Parallel TCP Sockets: Simple Model, Throughput and Validation

1. Parallel TCP Sockets: Simple Model, Throughput and Validation Milan Vojnović Microsoft ResearchUnited Kingdom Eitan Altman INRIA France Dhiman Barman UC Riverside United States Bruno Tuffin IRISA/INRIA France IEEE Infocom 2006 Talk, Barcelona, Spain, April 25, 2006

2. Motivation • Parallel TCP sockets used for bulk-data transfers • Throughput improvements • Ex GridFTP • Throughput characterization of AIMD (“Additive-Increase & Multiplicative Decrease”) connections • Known: throughput-loss formulae of a single AIMD • Given a loss process (stochastic; stationary; ergodic) • SQRT, Altman, Avrachenkov, Barakat (2000) • Our goal: Aggregate throughput of N AIMD connections competing for a bottleneck

3. Related Work • Partial results for the same problem by Altman, El Azouzi, Ross, Tuffin (2004) • For two connections only (N = 2) • Unnecessary assumptions on loss process • Experimental results by Hacker, Athey, Noble (2002) • Throughput increase exhibits diminishing-returns with the number of connections

4. This Talk • One main result: throughput formula for parallel, symmetric AIMD connections • For any given number of connections • For many loss polices (= assignment of congestion signal to competing connections) • Throughput second-moment for specific loss polices • Shows throughput higher-order statistic depends on the loss policy • Simulation & Internet experiment results

5. Origins of TCP throughput deficiency Bottleneck capacity • TCP window synchronization • TCP window control • Congestion avoidance • Receiver window limitation c Connection 1 send rate Connection 2 send rate 0 c 0 c 0

6. Model • Single link of capacity c • Congestion event whenever the aggregate arrival rate hits c • Model introduced by Baccelli & Hong (2002) 1 2 . . . i . . . AIMD connection Xi = send rate N Bottleneck capacity c

7. Model (2) • Assumption ONE: at a congestion event, exactly one connection undergoes multiplicative-decrease • TCP windows non synchronized • Example: 3 AIMD connections X(3) X(2) X(1) Slope h bX(1) Congestion event X(1) + X(2) + X(3) = c Time

8. Main Result: Throughput Formula • Consider N symmetric AIMD connections • b = multiplicative-decrease factor • Assume ONE = exactly one connection undergoes multiplicative-decrease per congestion event The aggregate throughput is:

9. Implications of the Result • Applies to a broad class of loss processes • A broad class of loss polices to select connection to undergo a multiplicative-decrease at congestion events • Can depend in many ways on the observed past of send rates, provided only the system is stable • Throughput-invariance • Loss policy is irrelevant • Special cases (for b = ½; TCP like): • N = 1 : Utilization = 0.75 c • N = 2 : Utilization = 6/7 c  0.86 c

10. Implications of the Result (2) • Throughput deficiency due to TCP window adaptation compensated with a few parallel connections • Utilization • > 90% for N=3 • almost 95% for N=6 Utilization (N) N

11. Proof Sketch = 1 if connection i selected at the n-th congestion event, else 0

12. Proof Sketch (2) • Palm inversion • The latter follows by taking expectation on both sides of the recurrence for Xi2(Tn) const

13. Example 1: Aggregate Throughput is Invariant • Connections: • RED (2) and BLUE (2) • A BLUE connection chosen with probability s Aggregate throughput Throughput of BLUE connections Throughput of RED connections Throughput (s) s

14. Example 2: Loss Polices • Beatdown • Pick a selected connection as long as possible • Rate-independent • Pick at random a connection with fixed probability • Rate-proportional • Pick at random a connection proportional to its send rate • Largest-rate • Pick a connection with largest send rate = round-robin (in steady-state, with symmetric connections)

15. Throughput: Higher-order Statistics Depends on Loss Policy • Result for N = 2 & b = ½ • Loss policy: second moment • Same type of result as in Altman, El Azouzi, Ross, Tuffin (2004) • But a correct version • Full proof; not symbolic math software solving

16. Validation • ns-2 simulations • Single bottleneck c = 10 Mb/s • Queue discipline either Threshold Dropper or DropTail or RED • N TCP connections • Internet experiments • PlanetLab on various end-to-end paths

17. Validation: ns-2 simulations • Queue discipline: threshold dropper • Drop only from a selected connection for a fixed time interval Th • Enforces assumption ONE • b = buffer size (pkts) Utilization (N)

18. Simulations with DropTail • Buffer size b = varying parameter • Suggests buffer-size sensitivity • Inspection suggests window synchronization Utilization (N) N N = 5

19. Simulations with RED • Buffer size b = varying parameter • Good conformance for some b and N Utilization (N) N = 10 N

20. Internet Experiments Utilization (N) Utilization (N) UMASS-Berkeley RTT = 97 ms INRIA-Stanford RTT = 195 ms Utilization (N) Utilization (N) Cornell-Greece RTT = 338 ms Fortiche-Titeuf RTT = 1.6 ms N N

21. Internet Experiments (2) Utilization (N) N N N

22. Conclusion • Obtained aggregate throughput formula of symmetric AIMD connections • Under given bottleneck model • And: one congestion signal per link congestion event • Throughput-invariance to loss policy which connection is signalled • A few connections suffice to compensate for throughput deficiency due to window adaptation • Higher-order throughput statistics is not invariant • Simulation and Internet experiments suggest TCP window synchronization may be common