On Selfish Routing In Internet-like Environments
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On Selfish Routing In On Selfish Routing In Internet-like Internet-like
EnvironmentsEnvironmentsLili Qiu Lili Qiu
Microsoft ResearchMicrosoft Research
March 18, 2004March 18, 2004
University of MarylandUniversity of Maryland
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Today’s Internet RoutingToday’s Internet Routing
• Network in charge of routing
• Route selection affects user performance
• IP routing yields sub-optimal user performance
UMD
MSNBC
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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
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Selfish RoutingSelfish Routing
• Selfish routing: users pick their own routes– Source routing (e.g., Nimrod)– Overlay routing (e.g., Detour, RON)
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Source RoutingSource Routing
UMD
MSNBC
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Overlay RoutingOverlay Routing
MSNBC
St. Louis
UMD
Salt Lake
Boston
Phoenix
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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 does selfish routing perform if everyone uses it?
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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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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?
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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
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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
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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]
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Source Routing: Average LatencySource Routing: Average Latency
Good news: Internet-like environments are far from the worst cases for selfish source
routing
0.0E+00
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selfish source routing
latency optimal routing
compliant routing (minimum network cost)
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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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selfish source routing
latency optimal routing
compliant routing (minimum network cost)
Source Routing: Network CostSource Routing: Network Cost
Bad news: Low latency comes at much higher network cost
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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
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Hop-count (load scale factor = 1)
7.6E+03
7.8E+03
8.0E+03
8.2E+03
8.4E+03
8.6E+03
8.8E+03
9.0E+03
bothcompl.
bothselfish
both latopt
selfish /compl.
selfish /latopt
latopt /compl.
Ave
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ten
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overlay 1 overlay 2
Horizontal InteractionsHorizontal Interactions(Two Overlays)(Two Overlays)
Different routing schemes coexist well.
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random weights (load scale factor = 1)
0.0E+00
8.0E+03
1.6E+04
2.4E+04
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4.0E+04
bothcompl.
bothselfish
both latopt selfish /compl.
selfish /latopt
latopt /compl.
Ave
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overlay 1 overlay 2
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.
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Horizontal Interactions Horizontal Interactions (Many Overlays)(Many Overlays)
0100020003000400050006000700080009000
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one overlay per src per src-dest infinite
Performance degradation due to competition among overlays is
insignificant.
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• 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
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OSPF optimizer interacts poorly with selfish overlays because it only has very coarse-grained
control.
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selfish + TE (OSPF)
Selfish Overlays vs. OSPF Selfish Overlays vs. OSPF OptimizerOptimizer
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selfish alone TE alone selfish + TE (MPLS)
Selfish Overlays vs. MPLS Selfish Overlays vs. MPLS OptimizerOptimizer
MPLS optimizer interacts with selfish overlays much more
effectively.
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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
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Other WorkOther Work
• Internet– Fault diagnosis– Web performance– Congestion control– IP telephony
• Wireless networks– Model the impact of wireless interference– Provision wireless networks– Manage wireless networks
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Fault DiagnosisFault Diagnosis
• Server-based Inference of Internet Performance. IEEE INFOCOM 2003.(Joint work with V. N. Padmanabhan and H. J. Wang)
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MotivationMotivation
C&W
AT&T
WebServer
Sprint
UUNet
Qwest Earthlink
AOL
It’s so slow!
Diagnosisengine
Ethernet
Why is itso slow?
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Network DiagnosisNetwork Diagnosis
Diagnosisengine
Tcpdump traces
Network topology
Troublespots location
Diagnosis results:Qwest access link: 63.232.180.230->63.232.33.134Peering between Sprint and AOL: 64.45.216.154->172.139.89.74
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Problem FormulationProblem Formulation
l1
l8l7l6
l2
l4 l5
l3
server
clientsp1 p2 p3 p4 p5
(1-l1)*(1-l2)*(1-l4) = (1-p1)
(1-l1)*(1-l2)*(1-l5) = (1-p2)…(1-l1)*(1-l3)*(1-l8) = (1-p5)
Challenges:• Under-constrained system
of equations• Measurement errors
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Gibbs SamplingGibbs Sampling
• D– observed packet transmission and loss at the clients
– ensemble of loss rates of links in the network
• Goal– determine the posterior distribution P(|D)
• Approach– Use Markov Chain Monte Carlo with Gibbs sampling
to obtain samples from P(|D)– Draw conclusions based on the samples
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Gibbs Sampling (Cont.)Gibbs Sampling (Cont.)
• Applying Gibbs sampling to fault diagnosis– 1) Initialize link loss rates arbitrarily– 2) For j = 1 : warmup
for each link i compute P(li|D, {li’}) where li is loss rate of link i, and {li’} = kI lk
– 3) For j = 1 : realSamples for each link i
compute P(li|D, {li’})– Use all the samples obtained at step 3 to
approximate P(|D)
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Summary of Internet Fault DiagnosisSummary of Internet Fault Diagnosis
• Gibbs sampling yields a high coverage (over 80%), and a low false positive rate (below 5-10%)
• Two other inference techniques trade-off accuracy for speed
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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)
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MotivationMotivation• Multihop wireless networks
– Community networks, sensor networks, military applications
• Important to compute wireless network capacity– Capacity planning – Evaluate the efficiency of 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
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Community Networking ScenarioCommunity Networking Scenario
Asymptotic analysis is not useful in this case
What is the maximum possible throughput?
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ChallengeChallenge
• 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
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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 independent sets in the conflict graph • Augment the linear program to obtain lower bound
on optimal throughput
4. Derive constraints on utilization of wireless links using cliques in the conflict graph• Augment the linear program to obtain upper bound
on optimal throughput
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Sample Results Using Our FrameworkSample Results Using Our Framework
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Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing
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Sample Results Using Our Sample Results Using Our Framework (Cont.)Framework (Cont.)
Scenario Aggregate Throughput
Baseline 0.5
Double range
0.5
Two ITAPs 1
Two Radios 1
Houses talk to immediate neighbors, all links are capacity 1, 802.11-like MAC, Multipath routing
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Future WorkFuture Work
• Trends– Networks become larger and more
heterogeneous
• Research problems– Internet management
• End-user based approach
– Wireless network design & management• Error-prone physical medium• Dynamic and unpredictable networks• Accessible physical medium, vulnerable to
attacks
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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
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Thank you!Thank you!
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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.
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Overlay Routing in Inter-Overlay Routing in Inter-domaindomain
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Avera
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selfish cooperative compliant
Selfish routing yields close to optimal latency, and better than compliant routing.
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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
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overlay-src: hop-count overlay-src: rand-weight
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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.
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Example: Conflict GraphExample: Conflict Graph
Connectivity Graph
A B C
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3 4
Conflict Graph