On Selfish Routing In Internet-like Environments Lili Qiu Microsoft Research Feb. 13, 2004 Johns Hopkins University

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

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

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

Source Routing JHU MSNBC

Overlay Routing MSNBC St. Louis JHU Salt Lake Boston Phoenix

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 selfish routing performs if everyone uses it?

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?

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

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  

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

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

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

Horizontal Interactions (Two Overlays) Different routing schemes coexist well without hurting each other.

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

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

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 Vertical Interactions

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.

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

Other Work Internet –Web performance –Network measurement/tomography –Congestion control –IP telephony Wireless networks –Model the impact of wireless interference –Provision wireless networks –Manage wireless networks

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

Motivation Multihop wireless networks –Community networks, sensor networks, military applications Important to compute wireless network capacity –Capacity planning –Evaluating the efficiency of routing 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

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

Challenges Model the impact of wireless interference 1 Mbps Throughput = 1 Mbps Throughput = 0.5 Mbps A B BA C C

Overview of Our Framework 1.Model the problem as a standard network flow problem 2.Represent interference among wireless links using a conflict graph 3.Derive constraints on utilization of wireless links using cliques in the conflict graph Augment the linear program to obtain upper bound on optimal throughput 4.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

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

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

Sample Results Using Our Framework (Cont.) ScenarioAggregate Throughput Baseline0.5 Double range0.5 Two ITAPs1 Two Radios1 Houses talk to immediate neighbors, all links are capacity 1, like MAC, Multipath routing

Future Work Trends –Networks become larger and more heterogeneous Research problems –Internet management End-user based approach in fault diagnosis –Wireless network management Error-prone physical medium Dynamic and unpredictable networks Accessible physical medium, vulnerable to attacks

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

Thank you!

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.

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: % nodes Edge coverage: edge nodes only