Converging an Overlay Network to a Gradient Topology

TL;DR

This paper analyzes the convergence properties of a gossip-based Gradient overlay network, providing theoretical conditions and bounds, and demonstrating its efficiency in a P2P live-streaming system through simulations.

Contribution

It offers a formal analysis of the convergence conditions for Gradient overlay networks and demonstrates their practical benefits in P2P streaming.

Findings

Proves necessary and sufficient conditions for network convergence.

Estimates convergence time and bounds on worst-case scenarios.

Shows improved efficiency in P2P live-streaming using the Gradient overlay.

Abstract

In this paper, we investigate the topology convergence problem for the gossip-based Gradient overlay network. In an overlay network where each node has a local utility value, a Gradient overlay network is characterized by the properties that each node has a set of neighbors with the same utility value (a similar view) and a set of neighbors containing higher utility values (gradient neighbor set), such that paths of increasing utilities emerge in the network topology. The Gradient overlay network is built using gossiping and a preference function that samples from nodes using a uniform random peer sampling service. We analyze it using tools from matrix analysis, and we prove both the necessary and sufficient conditions for convergence to a complete gradient structure, as well as estimating the convergence time and providing bounds on worst-case convergence time. Finally, we show in simulations the potential of the Gradient overlay, by building a more efficient live-streaming peer-to-peer (P2P) system than one built using uniform random peer sampling.