1. On Selfish Routing In Internet-like Environments Lili Qiu (Microsoft Research) Yang Richard Yang (Yale University) Yin Zhang (AT&T Labs – Research) Scott Shenker (ICSI) ACM SIGCOMM 2003

2. 8/28/2003SIGCOMM '20032 Selfish Routing IP routing is often sub-optimal in terms of user performance –Many causes Routing hierarchy, policy routing, failures, instability Emerging trend: Autonomous routing –End users choose their own routes Source routing (e.g. Nimrod) Overlay routing (e.g. Detour, RON) Autonomous routing is selfish by nature –End hosts or routing overlays greedily select routes to optimize their own performance without considering system-wide criteria

3. 8/28/2003SIGCOMM '20033 Bad News Roughgarden and Tardos showed that selfish routing can result in serious performance degradation with general latency functions and topologies SD L 0 (x) = x n L 1 (y) = 1 Total load: x + y = 1 Average latency: x L 0 (x) + y L 1 (y) The worst-case price-of- anarchy is unbounded Selfish source routing At equilibrium all traffic goes through the lower link  Average latency = 1 –Latency optimal routing To minimize average latency, set x = [1/(n+1)] 1/n  Average latency  0 as n  

4. 8/28/2003SIGCOMM '20034 Questions Selfish source routing –How does selfish source routing perform? Are Internet-like environments among the worst cases? Selfish overlay routing –How does selfish overlay routing perform? Note that routing on an overlay has much less flexibility than routing directly on the physical network. Horizontal interactions –Does selfish traffic co-exist well with the remaining traffic that uses default IP routing (e.g., OSPF)? –Do selfish overlays co-exist well with each other? Vertical interactions –How does selfish traffic interact with the underlying network control process, i.e. traffic engineering?

5. 8/28/2003SIGCOMM '20035 Our Approach We take a game-theoretic approach to partially answer these questions through simulations –Focus on equilibrium behavior Apply game theory to directly compute traffic equilibria Compare the performance of traffic equilibria with global optima and default IP routing –Focus on intra-domain environments Compare against theoretical worst-case results Can use realistic topologies, traffic demands, and latency functions Disclaimers –Lots of simplifications & assumptions in the paper Necessary to limit the parameter space –Raise more questions than what we answer Lots of ongoing and future work

6. 8/28/2003SIGCOMM '20036 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 Cooperative within an overlay, but selfish across overlays Compliant (i.e. default) routing: OSPF –Hop count, i.e. unit weight –Optimized weights Minimize network cost [FRT02] –Random weights

7. 8/28/2003SIGCOMM '20037 Internet-like Environments Network topologies –Real topology from an operational tier-1 ISP –Rocketfuel topologies –Random power-law topologies Logical overlay topology –Fully connected mesh (i.e. clique) Traffic demands –Real traffic demands from the tier-1 ISP –Synthetic traffic demands Link latency functions –Queuing delay: M/M/1, M/D/1, P/M/1, P/D/1, BPR Avoid discontinuity by using a linear tail at utilization > 99% –Propagation delay: fiber length or geographical distance divided by the speed of light Performance metrics –User: Average latency –System: Maximum link utilization, network cost [FRT02]

8. 8/28/2003SIGCOMM '20038 Selfish Source Routing: Average Latency Good news: Internet-like environments are far from the worst cases for selfish source routing

9. 8/28/2003SIGCOMM '20039 Selfish Source Routing: Network Cost Bad news: Low latency comes at much higher network cost

10. 8/28/2003SIGCOMM '200310 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

11. 8/28/2003SIGCOMM '200311 Horizontal Interactions Different routing schemes coexist well without hurting each other. With bad weights, selfish overlay also improves compliant traffic.

12. 8/28/2003SIGCOMM '200312 Vertical interaction: 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: –Will the system reach a state with both low latency and low network cost? Short Answer: –It depends on how much underlay routing has Vertical Interactions

13. 8/28/2003SIGCOMM '200313 OSPF optimizer interacts poorly with selfish overlays because it only has very coarse-grained control. Selfish Overlays vs. OSPF Optimizer

14. 8/28/2003SIGCOMM '200314 Selfish Overlays vs. MPLS Optimizer MPLS optimizer interacts with selfish overlays much more effectively.

15. 8/28/2003SIGCOMM '200315 Conclusions Formulate a set of important research questions on selfish routing Use game theory and simulations to partially answer them in the intra-domain context A number of interesting findings –In contrast to the theoretical worst cases, selfish routing achieves close to optimal latency in Internet-like environments. –Selfish overlays co-exist well both with each other and with traffic using default IP routing –Mismatch between objectives of selfish overlays and traffic engineering has significant impact on system performance

16. 8/28/2003SIGCOMM '200316 Lots of Future Work Answer the questions in inter-domain context Study dynamics of selfish routing (i.e., how are traffic equilibria reached?) Study alternative selfish routing objectives (e.g., loss and throughput) Study the effects of different logical overlay topologies Improve the interactions between selfish routing and traffic engineering

17. 8/28/2003SIGCOMM '200317 Thank you!

18. 8/28/2003SIGCOMM '200318 Computing Traffic Equilibrium of Selfish Routing Computing traffic equilibrium of non-overlay 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 selfish 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 In each round, each overlay computes its best response by fixing the other overlays’ traffic; then the best response and the previous state are merged using decreasing relaxation factors.