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) University of California, San Diego

Selfish Routing IP routing is sub-optimal for user performance –Routing hierarchy and policy routing –Equipment failure and transient instability –Slow reaction (if any) to network congestion Autonomous routing: users pick 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 –Optimize their own performance goals –… without considering system-wide criteria

Bad News Selfish routing can seriously degrade performance [Roughgarden & Tardos] SD L 0 (x) = x n L 1 (y) = 1 Total load: x + y = 1 Mean latency: x L 0 (x) + y L 1 (y) 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  

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?

Outline Overview Performance results –Physical routing –Overlay routing –Multiple overlays –Interaction with traffic engineering Summary Ongoing and future work

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

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

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]

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

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

Difference between Source Routing and Overlay Routing Even if the overlay includes all network nodes, routing on an overlay is still different –Network-level routing can prevent overlay traffic from using a link by setting the corresponding entry in routing matrix to 0 (in OSPF this is achieved by assigning a large weight) –Certain physical routes cannot be implemented by any overlay routing Routing flexibility is further reduced when only a fraction of nodes belong to an overlay

Selfish Overlay Routing (Full Overlay Coverage) 1)overlay-src with opt-weight and hop-count perform similarly as source routing 2)overlay-src with random-weight performs much worse.

Selfish Overlay Routing (Partial Overlay Coverage) (Cont.) Random selection of overlay nodes

Selfish Overlay Routing (Partial Overlay Coverage) Overlay is formed from all edge nodes in ISPTopo The effects of partial overlay coverage is small in backbone topologies.

Horizontal Interactions Different routing schemes coexist well without hurting each other. With bad weights, selfish overlay also improves compliant traffic.

Recap Good news: Unlike the theoretical worst cases, selfish routing in Internet-like environments yields close to optimal latency –The above result is true for both source routing and overlay routing –Selfish routing can achieve good performance without hurting the traffic that is using default routing Bad news: Selfish routing achieves low latency at the cost of overloading network

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 underlay routing has Vertical Interactions

One Round during Vertical Interaction T(t) = Traffic matrix when routing matrix is R(t-1) R(t) = OptimizedRoutingMatrix(T(t)) Traffic engineering installs R(t) to network Selfish routing redistributes traffic to be T(t+1)

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

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

Conclusions Contributions –Important questions on selfish routing –Computation of traffic equilibria –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

Lots of Future Work Extensions –Multi-domain IP networks Model inter-domain topology Model inter-domain traffic demands Reduce computation complexity –Different overlay topologies Tree, ring, … What overlay topology to form to improve performance and/or robustness? –Alternative selfish-routing objectives Throughput, loss rate, …

Lots of Future Work (Cont.) Study dynamics of selfish routing –How are traffic equilibria reached? –What routing protocols enable us to reach equilibria quickly? Improve interactions –Between selfish routing & traffic engineering Bi-level programming? –Between competing overlay networks

How to achieve traffic equilibria? Challenges –Distributed algorithm –Responsive to changes in traffic Approach –Probabilistic routing based on distributed learning For each destination k, node i maintains a routing probability P(i, k, j) for each neighbor j

How to achieve traffic equilibria? (Cont.) Protocol –For every T seconds Send latency L ik (t) to all neighbors Receive latency L jk (t) to all neighbors Compute L ik (t+1) Update p ik j (t+1) for all neighbors j Properties –Converge to Wardrop equilibria or global minimum latency –Responsive to traffic stimuli (e.g., spike, step function, linear function)

Thank you!

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.

Selfish Overlay Routing (Full Overlay Coverage) 1)overlay-src with opt-weight and hop-count perform similarly as source routing 2)overlay-src with random-weight performs much worse.

Selfish Overlay Routing (Full Overlay Coverage) Direct Link Shortest [DLS] –For any physically adjacent nodes A and B, all the traffic from A to B is routed through the direct link AB without involving any other links. (e.g., hop-count- based OSPF) For an overlay that covers all network nodes and satisfies DLS –routing on the overlay = routing on the underlay Hop-count-based OSPF and optimized OSPF weights satisfy DLS  they perform similarly as source routing Random OSPF weights violate DLS  some links are pruned, and performance degrades

Selfish Overlay Routing Similar results apply for overlay routing –Achieves close to optimal average latency –Low latency comes at higher network cost Even if overlay covers a fraction of nodes –Random coverage: % nodes –Edge coverage: edge nodes only