Post on 18-Jan-2018
description
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