1. On Self Adaptive Routing in Dynamic Environments -- A probabilistic routing scheme Haiyong Xie, Lili Qiu, Yang Richard Yang and Yin Zhang @ Yale, MR and AT&T Presented by Joe, W.J.Jiang 28-08-2004

2. Outline Overview of Adaptive Routing Related Work Probabilistic Routing Scheme Convergence Analysis Simulation Results Conclusion

3. Where are you? Overview of Adaptive Routing Related Work Probabilistic Routing Scheme Convergence Analysis Simulation Results Conclusion

4. Introduction to adaptive routing Routing in the Internet: interior gateway routing – OSPF exterior gateway routing – BGP Static routing, based on hop counts There is an inherent inefficiency in IP routing from user’s perspective: latency, bandwidth, loss rate, etc Adaptive routing, allowing end hosts to select routes by themselves.

5. Selfish Routing (user-optimal routing) Each end host selects a route with minimum latency. Shortest path routing, metric -- latency, additive Two approaches: source routing -- Nimrod overlay routing -- Detour, RON Selfish by nature -- selfish routing

6. Illustration of source routing n1n2n3n4n5 n1-n2-n3-n4-n5

7. Illustration of overlay routing

8. Problems I -- Oscillation Ring Network (Data Networks) Simultaneous Overlay Network Primary Paths Bottleneck Phy. Link 1+  Mbps (L2) 2 Mbps L1 1 Mbps (L3) Sources Destinations Alternate Paths Ov.Nw. Nodes (2 Ovns)

9. Problem II -- Performance Degradation Nash Equilibrium Well known that Nash Equilibrium do not in general optimize social welfare. Braess’s Paradox x1 s t x1 1/2 0 1 Performance degradation: selfish routing : global optimal = 2/(0.5+1) = 4/3

10. Where are you? Overview of Adaptive Routing Related Work Probabilistic Routing Scheme Convergence Analysis Simulation Results Conclusion

11. Related Work Wardrop equilibrium: a research aspect in economics of transportation. The proof of existence of unique equilibrium and some extensions. Network optimal routing - Data Networks - Frank-Wolfe Method - Projection Method These are centralized algorithms. Distributed version for optimal routing - Parallel and Distributed Computation

12. Related Work (Cont) “How bad is selfish routing?” - There exists unique Nash Equilibrium for selfish routing under network flow model. - The performance (average delay) ratio between selfish routing and global routing could be unbounded for arbitrary network. - The upper bound for network with linear delay function is 4/3. “On selfish routing in Internet-like environment” - Based on simulation, selfish routing and global optimal routing exhibit similar performance, under different network topology and traffic models.

13. Related Work (cont) If individual users are allowed to select routes selfishly without coordination, how to ensure these behaviors will converge to an equilibrium? “Dynamic Cesaro-Wardrop equilibration in Networks” - a model to ensure the convergence of probabilistic routing scheme “On self adaptive routing in dynamic environments”

14. Where are you? Overview of Adaptive Routing Related Work Probabilistic Routing Scheme Convergence Analysis Simulation Results Conclusion

15. Routing Scheme - Data Path Component Data path component - similar to distance vector routing - destination could be all overlay nodes. - - a generalization of normal Internet routing.

16. Routing Scheme - Control Path Component Control path component - how routing probabilities are updated. Selfish routing, Wardrop routing, user-optimal routing property - Given a source-destination pair with a given amount of traffic, the routes with positive traffic should have equal latency, no larger than those unused routes for this source-destination pair.

17. Routing Scheme: Notation l j i the latency of link from node i to its neighbor j L j ik the estimated delay from i to destination k through node j q j ik the internal probability from node i to destination k through neighbor j p j ik the routing probability from node i to destination k through neighbor j {q j ik } will converge to the Wardrop equilibrium {p j ik } are ε- approximate of {q j ik }

18. Update of routing probabilities (1) Node i first computes the new delay Δ j ik = l j i + L jk L jk is the estimated latency from node j to node k node i update the new latency estimation L j ik = (1-α(n)) L j ik + α(n) Δ j ik α(n) is the delay learning factor. then node i computes its overall delay estimation L ik to destination k

19. Update of routing probabilities (2) Node i reports L ik to its neighbors after some delay, and the delay is a random value between T/2 to T, to avoid synchronization. node i updates its internal routing probabilities: β(n’) is routing learning factor ξ j ik is i.i.d uniform random routing vectors to add disturbance to avoid non-Wardrop solutions

20. Update of routing probabilities (3) Projection: node i projects the internal routing probabilities to the subspace of [0,1] N(i), which is equivalent to solving the following problem:

21. Update of routing probabilities (4) Node i compute the routing probabilities:

22. Protocol to implement user-optimal routing

23. Comments on measuring About measuring l j i, two approaches: - measured by node i - measured by node j The advantage of the second method: - unnecessary for clock synchronization - Δ j ik = l j i + L jk, there is an offset which is just the clock difference between i and the destination, independent of j. - - overhead is to stamp packets

24. Probabilistic Scheme for network optimal routing Overview of network optimal routing to solve the convex programming:

25. Probabilistic Scheme for network optimal routing (cont) Proved in “ How bad is selfish routing ”.

26. Probabilistic Scheme for network optimal routing (cont) For network optimal routing, replace l j i with marginal cost function: mc j i = l j i + f j i s j i s j i is the rate of change in the latency from node i to node j at traffic amount f j i Without knowing the analytical expression of latency functions. However, the paper does not mention the scheme to measure the rate of change in the latency.

27. Where are you? Overview of Adaptive Routing Related Work Probabilistic Routing Scheme Convergence Analysis Simulation Results Conclusion

28. Convergence analysis - Intuition Consider a network with only two links p1, p2 >=0, p1+p2=1 Five cases. - (a) link 1 has higher latency - (b) link 1 has lower latency - (c) link 1 and 2 has the same latency - (d) link 1 has all of the traffic - (e) link 2 has all of the traffic

29. Convergence Analysis - Assumption A1 - latency function is continuous, non- decreasing and bounded. A2 - the updates are frequent enough compared with the change rate in the underlying network states. A3 -

30. Convergence Analysis - Assumption A4 -

31. Where are you? Overview of Adaptive Routing Related Work Probabilistic Routing Scheme Convergence Analysis Simulation Results Conclusion

32. Evaluation Methodologies Network topologies: ATT, Sprint, Tiscali Traffic demands Traffic stimuli: - Traffic spike - Step function - Linear function Performance metrics: - average latency - average convergence time - link utilization

33. Dynamics of user-optimal routing and network-optimal routing

34. Conclusion Overview of Adaptive Routing Related Work Probabilistic Routing Scheme Convergence Analysis Simulation Results Conclusion

35. This paper introduces a probabilistic routing scheme to achieve both user- optimal (selfish) routing and network optimal routing. An application of enforcement learning. Not consider the issue of fairness between users (or overlays).

36. Thank you!