1. A Simulation-Based Study of Overlay Routing Performance CS 268 Course Project Andrey Ermolinskiy, Hovig Bayandorian, Daniel Chen

2. Problem Statement The current Internet infrastructure is highly resistant to change; new network-layer functionality is difficult to implement and costly to deploy. Standard Internet routing protocols (BGP, OSPF) generally fail to deliver low- latency and high-throughput routing paths. –Coarse-grained routing metrics (e.g., hop count) –BGP policies –Lack of economic incentives to provide performance-based routing Overlay networks offer an alternative method for deploying new routing functionality: –Set up an application-level “logical network”. –Deploy a higher-level routing protocol that routes packets according to any desired routing metric. Question 1: Given an alternative routing protocol that implements an arbitrary routing metric, to what extent can an overlay-based solution approximate a network-layer deployment? Question 2: What is the best way to select overlay nodes?

3. Approach Assume the existence of two distinct routing metrics: {W B (base), W O (overlay)} and two routing protocols {R B, R O } that implement shortest path routing for W B and W O, respectively. Model the topology as a dual–weighted graph: G = (V, W B, W O ). R B is the default routing algorithm in G, but a subset of nodes Ω implements R O via an overlay mechanism. C O (V 1 -V 2 -V 5 -V 6 ) = 17C O (V 1 -V 3 -V 2 -V 4 -V 5 -V 6 ) = 9

4. Approach To evaluate the performance of a given choice of Ω, compute the topology stretch. Logical overlay subgraphDual-weighted topology graph Stretch(v 1, v 6 ) = 11 / 9 Stretch(v 1, v 6 ) = 9 / 9 = 1 (Optimal Path) Ω = {v 2, v 4, v 5 } Ω = {v 2, v 3, v 4, v 5 }

5. Results: Distribution of Stretch Values 11 overlay nodes are required to achieve optimal routing. Exhaustive search through the space of all subsets of nodes in two uniform random topologies from ζ(N, p), N = 20, p = 0.1 N = 20, p = 0.5 Only 2 overlay nodes are required to achieve optimal routing. 90% of all overlays of size 11 or more achieve stretch value of 1.03.

6. For p = 0.1: 100 overlay nodes provide 66.0% of the achievable improvement. For p = 0.5: 100 overlay nodes provide 86.4%. For p = 0.9:100 overlay nodes provide 89.9%. Estimated average stretch for three uniform random topologies drawn from ζ(1000, p). A large fraction of the maximum achievable improvement lies with small selections of overlay nodes: Average Stretch in Large Random Topologies

7. Choice of the Topology Model Uniform random from ζ(1050, 0.0196). Waxman (N = 1050, α = 0.086, β = 0.2). Transit-stub 1 transit domain with 50 nodes; 1 stub domain per transit node; 20 nodes per stub domain, each domain is a complete subgraph.

8. Alternative Weight Distributions Gaussian with negatively correlated weights produces stretch bounded away from 1. Distribution does not appear to affect the shape of the curve. Edge weights W B (v i, v j ) and W O (v i,v j ) were drawn from a bivariate Gaussian distribution. Positively correlated weightsNegatively correlated weights

9. Computational Complexity of Optimal Overlay Search OPTOVERLAY(G, k): “Given a dual- weighted graph G, find an optimal overlay of size at most k if one exists”. We can show that OPTOVERLAY is NP- complete: –The proof involves reducing 3-SAT to the decision problem “Does there exist an optimal overlay of size k?” The figure to the left illustrates a sample construction that corresponds to the Boolean formula (x 1 + ~x 2 + ~x 3 ) (x 2 + x 3 + ~x 4 )

10. Node Selection Heuristics We investigated several node selection heuristics, including: – Selecting a random subset – Selecting the best of k random subsets – Degree sorting selecting nodes with the highest degree – Importance sorting: selecting the “most important” nodes Node importance is defined as the number of pairwise shortest paths in the topology to which the node belongs. –“Structure-aware” selection (for transit-stub topologies): Selecting only the transit nodes Selecting only the periphery nodes Selecting one node from each domain, etc.

11. Heuristics Results Transit-stub topology: 4 transit domains; 25 nodes per transit domain; 1 stub domain per transit node; 9 nodes per stub domain Waxman topology: N = 1050, α = 0.086, β = 0.2 Degree sorting works best. 1 node from every stub domain works best.

12. Summary and Conclusions Overlay networks work well on a range of simulated topology models and most of the improvement can be achieved with a fairly small selection of overlay nodes. Picking an optimal overlay is hard, but degree sorting and other heuristics provide efficient approximations. Random node selection works surprisingly well.

13. Heuristics Results