Dynamic Internet Congestion with Bursts

1. Dynamic Internet Congestion with Bursts Stefan Schmid Roger Wattenhofer Distributed Computing Group, ETH Zurich 13th International Conference On High Performance Computing (HiPC) Bangalore, India, December 2006

2. Dynamic Internet Internet Stefan Schmid, ETH Zurich @ HiPC 2006

3. Dynamic Internet Stefan Schmid, ETH Zurich @ HiPC 2006

4. Dynamic Internet Stefan Schmid, ETH Zurich @ HiPC 2006

5. Dynamic Internet Stefan Schmid, ETH Zurich @ HiPC 2006

6. TCP Congestion Control The available bandwidth changes dynamically over time depending on the demands of other computers. • In order to prevent collapses, hosts in the Internet collaboratively reduce load in busy times of high congestion! • Successful strategy: TCP congestion control • Additive Increase, Muliplicative Decrease (AIMD) • Indications for congestion: e.g., packet loss Stefan Schmid, ETH Zurich @ HiPC 2006

7. Selfish Behavior (1) Stefan Schmid, ETH Zurich @ HiPC 2006

8. Selfish Behavior (2) Some participants may not care about stability of Internet, but selfishly aim at maximizing own throughput! Given the dynamics of the available bandwidth, selfish throughput maximization constitutes an optimization problem! Stefan Schmid, ETH Zurich @ HiPC 2006

9. In this Paper… Introduction of models for dynamic changes of congestion. Study of selfish (online) algorithms which maximize throughput. Stefan Schmid, ETH Zurich @ HiPC 2006

10. Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion Stefan Schmid, ETH Zurich @ HiPC 2006

11. Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion Stefan Schmid, ETH Zurich @ HiPC 2006

12. Model (1) • We divide time into rounds t, for t = 1, 2, ….! • The available bandwidth at time t is ut • The selfish sender uses a sending rate xt at time t • Selfish player does not know ut: All a sender knows is whether her sending in the last round was larger than the available bandwidth (i.e., xt>ut, hence congestion!), or not (binary feedback). • If xt>ut packets are dropped by routers. • Consequently, a selfish transfer protocol has to decide xt without knowing the present or future available bandwidth: framework for online algorithms! Stefan Schmid, ETH Zurich @ HiPC 2006

13. Model (2) • The optimization problem can be formalized as follows! • Gain of optimal (offline algorithm) OPT: • Gain of online algorithm ALG: Maybe harsh, but retransmissions, timeouts, etc. is overhead! rate Sending rate too large, no transmission at all! ut xt t Packets come through, but opportunity costs! Stefan Schmid, ETH Zurich @ HiPC 2006

14. Model (3) • Goal of the online algorithm is to send always at the rate of the available bandwidth, or slightly lower! • We are interested in minimizing the strict competitive ratio (worst-case!): That is, the gain of ALG should be almost as large as the one of the optimal offline algorithm OPT! Stefan Schmid, ETH Zurich @ HiPC 2006

15. Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion Stefan Schmid, ETH Zurich @ HiPC 2006

16. Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion Stefan Schmid, ETH Zurich @ HiPC 2006

17. Multiplicative Dynamics (1) If ut can change arbitrarily over time, there is no competitive algorithm: ut can always be chosen slightly smaller than xt! However, assuming arbitrary changes may also be too pessimistic! Consequently, we want to restrict the dynamics. Model 1: Multiplicative dynamics changes max by a constant factor μ, i.e., an adversary (worst-case!) can choose the available bandwidth from the interval Stefan Schmid, ETH Zurich @ HiPC 2006

18. Multiplicative Dynamics (2) • Online Algorithm: After a round with sending rate lower or equal the available bandwidth, increase rate by a factor of μ, otherwise reduce sending rate by a factor μ3 • Analysis: • After a „bad“ round, there will always be a „good“ round due to the sharp cut of the sending rate. • Good rounds are at most μ4-competitive. • The gain of OPT in bad round is at most a factor μlarger than the gain of ALG in the preceding good round. • Consequently, Stefan Schmid, ETH Zurich @ HiPC 2006

19. Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion Stefan Schmid, ETH Zurich @ HiPC 2006

20. Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion Stefan Schmid, ETH Zurich @ HiPC 2006

21. Bursty Dynamics (1) • So far: Adversary can change congestion by at most a constant factor in each round. • There are many additional models for congestion dynamics, waiting for efficient online algorithms! • One dynamics model studied on the network layer is network calculus! Stefan Schmid, ETH Zurich @ HiPC 2006

22. Bursty Dynamics (2) Network Calculus is used to analyse queuing strategies in networks from a worst-case perspective (worst-case queuing)! Network Caculus are not only interesting on the network layer, but may serve as a good dynamics model on the transport layer as well! In our paper, we propose to study Network Calculus models for congestion control! Stefan Schmid, ETH Zurich @ HiPC 2006

23. Network Calculus (1) • Traditional Network Calculus • Defines arrival curves (e.g., leaky-bucket arrival curve) • Traffic coming out of a router is assumed to adhere to arrival curve. • If this is the case, bounds for queue lengths and delays can be computed (with min-plus algebra). Arrival curve: max burst b and rate r Total number of bits coming out of router should never exceed arrival curve attached at all points! Stefan Schmid, ETH Zurich @ HiPC 2006

24. Network Calculus (2) • Leaky-bucket arrival curve allows for bursts in the traffic, as long as they are only temporal. • After quite times with low rates, power can be accumulated for another traffic burst. Stefan Schmid, ETH Zurich @ HiPC 2006

25. Dynamic Network Calculus Congestion We adopt these properties and allow our congestion adversary to change the available bandwidth with bursts! The adversary can choose the new bandwidth as follows: Thereby, Change in round t Arrival curve: accumulate during quiet times with few changes, but at most factor B Stefan Schmid, ETH Zurich @ HiPC 2006

26. Results Upper Bound: Online algorithm which cuts sending rate by half after bad rounds, and increases the rate by μB1/3 yields a competitive ratio of • Lower Bound: No online algorithm can achieve a competitive ratio better than against a Network Calculus adversary. Stefan Schmid, ETH Zurich @ HiPC 2006

27. Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion Stefan Schmid, ETH Zurich @ HiPC 2006

28. Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion Stefan Schmid, ETH Zurich @ HiPC 2006

29. Open Research Questions Selfish TCP: A real threat? Verification of model in practice! Fill gap between our upper and lower bound! Randomized algorithms (also for multiplicative adversary) Other arrival curves, study of different dynamics More generally: Adaption and analysis of network calculus for other dynamic models! Limitations? Stefan Schmid, ETH Zurich @ HiPC 2006

30. Discussion • Selfishness in congestion control - Devise throughput maximizing protocols • Network Calculus: An interesting model for dynamics! • Lots of future research! • However, challenging analysis! • Transport layer: Algorithmically less understood than other layers! Stefan Schmid, ETH Zurich @ HiPC 2006

31. Questions and Comments? Thank you for your attention! Stefan Schmid Distributed Computing Group schmiste@ethz.ch http://dcg.ethz.ch/members/stefan.html Stefan Schmid, ETH Zurich @ HiPC 2006