Modeling Impact of Delay Spikes on TCP Performance on a Low Bandwidth Link

Transcription

1 Modeling Impact of Delay Spikes on TCP Performance on a Low Bandwidth Link Pasi Lassila and Pirkko Kuusela Networking Laboratory Helsinki University of Technology (HUT) Espoo, Finland {Pasi.Lassila,Pirkko.Kuusela }@hut.fi February 10, 2004

2 AB HUT, Networking Laboratory 2(20) Outline RTT spikes & TCP behavior renewal model & TCP goodput formula simple p-formula model validation & evaluation with ns2 misc. & summary

3 AB HUT, Networking Laboratory 3(20) TCP in wireless TCP designed for fixed networks control actions: halving or drastic reduction of sending window delayed packets may be taken as lost packets timeout timer relies on RTT (round trip time) estimation RTTs can be highly variable

4 AB HUT, Networking Laboratory 4(20) RTT spikes sudden increase in RTT = delay spike may occur due to: handovers link error recovery scheduling between calls and data (GPRS) delay spikes trigger spurious timeouts (packets not lost, simply delayed)

5 AB HUT, Networking Laboratory 5(20) Illustration of RTT spikes! Figure by Andrei Gurtov (see A.Gurtov, Effect of Delays on TCP Performance)

6 AB HUT, Networking Laboratory 6(20) Our model scenario I one TCP source on a low bandwidth wireless link (e.g. GPRS) RTT spikes occur TCP evolution (grey box approach) 1. silence for time SD due to an RTT spike 2. exponential increase in sending window (slow start) 3. sending rate limited by the low bandwidth RTT spikes independent of TCP do not model TCP exponential backoff (OK, if SD < 10 sec.) look at actual sending window (not congestion window, which is larger) OUTCOME: a TCP goodput formula

7 AB HUT, Networking Laboratory 7(20) Our model scenario II Illustration of TCP behavior C max SD SD SD SD SD silence for time SD due to an RTT spike SD= mean value of RTT spike lengths exponential increase in sending window (slow start) sending rate limited by the low bandwidth

8 AB HUT, Networking Laboratory 8(20) Renewal reward model Z n T n X n A n = nth RTT spike, renewal time = Z n Z n 1, time between spikes = TCP sending window = # of packets sent = T n 0 X n (u)du, the reward X n (t) = 0, t < SD, 2 t SD RTT, SD t L + SD, C max, t > L + SD, L = RT T ln 2 ln C max

9 AB HUT, Networking Laboratory 9(20) Goodput with i.i.d. spike intervals Assume T n s i.i.d. with probability density f T, E(T ) = A t = cumulative total reward up to time t, Renewal reward theorem: E(A t ) lim t t Goodput formula G TCP = E(A) E(T ) E(A) = = RTT ln 2 T = E(A) E(T ) X(t)dt 0( L+SD SD where L = time to reach C max input: SD, RTT, C max, spike distribution ) (2 y SD RTT 1)fT (y)dy + (C max 1) f T (y)dy + L+SD C max (y L SD)f T (y)dy, L+SD

10 AB HUT, Networking Laboratory 10(20) Goodput with exponential intervals Assume: RTT spike intervals from exponential distribution with parameter 1/E(T ) Exponential goodput formula G TCP = E(A) E(T ) = e SD/E(T ) ( RTT E(T ) ) ) ln 2) ln 2C1 RTT/(E(T max. RTT/E(T ) ln 2 depends on SD E(T ), RTT E(T ) rations and C max

11 AB HUT, Networking Laboratory 11(20) Markov Renewal Model introduce correlations between T n s cycles no longer i.i.d., but modulated by Markov chain B n assume: modulating background process slower than RTT spike process simple case: Markov chain with states 0 and 1, invariant distribution π

12 AB HUT, Networking Laboratory 12(20) Markov Goodput Formula Markov Renewal Reward Theorem: 1 lim t t A t = E π(a) E π (T ). Backgound B n with probability density f 0 (t) at state 0 and f 1 (t) at state 1 gives ( ) T E π 0 X(u)du G T CP = E π (T ) = π(0) 0 f 0 (t) t 0 X(u)du dt + π(1) 0 f 1 (t) t 0 X(u)du dt π(0) 0 f 0 (t)tdt + π(1), 0 f 1 (t)tdt π(0) and π(1) equilibrium probabilities of states 0 and 1

13 AB HUT, Networking Laboratory 13(20) Markov with exponential intervals Take exponential probability densities to get f 0 (t) = 1/µ 0 e t/µ 0 and f 1 (t) = 1/µ 1 e t/µ 1 RTT µ 0 ln 2 G T CP = π 0e SD/µ 0µ 0 RTT µ 0 ln 2C 1 RTT µ 0 ln 2 max + π 1 e SD/µ 1µ 1 RTT µ 1 ln 2C RTT µ 1 ln 2 1 µ RTT 1 ln 2 max π 0 µ 0 + π 1 µ 1.

14 AB HUT, Networking Laboratory 14(20) Simple p-formula I P {packet experiences an RTT spike} = p A n geom(p), so E(A n ) = 1/p TCP sending rate at time t (after SD has ellapsed) g(t) = min(2 t/rtt 1/2, C max ) H = time to sent 1/p packets C max 1 p SD H

15 AB HUT, Networking Laboratory 15(20) Simple p-formula II H = time to sent 1/p packets Throughput: T TCP = 1/p H + SD Result: If p > ln 4 RTT(2C max 2) T TCP = ln 2 p(rtt ln(1 + 2 ln 2/(pRTT)) + SD ln 2 otherwise (TYPICAL CASE!) C max ln 4 T TCP = ln 4 + prtt( 2 + C max (ln ln C max )) + SDpC max ln 4

16 AB HUT, Networking Laboratory 16(20) Validation with ns2 RTT spike generator by A. Gurtov turns link on/off for random periods at random intervals TCP SACK parameters: packet size = 576 bytes link one-way delay = 100 ms RTT = 2 link delay + packet transmission time

17 AB HUT, Networking Laboratory 17(20) Long spike duration RTT spikes Uni[5,10], SD =7.5 s. 40k C Max = 40 kbps 100k C Max = 100 kbps G TC P 35k 30k Renewal model P model NS2, 0% loss NS2, 2% loss NS2, 5% loss G TC P 90k 80k 70k 25k 60k EHTL EHTL Low bandwidth: excellent agreement OK, if 2% losses (Note: losses not modelled) Higher bandwidth: Nice (although model made for low bandwidth)

18 AB HUT, Networking Laboratory 18(20) Short spike duration RTT spikes Uni[1,5], SD =3 s. 40k C Max = 40 kbps 100k C Max = 100 kbps G TC P 35k 30k Renewal model P model NS2, 0% loss NS2, 2% loss NS2, 5% loss G TC P 90k 80k 70k 25k 60k EHTL EHTL TCP learns the spike process, less timeouts model underestimates now losses have a bigger impact

19 AB HUT, Networking Laboratory 19(20) Distribution sensitivity pareto with aba x a+1, a = 1.5, x b Markov with exp distributions, π 0 = π 1 = 1/2 and µ 0 = 1/4E(T ), µ 1 = 1.75E(T ) C max =8.68 packets, RTT=720 ms and SD=5 sec exp G TC P pareto uniform Mmod exp 5000 pformula ET bursty spikes give better goodput! p-formula is a lower bound!

20 AB HUT, Networking Laboratory 20(20) Summary TCP goodput formula for low bandwidth links with RTT spikes grey box approach to TCP correlations to RTT spike process using Markov modulation model not complicated, allows to ellaborate more on spike process simple p-formula (gives lower bounds) excellent agreement with ns2 future include packet losses (congestion control phase) add distribution on RTT spike lengths