Propagation Time in Stochastic Communication Networks

Document Type

Presentation Abstract

Presentation Date

9-23-2005

Abstract

Dynamical processes taking place on networks have received much attention in recent years, especially on various models of random graphs (including "small world" and "scale free" networks). They model a variety of phenomena, including the spread of information on the Internet; the outbreak of epidemics in a spatially structured population; and communication between randomly dispersed processors in an ad hoc wireless network. Typically, research has concentrated on the existence and size of a large connected component (representing, say, the size of the epidemic) in a percolation model, or uses differential equations to study the dynamics using a mean-field approximation in an infinite graph. Here we investigate the time taken for information to propagate from a single source through a finite network, as a function of the number of nodes and the network topology. We assume that time is discrete, and that nodes attempt to transmit to their neighbors in parallel, with a given probability of success. We solve this problem exactly for several specific topologies, and use a large-deviation theorem to derive general asymptotic bounds, which we use, for example, to show that a scale-free network has propagation time logarithmic in the number of nodes, and inversely proportional to the transmission probability.

Additional Details

Friday, 23 September 2005
4:10 p.m. in Jour 304

This document is currently not available here.

Share

COinS