On Selfish Routing In On Selfish Routing In Internet-like Internet-like

EnvironmentsEnvironmentsLili Qiu Lili Qiu

Microsoft ResearchMicrosoft Research

Feb. 13, 2004Feb. 13, 2004

Johns Hopkins UniversityJohns Hopkins University

Today’s Internet RoutingToday’s Internet Routing

• Network in charge of routing

• Route selection affects user performance

• IP routing yields sub-optimal user performance

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Deficiency in IP RoutingDeficiency 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 RoutingSelfish Routing

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

Source RoutingSource Routing

JHU

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Overlay RoutingOverlay Routing

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Selfish RoutingSelfish 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 NewsBad News

• Selfish routing can seriously degrade performance [Roughgarden & Tardos]

S D

L0(x) = xn

L1(y) = 1

Total load: x + y = 1Mean latency: x L0(x) + y L1(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

QuestionsQuestions

• 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 ApproachOur 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 SchemesRouting 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 EnvironmentsInternet-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 LatencySource Routing: Average Latency

Good news: Internet-like environments are far from the worst cases for selfish source

routing

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compliant routing (minimum network cost)

Bad NewsBad News

• Selfish routing can seriously degrade performance [Roughgarden & Tardos]

S D

L0(x) = xn

L1(y) = 1

Total load: x + y = 1Mean latency: x L0(x) + y L1(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

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Source Routing: Network CostSource Routing: Network Cost

Bad news: Low latency comes at much higher network cost

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Selfish Overlay Routing: Selfish Overlay Routing:

Full Overlay CoverageFull Overlay Coverage

Overlay source routing perform similarly as source routing (except for very bad weight settings)

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Selfish Overlay Routing:Selfish Overlay Routing: Partial Overlay Coverage (only edge Partial Overlay Coverage (only edge

nodes)nodes)

The effects of partial overlay coverage is insignificant in backbone topologies.

Hop-count (load scale factor = 1)

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Horizontal InteractionsHorizontal Interactions(Two Overlays)(Two Overlays)

Different routing schemes coexist well without hurting each other.

random weights (load scale factor = 1)

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Horizontal Interactions Horizontal Interactions (Two Overlays) (Cont.)(Two Overlays) (Cont.)

With bad weights, selfish overlay improves the performance of compliant traffic as well as its own.

Horizontal Interactions Horizontal Interactions (Many Overlays)(Many Overlays)

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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 InteractionsVertical Interactions

OSPF optimizer interacts poorly with selfish overlays because it only has very coarse-grained

control.

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Selfish Overlays vs. OSPF Selfish Overlays vs. OSPF OptimizerOptimizer

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Selfish Overlays vs. MPLS Selfish Overlays vs. MPLS OptimizerOptimizer

MPLS optimizer interacts with selfish overlays much more

effectively.

SummarySummary• 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 WorkOther 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 Model the Impact of Wireless InterferenceWireless Interference

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

MotivationMotivation• 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 ScenarioCommunity Networking Scenario

Asymptotic analysis is not useful in this case

What is the maximum possible throughput?

ChallengesChallenges

• Model the impact of wireless interference

1 Mbps 1 Mbps

1 Mbps 1 Mbps

Throughput = 1 Mbps

Throughput = 0.5 Mbps

A B

BA

C

C

Overview of Our FrameworkOverview of Our Framework1. Model the problem as a standard network flow

problem2. Represent interference among wireless links

using a conflict graph3. 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 ApproachAdvantages 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 FrameworkSample Results Using Our Framework

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Sample Results Using Our Sample Results Using Our Framework (Cont.)Framework (Cont.)

Scenario Aggregate Throughput

Baseline 0.5

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Two Radios 1

Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing

Future WorkFuture 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.)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!Thank you!

Computing Traffic Equilibrium Computing Traffic Equilibrium of Selfish Routingof 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 RoutingSelfish 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