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 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]
Worst-case ratio is unbounded
L1(y) = 1
S
D
L0(x) = xn
Total load: x + y = 1
Mean latency: x L0(x) + y L1(y)
• 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]
25000
20000
15000
10000
5000
selfish source routing
Load scale factor=1
latency optimal routing
compliant routing (minimum network cost)
Good news: Internet-like environments are far
from the worst cases for selfish source routing
PowerD10
PowerD5
PowerD2
Verio
Tiscali
Telstra
Sprint
Level3
Exodus
EBONE
ATT
0
Abovenet
Average latency (us)
Source Routing: Average Latency
Source Routing: Network Cost
Network cost
10000
1000
100
10
PowerD10
PowerD5
PowerD2
Verio
Tiscali
Telstra
Sprint
Level3
Exodus
EBONE
ATT
Abovenet
1
selfish source
routing
Load scale
factor=1
latency optimal routing
compliant routing (minimum network cost)
Bad news: Low latency comes at much higher network cost
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: 20-100% nodes
– Edge coverage: edge nodes only
Horizontal Interactions
random weights (load scale factor = 1)
Average latency (us)
4.0E+04
3.2E+04
2.4E+04
1.6E+04
8.0E+03
0.0E+00
both
compl.
both
selfish
both
latopt
overlay 1
selfish /
compl.
selfish /
latopt
latopt /
compl.
overlay 2
Different routing schemes coexist well without hurting each other.
With bad weights, selfish overlay also improves compliant traffic.
Vertical Interactions
• 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 has
Selfish Overlays vs. OSPF Optimizer
200
2.5E+04
Max link utilization (%)
Average latency (us)
180
2.0E+04
1.5E+04
1.0E+04
5.0E+03
160
140
120
100
80
60
40
20
0
0.0E+00
0
10
20
30
40
50
0
10
selfish + TE (OSPF)
TE alone
30
40
Round
Round
selfish alone
20
selfish alone
TE alone
selfish + TE (OSPF)
OSPF optimizer interacts poorly with selfish overlays
because it only has very coarse-grained control.
50
1.4E+04
120
1.2E+04
100
Max link utilization (%)
Average latency (us)
Selfish Overlays vs. MPLS Optimizer
1.0E+04
80
8.0E+03
60
6.0E+03
40
4.0E+03
2.0E+03
20
0.0E+00
0
0
10
20
30
40
50
0
10
Round
selfish alone
TE alone
20
30
40
50
Round
selfish + TE (MPLS)
selfish alone
TE alone
MPLS optimizer interacts with
selfish overlays much more effectively.
selfish + TE (MPLS)
Conclusions
• 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
Lots of Future Work
• Extensions
– Multi-domain IP networks
– Different overlay topologies
– Alternative selfish-routing objectives
• Study dynamics of selfish routing
– How are traffic equilibria reached?
• Improve interactions
– Between selfish routing & traffic engineering
– Between competing overlay networks
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.