On Selfish Routing In Internet-like Environments

1. On Selfish Routing In Internet-like Environments Lili Qiu Microsoft Research March 18, 2004 University of Maryland

2. Today’s Internet Routing • Network in charge of routing • Route selection affects user performance • IP routing yields sub-optimal user performance MSNBC UMD

3. Deficiency in IP Routing • IP routing is sub-optimal for user performance • Routing hierarchy • Policy routing • Equipment failure and transient instability • Slow reaction (if any) to network congestion

4. Selfish Routing • Selfish routing: users pick their own routes • Source routing (e.g., Nimrod) • Overlay routing (e.g., Detour, RON)

5. Source Routing MSNBC UMD

6. Overlay Routing MSNBC Boston Salt Lake St. Louis Phoenix UMD

7. Selfish Routing • Selfish nature • End hosts or routing overlays greedily select routes • Optimize their own performance goals • Not considering system-wide criteria • Studies based on small scale deployment show it improves performance • How well does selfish routing perform if everyone uses it?

8. L1(y) = 1 S D L0(x) = xn Total load: x + y = 1 Mean latency: x L0(x) + y L1(y) Bad News • Selfish routing can seriously degrade performance [Roughgarden & Tardos] • Worst-case ratio is unbounded • - Selfish source routing • All traffic through lower link •  Mean latency = 1 • Latency optimal routing • To minimize mean latency, set x = [1/(n+1)] 1/n •  Mean latency  0 as n  

9. Questions • Selfish source routing • How does selfish source routing perform? • Are Internet environments among the worst cases? • Selfish overlay routing • How does selfish overlay routing perform? • Does the reduced flexibility avoid the bad cases? • Horizontal interactions • Does selfish traffic coexist well with other traffic? • Do selfish overlays coexist well with each other? • Vertical interactions • Does selfish routing interact well with network traffic engineering?

10. Our Approach • Game-theoretic approach with simulations • Equilibrium behavior • Apply game theory to compute traffic equilibria • Compare with global optima and default IP routing • Intra-domain environments • Compare against theoretical worst-case results • Realistic topologies, traffic demands, and latency functions • Disclaimers • Lots of simplifications & assumptions • Necessary to limit the parameter space • Raise more questions than what we answer • Lots of ongoing and future work

11. Routing Schemes • Routing on the physical network • Source routing • Latency optimal routing • Routing on an overlay (less flexible!) • Overlay source routing • Overlay latency optimal routing • Compliant (i.e. default) routing: OSPF • Hop count, i.e. unit weight • Optimized weights, i.e. [FRT02] • Random weights

12. Internet-like Environments • Network topologies • Real tier-1 ISP, Rocketfuel, random power-law graphs • Logical overlay topology • Fully connected mesh (i.e. clique) • Traffic demands • Real and synthetic traffic demands • Link latency functions • Queuing: M/M/1, M/D/1, P/M/1, P/D/1, and BPR • Propagation: fiber length or geographical distance • Performance metrics • User: Average latency • System: Max link utilization, network cost [FRT02]

13. Source Routing: Average Latency Good news: Internet-like environments are far from the worst cases for selfish source routing

14. L1(y) = 1 S D L0(x) = xn Total load: x + y = 1 Mean latency: x L0(x) + y L1(y) Bad News • Selfish routing can seriously degrade performance [Roughgarden & Tardos] • Worst-case ratio is unbounded • - Selfish source routing • All traffic through lower link •  Mean latency = 1 • Latency optimal routing • To minimize mean latency, set x = [1/(n+1)] 1/n •  Mean latency  0 as n  

15. Source Routing: Network Cost Bad news: Low latency comes at much higher network cost

16. Selfish Overlay Routing • Similar results apply • Selfish overlay routing achieves close to optimal average latency • Low latency comes at higher network cost • The results apply when the overlay only covers a fraction of nodes • Scenarios tested: • Random coverage: 20-100% nodes • Edge coverage: edge nodes only

17. Horizontal Interactions(Two Overlays) Different routing schemes coexist well.

18. Horizontal Interactions (Two Overlays) (Cont.) With bad weights, selfish overlay improves the performance of compliant traffic as well as its own.

19. Horizontal Interactions (Many Overlays) Performance degradation due to competition among overlays is insignificant.

20. Vertical Interactions • An iterative process between two players • Traffic engineering: minimize network cost • current traffic pattern  new routing matrix • Selfish overlays: minimize user latency • current routing matrix  new traffic pattern • Question: • Does system reach a state with both low latency and low network cost? • Short answer: • Depends on how much control the network has

21. Selfish Overlays vs. OSPF Optimizer OSPF optimizer interacts poorly with selfish overlays because it only has very coarse-grained control.

22. Selfish Overlays vs. MPLS Optimizer MPLS optimizer interacts with selfish overlays much more effectively.

23. Summary • Contributions • Important questions on selfish routing • Simulations that partially answer questions • Main findings on selfish routing • Near-optimal latency in Internet-like environments • In sharp contrast with the theoretical worst cases • Coexists well with other overlays & regular IP traffic • Background traffic may even benefit in some cases • Big interactions with network traffic engineering • Tension between optimizing user latency vs. network load

24. Other Work • Internet • Fault diagnosis • Web performance • Congestion control • IP telephony • Wireless networks • Model the impact of wireless interference • Provision wireless networks • Manage wireless networks

25. Fault Diagnosis • Server-based Inference of Internet Performance. IEEE INFOCOM 2003.(Joint work with V. N. Padmanabhan and H. J. Wang)

26. Why is it so slow? Diagnosis engine It’s so slow! Motivation Web Server Ethernet AT&T C&W UUNet Sprint AOL Qwest Earthlink

27. Diagnosis engine Networktopology Trouble spotslocation Diagnosis results: Qwest access link: 63.232.180.230->63.232.33.134 Peering between Sprint and AOL: 64.45.216.154->172.139.89.74 Tcpdump traces Network Diagnosis

28. Problem Formulation • (1-l1)*(1-l2)*(1-l4) = (1-p1) • (1-l1)*(1-l2)*(1-l5) = (1-p2) • … • (1-l1)*(1-l3)*(1-l8) = (1-p5) • Challenges: • Under-constrained system of equations • Measurement errors server l1 l3 l2 l4 l5 l6 l7 l8 clients p1 p2 p3 p4 p5

29. Gibbs Sampling • D • observed packet transmission and loss at the clients •  • ensemble of loss rates of links in the network • Goal • determine the posterior distribution P(|D) • Approach • Use Markov Chain Monte Carlo with Gibbs sampling to obtain samples from P(|D) • Draw conclusions based on the samples

30. Gibbs Sampling (Cont.) • Applying Gibbs sampling to fault diagnosis • 1) Initialize link loss rates arbitrarily • 2) For j = 1 : warmup for each link i compute P(li|D, {li’}) where li is loss rate of link i, and {li’} = kI lk • 3) For j = 1 : realSamples for each link i compute P(li|D, {li’}) • Use all the samples obtained at step 3 to approximate P(|D)

31. Summary of Internet Fault Diagnosis • Gibbs sampling yields a high coverage (over 80%), and a low false positive rate (below 5-10%) • Two other inference techniques trade-off accuracy for speed

32. Model the Impact of Wireless Interference • Impact of Interference on Multihop Wireless Network Performance. ACM MOBICOM 2003. (Joint work with K. Jain, J. Padhye, and V. N. Padmanabhan)

33. Motivation • Multihop wireless networks • Community networks, sensor networks, military applications • Important to compute wireless network capacity • Capacity planning • Evaluate the efficiency of protocols • A lot of research on capacity of multi-hop wireless networks • Much of previous work studies asymptotic performance bounds • Gupta and Kumar 2000: O(1/sqrt(N)) • We present a framework to answer questions about capacity of specific topologies with specific traffic patterns

34. Community Networking Scenario What is the maximum possible throughput? Asymptotic analysis is not useful in this case

35. Challenge • Model the impact of wireless interference 1 Mbps 1 Mbps B C A Throughput = 1 Mbps A B C 1 Mbps 1 Mbps Throughput = 0.5 Mbps

36. Overview of Our Framework • Model the problem as a standard network flow problem • Represent interference among wireless links using a conflict graph • Derive constraints on utilization of wireless links using independent sets in the conflict graph • Augment the linear program to obtain lower bound on optimal throughput • Derive constraints on utilization of wireless links using cliques in the conflict graph • Augment the linear program to obtain upper bound on optimal throughput

37. Sample Results Using Our Framework Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing

38. Sample Results Using Our Framework (Cont.) Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing

39. Future Work • Trends • Networks become larger and more heterogeneous • Research problems • Internet management • End-user based approach • Wireless network design & management • Error-prone physical medium • Dynamic and unpredictable networks • Accessible physical medium, vulnerable to attacks

40. Future Work (Cont.) • Trends • Network protocols become more complicated, e.g., various optimizations are proposed for different network layers • Network users and providers have different and sometimes conflicting goals • Research problems • How to optimize network performance? • Cross different network layers • Satisfy the need of different users and network providers

41. Thank you!

42. Computing Traffic Equilibrium of Selfish Routing • Computing traffic equilibrium of source routing traffic • Use the linear approximation algorithm • A variant of the Frank-Wolfe algorithm, which is a gradient-based line search algorithm • Computing traffic equilibrium of overlay routing • Construct a logical overlay network • Use Jacob's relaxation algorithm on top of Sheffi's diagonalization method for asymmetric logical networks • Use modified linear approximation algo. in symmetric case • Computing traffic equilibrium of multiple overlays • Use a relaxation framework • Each overlay computes its best response by fixing the other overlays’ traffic • Merge the best response and the previous state using decreasing relaxation factors.

43. Overlay Routing in Inter-domain Selfish routing yields close to optimal latency, and better than compliant routing.

44. Advantages of Our Approach • “Real” numbers instead of asymptotic bounds • Optimal bound, may not be achieved in practice • Useful for “what if” analysis • Permits several generalizations: • Different routing • single path or multi-path routing • Different wireless interference models • Different antennas/radios • directional or unidirectional, different ranges, data rates, multiple radios/channels • Different senders • senders with limited (but constant) demand • Different topologies • Different performance metrics • throughput, fairness, revenue

45. Selfish Overlay Routing: Full Overlay Coverage Overlay source routing perform similarly as source routing (except for very bad weight settings)

46. Selfish Overlay Routing:Partial Overlay Coverage (only edge nodes) The effects of partial overlay coverage is insignificant in backbone topologies.

47. Example: Conflict Graph Connectivity Graph 2 1 C B A 4 3 Conflict Graph 2 1 3 4