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. Stefan Schmid, ETH Zurich @ HiPC 20062 Dynamic Internet Internet

3. Stefan Schmid, ETH Zurich @ HiPC 20063 Dynamic Internet

4. Stefan Schmid, ETH Zurich @ HiPC 20064 Dynamic Internet

5. Stefan Schmid, ETH Zurich @ HiPC 20065 Dynamic Internet

6. Stefan Schmid, ETH Zurich @ HiPC 20066 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

7. Stefan Schmid, ETH Zurich @ HiPC 20067 Selfish Behavior (1)

8. Stefan Schmid, ETH Zurich @ HiPC 20068 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!

9. Stefan Schmid, ETH Zurich @ HiPC 20069 In this Paper… Introduction of models for dynamic changes of congestion. Study of selfish (online) algorithms which maximize throughput.

10. Stefan Schmid, ETH Zurich @ HiPC 200610 Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion

11. Stefan Schmid, ETH Zurich @ HiPC 200611 Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion

12. Stefan Schmid, ETH Zurich @ HiPC 200612 Model (1) We divide time into rounds t, for t = 1, 2, ….! The available bandwidth at time t is u t The selfish sender uses a sending rate x t at time t Selfish player does not know u t : All a sender knows is whether her sending in the last round was larger than the available bandwidth (i.e., x t >u t, hence congestion!), or not (binary feedback). - If x t >u t packets are dropped by routers. - Consequently, a selfish transfer protocol has to decide x t without knowing the present or future available bandwidth: framework for online algorithms!

13. Stefan Schmid, ETH Zurich @ HiPC 200613 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! t rate utut xtxt Packets come through, but opportunity costs! Sending rate too large, no transmission at all!

14. Stefan Schmid, ETH Zurich @ HiPC 200614 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!

15. Stefan Schmid, ETH Zurich @ HiPC 200615 Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion

16. Stefan Schmid, ETH Zurich @ HiPC 200616 Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion

17. Stefan Schmid, ETH Zurich @ HiPC 200617 Multiplicative Dynamics (1) If u t can change arbitrarily over time, there is no competitive algorithm: u t can always be chosen slightly smaller than x t ! 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

18. Stefan Schmid, ETH Zurich @ HiPC 200618 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 μ 3 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 μ 4 -competitive. - The gain of OPT in bad round is at most a factor μ larger than the gain of ALG in the preceding good round. - Consequently,

19. Stefan Schmid, ETH Zurich @ HiPC 200619 Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion

20. Stefan Schmid, ETH Zurich @ HiPC 200620 Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion

21. Stefan Schmid, ETH Zurich @ HiPC 200621 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!

22. Stefan Schmid, ETH Zurich @ HiPC 200622 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!

23. Stefan Schmid, ETH Zurich @ HiPC 200623 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!

24. Stefan Schmid, ETH Zurich @ HiPC 200624 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.

25. Stefan Schmid, ETH Zurich @ HiPC 200625 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, Arrival curve: accumulate during quiet times with few changes, but at most factor B Change in round t

26. Stefan Schmid, ETH Zurich @ HiPC 200626 Results Upper Bound: Online algorithm which cuts sending rate by half after bad rounds, and increases the rate by μ B 1/3 yields a competitive ratio of Lower Bound: No online algorithm can achieve a competitive ratio better than against a Network Calculus adversary.

27. Stefan Schmid, ETH Zurich @ HiPC 200627 Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion

28. Stefan Schmid, ETH Zurich @ HiPC 200628 Talk Overview Model Multiplicative Dynamics „Bursty Dynamics“ Open Research Questions and Conclusion

29. Stefan Schmid, ETH Zurich @ HiPC 200629 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?

30. Stefan Schmid, ETH Zurich @ HiPC 200630 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!

31. Stefan Schmid, ETH Zurich @ HiPC 200631 Questions and Comments? Stefan Schmid Distributed Computing Group schmiste@ethz.ch http://dcg.ethz.ch/members/stefan.html Thank you for your attention!