A Simulation-Based Study of Overlay Routing Performance

CS 268 Course Project

Andrey Ermolinskiy, Hovig Bayandorian, Daniel Chen

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?

Approach • Assume the existence of two distinct routing metrics: {WB

(base), WO (overlay)} and two routing protocols {RB, RO} that implement shortest path routing for WB and WO , respectively.

• Model the topology as a dual–weighted graph: G = (V, WB, WO).

• RB is the default routing algorithm in G, but a subset of nodes Ω implements RO via an overlay mechanism.

CO(V1-V2-V5-V6) = 17 CO(V1-V3-V2-V4-V5-V6) = 9

Approach • To evaluate the performance of a given

choice of Ω, compute the topology stretch.Logical overlay subgraphDual-weighted topology graph

Stretch(v1, v6) = 11 / 9

Stretch(v1, v6) = 9 / 9 = 1 (Optimal Path)

Ω = {v2, v4, v5}

Ω = {v2, v3 , v4, v5}

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.

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

Choice of the Topology Model

Uniform random from ζ(1050, 0.0196).

Waxman (N = 1050, α = 0.086, β = 0.2).

Transit-stub1 transit domain with 50 nodes;1 stub domain per transit node;20 nodes per stub domain, each domain is a complete subgraph.

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 WB(vi, vj) and WO(vi,vj) were drawn from a bivariate Gaussian distribution.

Positively correlated weights Negatively correlated weights

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 (x1 + ~x2 + ~x3) (x2 + x3 + ~x4)

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.

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.

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.

Heuristics Results