to 12 secons. For each p, I, D, RT T combination, we run the for 0 times, with each time run for 0 secons to make the result statistically trustable. V. RESULTS In this section, to evaluate the effectiveness of our propose moel, we compare the sening rate an throughput preicte by our moel an the against the values obtaine from. To fin out the sensitivity of these two moels to ifferent values of /E(I) ratio, RT T, an p, we also compare the mean square estimation error an the 9% confience interval error range of the two moels versus these parameters. A. Comparison of sening rate estimation We compare the preicte sening rate from our propose moel an against results. Figs. an 6 show the scenarios where RT T = 0ms, E(I) = an =6 3 Fig =8 =12 3 Sening rate estimation for RT T =0ms, E(I)=240 sec. secons, an ranging from 6 to 12 secons. Fig. shows that the can preict the sening rate more accurately than the. It is also shown that when increases, as expecte, the gap between the an the result increases, but the accommoates the increase of well. When E(I) is increase to 240 (Fig. 6), implying that the long elays are much more sparse than I = scenario, thus the estimation from the propose moel an the are rather close. We repeat the above experiments for RT T = 400ms, an obtaine similar results as shown in Figs. 7 an 8. B. Comparison of throughput estimation Next, we compare the preicte throughput from the propose moel an the against the values obtaine from.

7 7 =6 =8 =12 3 =6 3 3 =8 =12 3 Fig. 7. Sening rate estimation for RT T =400ms, E(I)= sec. Fig. 9. Throughput estimation for RT T =0ms, E(I)= sec. =6 =8 =12 3 =6 3 3 =8 =12 3 Fig. 8. Sening rate estimation for RT T =400ms, E(I)=240 sec. Fig.. Throughput estimation for RT T =0ms, E(I)=240 sec. Figs. 9 an show the results for RT T = 0ms, E(I) = an 240 secons, an ranging from 6 to 12 secons. Fig. 9 shows that the can also preict the actual throughput more accurately than the. It s also shown that when increases, the ifference between the an the result increases, but the propose moel accommoates this increase well. When E(I) is increase to 240 (Fig. ), the estimation from the propose moel an the are close. We then repeat the these comparisons for RT T equals 400ms, an we obtaine the similar results as shown in Figs. 11 an 12. C. Mean square estimation error an error range To investigate an compare the sensitivity of our propose moel an the to /E(I), RT T, an p, we efine Square Estimation Errors for sening rate an throughput as ɛ 2 B = Ba B s ( ) 2 ( ) B s an ɛ 2 T = Ta T 2, s T s respectively. Here, B a an B s are the sening rate obtaine from analytical moels an s, respectively, an T a, an T s are the throughput obtaine from analytical moels an s, respectively. The Mean Square Estimation Error (MSEE) is efine as the mean of the Square Estimation Errors for sening rate an throughput as ɛ 2 B an ɛ2 T, respectively. The 9% confience interval for ɛ 2 B an ɛ2 T are represente by ɛ 2 B an ɛ 2 T We compute an plot the ɛ 2 B an ɛ2 T for both the propose moel an. Also plotte are the ɛ 2 B an ɛ 2 T of the two moels, which inicates how much the estimation error can oscillate aroun it s mean value. First, we investigate the impact of /E(I) ratio on the

8 8 =6 Fig. 11. =8 =12 Throughput estimation for RT T =400ms, E(I)= sec. MSEE of sening rate estimation (%) Fig. 13. Error range () MSEE () Error range () MSEE () 2 1 LDF Sening rate estimation error vs. LDF. =6 =8 =12 MSEE of throughput estimation (%) 3 1 Fig. 14. Error range () MSEE () Error range () MSEE () 2 1 LDF Throughput estimation error vs. LDF. Fig. 12. Throughput estimation for RT T =400ms, E(I)=240 sec. ɛ 2 B an ɛ2 T of these two moels. We efine the /E(I) ratio as Long Delay Frequency (LDF), which represents the frequency of the long elays within a perio of time. Figs. 13 an 14 show the ɛ 2 B an ɛ2 T an the ɛ 2 B an ɛ 2 T versus LDF. When LDF increases, the s ɛ 2 B an ɛ2 T increase ramatically. However, we can observe that the propose moel s ɛ 2 B an ɛ2 T are almost constant with the increase of LDF values. This is because a higher D/I ratio means longer elays with relatively short intervals, thereby making the impact of long elays on the more severe. To see how the ɛ 2 B an ɛ2 T of the two moels change as a function of RT T, we investigate the sensitivity of the ɛ 2 B an ɛ 2 T versus RT T. Figs. 1 an 16 show the ɛ2 B an ɛ2 T an the ɛ 2 B an ɛ 2 T versus RT T. When the RT T increases, both ɛ2 B an ɛ2 T ecrease. This is ue to the fact that the impact of long elays on the sening rate an throughput becomes insignificant when the RT T increases. Figs. 17 an 18 show the ɛ 2 B an ɛ2 T an ɛ 2 B an ɛ 2 T versus packet error rates. When p increases, both ɛ 2 B an ɛ2 T increase. We can see that if we can control p < 0.1, we can expect the ɛ 2 B an ɛ2 T of the to be uner %. VI. CONCLUSION TCP has been foun to perform poorly in the presence of spurious timeouts cause by elay spikes which are more frequent in toay s wireless mobile networks as compare to traitional wire network. Previous analytical moels in t consier the effect of spurious timeouts on the steay state performance of TCP. In this paper, we evelope an analytical moel to stuy TCP sening rate an throughput as a function of packet error rate an the characteristics of long elays. We have use results to valiate accuracy of the an

9 9 Error range () MSEE () Error range () MSEE () 40 3 Error range () MSEE () Error range () MSEE () MSEE of sening rate estimation (%) 1 MSEE of throughput estimation (%) RTT (sec.) 0 Fig. 1. Sening rate estimation error vs. RT T. Fig. 18. Throughput estimation error vs. p. MSEE of throughput estimation (%) 1 Error range () MSEE () Error range () MSEE () RTT (sec.) Fig. 16. Throughput estimation error vs. RT T. MSEE of sening rate estimation (%) Error range () MSEE () Error range () MSEE () Fig. 17. Sening rate estimation error vs. p. compare with that of the. We have shown that the is more accurate than the in estimating the steay state sening rate an throughput of TCP in presence of frequent long elays. Due to space limitations, we coul not present the extension of our moel to the finite receiver buffer case. However, the extension can be one by changing Eqns. (), (6), an (11), an following the approach use in [13]. REFERENCES [1] A. Gurtov, Effect of elays on TCP performance, in IFIP Personal Wireless Communications, August 01. [2] F. Khafizov an M. Yavuz, Running TCP over IS-00, in IEEE International Conference on Communications, New York, April 02, pp [3] M. Yavuz an F. Khafizov, TCP over wireless links with variable banwith, in 6th IEEE Vehicular Technology Conference, Vancouver, September 02, pp [4] D. S. Eom, H. Lee, an M. Sugano et. al., Improving TCP hanoff performance in mobile IP base networks, Computer Communications, vol., no. 7, pp , May 02. [] A. Gurtov an R. Luwig, Making TCP robust against elay spikes, Internet Draft, raft-gurtov-tsvwg-tcp-elay-spikes-00.txt, February 02. [6] P. Karn an C. Partrige, Improving Roun-Trip Time estimates in reliable transport protocols, ACM Computer Communications Review, vol. 17, no., pp , August [7] R. Luwig an R. H. Katz, The Eifel algorithm: Making TCP robust against spurious retransmission, ACM Computer Communications Review, vol., no. 1, pp. 36, January 00. [8] R. Luwig, The TCP retransmit (rxt) flag, Internet Draft, raft-luwigtsvwg-tcp-rxt-flag-02.txt, November 01. [9] E. Blanton an M. Allman, Using TCP DSACKs an SCTP Duplicate TSNs to etect spurious retransmissions, Internet Draft, raft-blantonsack-use-01.txt, August 01. [] T.V. Lakshman an U. Mahow, The performance of TCP/IP for networks with high banwith-elay proucts an ranom loss, IEEE/ACM Transactions on Networking, vol., no. 3, pp , June [11] M. Mathis, J. Semke, an J. Mahavi, The macroscopic behavior of the TCP congestion avoiance algorithm, Computer Communications Review, vol. 27, no. 3, pp , July [12] A. Kumar, Comparative performance analysis of versions of TCP in a local network with a lossy link, IEEE/ACM Transactions on Networking, vol. 6, no. 4, pp , August [13] J. Pahye, V. Firoiu, D.F. Towsley, an J.F. Kurose, Moeling TCP Reno performance: a simple moel an its empirical valiation, IEEE/ACM Transactions on Networking, vol. 8, no. 2, pp , April 00.

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