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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. Selfish Routing. IP routing is often sub-optimal in terms of user performance Many causes
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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
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 SIGCOMM '2003
L1(y) = 1 S D L0(x) = xn Total load: x + y = 1 Average latency: x L0(x) + y L1(y) Bad News • Roughgarden and Tardos showed that selfish routing can result in serious performance degradation with general latency functions and topologies • 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 SIGCOMM '2003
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? SIGCOMM '2003
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 SIGCOMM '2003
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 SIGCOMM '2003
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] SIGCOMM '2003
Selfish Source Routing: Average Latency Good news: Internet-like environments are far from the worst cases for selfish source routing SIGCOMM '2003
Selfish Source Routing: Network Cost Bad news: Low latency comes at much higher network cost SIGCOMM '2003
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 SIGCOMM '2003
Horizontal Interactions Different routing schemes coexist well without hurting each other. With bad weights, selfish overlay also improves compliant traffic. SIGCOMM '2003
Vertical Interactions • 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 SIGCOMM '2003
Selfish Overlays vs. OSPF Optimizer OSPF optimizer interacts poorly with selfish overlays because it only has very coarse-grained control. SIGCOMM '2003
Selfish Overlays vs. MPLS Optimizer MPLS optimizer interacts with selfish overlays much more effectively. SIGCOMM '2003
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 SIGCOMM '2003
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 SIGCOMM '2003
Thank you! SIGCOMM '2003
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. SIGCOMM '2003