Reaching consensus in wireless networks with probabilistic broadcast

Authors:
Tuncer C. Aysal;Anand D. Sarwate;Alexandros G. Dimakis
Affiliations:
Pixsta Research, London;Information Theory and Applications Center, University of California, San Diego, La Jolla, CA;Dept. of Electrical Engineering-Systems, University of Southern California, Los Angeles, CA
Venue:
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Year:
2009

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Abstract

Reaching consensus in a network is an important problem in control, estimation, and resource allocation. While many algorithms focus on computing the exact average of the initial values in the network, in some cases it is more important for nodes to reach a consensus quickly. In a distributed system establishing two-way communication may also be difficult or unreliable. In this paper, the effect of the wireless medium on simple consensus protocol is explored. In a wireless environment, a node's transmission is a broadcast to all nodes which can hear it, and due to signal propagation effects, the neighborhood size may change with time. A class of non-sum preserving algorithms involving unidirectional broadcasting is extended to a time-varying connection model. This algorithm converges almost surely and its expected consensus value is the true average. A simple bound is given on the convergence time.