Characterizing continuous time random walks on time varying graphs

Authors:
Daniel Figueiredo;Philippe Nain;Bruno Ribeiro;Edmundo de Souza e Silva;Don Towsley
Affiliations:
Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil;INRIA, Sophia-Antipolis, MA, France;University of Massachusetts Amherst, Amherst, MA, USA;Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil;University of Massachusetts Amherst, Amherst, MA, USA
Venue:
Proceedings of the 12th ACM SIGMETRICS/PERFORMANCE joint international conference on Measurement and Modeling of Computer Systems
Year:
2012

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Abstract

In this paper we study the behavior of a continuous time random walk (CTRW) on a stationary and ergodic time varying dynamic graph. We establish conditions under which the CTRW is a stationary and ergodic process. In general, the stationary distribution of the walker depends on the walker rate and is difficult to characterize. However, we characterize the stationary distribution in the following cases: i) the walker rate is significantly larger or smaller than the rate in which the graph changes (time-scale separation), ii) the walker rate is proportional to the degree of the node that it resides on (coupled dynamics), and iii) the degrees of node belonging to the same connected component are identical (structural constraints). We provide examples that illustrate our theoretical findings.