April 21, 2023 1

On Selfish Routing in Internet-like Environments

paper by

Lili Qiu, Yang Richard Yang, Yin Zhang, Scott Shenker

presentation by

Ed Spitznagel

April 21, 2023 2

Selfish Routing

• Selfish routing: allowing hosts to choose routes themselves (e.g. source routing) or use overlay routing networks (e.g. Detour, RON)– routing decisions designed to optimize host-based or

overlay-based metrics, rather than system-wide metrics

April 21, 2023 3

Selfish Routing

• Theoretical results have shown that selfish routing can result in “suboptimal system behaviour”– “price of anarchy” (latency of selfish routing vs.

globally optimal) can be unbounded for general latency functions [Roughgardern and Tardos]

• Does this happen in Internet-like environments?

April 21, 2023 4

Outline

• Models and Methodology

• Selfish Source Routing

• Selfish Overlay Routing

• Selfish Routing vs. Traffic Engineering

• Conclusion

April 21, 2023 5

Network Model• Physical network: directed graph G = (V, E) where latency

of each link is a function of its load• Demands: Network traffic is partitioned into traffic

demands• Overlays: an overlay consists of overlay nodes, directed

overlay links, and a set of demands originated from the overlay nodes.– paper considers the fully connected overlay topology only

• Users: originators of traffic. Their objective is to minimize latency.

April 21, 2023 6

Network Model

• Route Controller: controls the network-level routing.– OSPF routing: three methods for weight assignment are

used: Hop-count Random-weight Optimized-compliant: weights are set to minimize network

cost, assuming all traffic is compliant.

– MPLS routing: uses multi-commodity flow routing

April 21, 2023 7

Routing and Traffic Equilibria

• Evaluate each selfish routing scheme by computing its performance at traffic equilibria

• Game-theoretic approach: equilibrium is a state where no user can improve his traffic’s latency

• Computed directly by algorithms in the appendix (faster than using simulation techniques)

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Routing• Routing on the physical network

– Source Routing: results in selfish routing of the type most often studied

– Optimal Routing: routing that achieves minimal average latency over all traffic demands

• Overlay routing– Overlay Source Routing: selfish routing through overlay nodes

– Overlay Optimal Routing: routing through the overlay that achieves minimal average latency

• Compliant routing: follow the routes determined by the network-level routing protocol

April 21, 2023 9

Network Topologies• A real tier-1 ISP (referred to as ISPTopo) with ~100

backbone routers connected via OC48 and OC192 links• Other ISP topologies as mapped by Rocketfuel:

• Random power-law topologies generated using BRITE

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Traffic demands• Real traffic demands: measured on ISPTopo for

three randomly chosen hours in November 2002

• Synthetic traffic demands: randomly map POPs in ISPTopo to non-leaf nodes in the Rocketfuel topology.

• Load scale factor: scale up demands so that, when all traffic is compliant and routed based on shortest hop-count, the max link utilization is 100·F%, where F is the load scale factor

April 21, 2023 11

Link Latency Functions• Several link latency functions are used:

• “To avoid the discontinuity when the load approaches capacity, we approximate the M/M/1 or M/D/1 function with a linear function beyond 99% utilization”– (not sure if this makes sense)

April 21, 2023 12

Performance Metrics• Average latency

• Maximum link utilization

• “Network cost” metric:– cost for a link with load x and capacity c is:

– cost of a network is the sum of its links’ costs

April 21, 2023 13

Outline

• Models and Methodology

• Selfish Source Routing

• Selfish Overlay Routing

• Selfish Routing vs. Traffic Engineering

• Conclusion

April 21, 2023 14

Selfish Source Routing

• Are Internet-like environments among the worst cases?

April 21, 2023 15

Selfish Source Routing• Effect of network load

on average latency:

April 21, 2023 16

Selfish Source Routing• User latency for all topologies, using M/M/1 latency

function

April 21, 2023 17

Selfish Source Routing• User latency for ISPTopo, varying the latency function

April 21, 2023 18

System-wide cost for selfish source routing• Effect of network load

on max link utilization:

April 21, 2023 19

System-wide cost for selfish source routing• Effects of network topologies:

• selfish routing: highest max link utilization, highest network cost

• selfish routing may make a network more prone to overload, especially when failures occur

April 21, 2023 20

System-wide cost for selfish source routing• Effects of latency functions:

– results for different latency functions are qualitatively the same

April 21, 2023 21

Outline

• Models and Methodology

• Selfish Source Routing

• Selfish Overlay Routing

• Selfish Routing vs. Traffic Engineering

• Conclusion

April 21, 2023 22

When every node is in the overlay• ISPTopo, using OSPF for network-level routing

• three choices of OSPF weight assignments

• 3 of the 4 curves overlap

April 21, 2023 23

When every node is in the overlay• Again, but with other topologies• Selfish routing achieves latency close to optimal (and

usually better than compliant routing)• ...but at the cost of higher maximum link utilization

April 21, 2023 24

When not every node is in the overlay

• ISPTopo, overlay covers edge nodes only• curves almost completely overlap

– Internet backbone is fairly well-connected and well-provisioned

April 21, 2023 25

When not every node is in the overlay

• Random partial coverage: latency similar to full coverage; full coverage has higher max link utilization

April 21, 2023 26

Interactions Among Competing Overlays• Competing demands at the same nodes, using

same underlying network

• Foreground and background traffic at 50% each

Different topologiesDifferent methods for computing OSPF weights

April 21, 2023 27

Can Many Overlays Coexist Well? • Results for ISPTopo, with various multiple-

overlay configurations:

April 21, 2023 28

Outline

• Models and Methodology

• Selfish Source Routing

• Selfish Overlay Routing

• Selfish Routing vs. Traffic Engineering

• Conclusion

April 21, 2023 29

Selfish Routing vs. Traffic Engineering• Traffic engineering: adjust physical routing based

on network traffic patterns (traffic matrix)

• Selfish routing will then adjust the traffic matrix in response to that…

• … which causes the traffic engineering to produce a new routing matrix

• And the process repeats…

April 21, 2023 30

Selfish Routing and OSPF optimizer• Optimizer chooses link weights for OSPF

• Selfish routing + traffic engineering: considerably worse performance than either one alone

April 21, 2023 31

Selfish Routing and MPLS optimizer

• Better, perhaps due to MPLS’s finer-grained control (can adjust routing matrix without reducing available resources, unlike OSPF)

• Almost as good as using only selfish routing or only TE

• MPLS TE requires solving very large linear programming problem

April 21, 2023 32

Conclusion• Unlike the worst-case scenarios, selfish routing in

Internet-like environments achieves close to optimal – often at the cost of overloading certain links

– can become worse due to interaction with traffic engineering

• Future work– investigate how the multi-AS nature of Internet affects routing

performance

– dynamics of selfish routing (how equilibria are reached)

– better understanding of interactions between traffic engineering and selfish routing

– study of selfish routing with other metrics (loss, throughput)

April 21, 2023 33

End of Presentation

• Questions?