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

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

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

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

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

9. 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  = ½; TCP like): –N = 1 : Utilization = 0.75 c –N = 2 : Utilization = 6/7 c  0.86 c

10. 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 N Utilization (N)

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

12. 12 Proof Sketch (2) Palm inversion The latter follows by taking expectation on both sides of the recurrence for X i 2 (T n ) const

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

14. 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. 15 Throughput: Higher-order Statistics Depends on Loss Policy Result for N = 2 &  = 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. 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. 17 Validation: ns-2 simulations Queue discipline: threshold dropper –Drop only from a selected connection for a fixed time interval T h –Enforces assumption ONE –b = buffer size (pkts) Utilization (N)

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

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

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

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

22. 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