Title: Power-delay analysis of consensus algorithms on wireless networks with interference

Authors: S. Vanka, V. Gupta, M. Haenggi

Addresses: Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA. ' Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA. ' Department of Electrical Engineering, University of Notre Dame, Notre Dame, Indiana 46556, USA

Abstract: We study the convergence of the average consensus algorithm in wireless networks in the presence of interference. For regular lattices with periodic boundary conditions, we characterise the convergence properties of an optimal Time Division Multiple Access (TDMA) protocol that maximises the speed of convergence on these networks. We provide analytical upper and lower bounds for the convergence rate for these networks. Our results show that in an interference-limited scenario, the fastest converging interconnection topology for the consensus algorithm crucially depends on the geometry of node placement. In particular, we prove that asymptotically in the number of nodes, increasing the transmit power to allow long-range interconnections improves the convergence rate in one-dimensional tori, while it has the opposite effect in higher dimensions.

Keywords: consensus algorithms; interference; MAC protocol; wireless networks; power delay; medium access control; time division multiple access; TDMA protocol; node placement.

DOI: 10.1504/IJSCC.2010.031166

International Journal of Systems, Control and Communications, 2010 Vol.2 No.1/2/3, pp.256 - 274

Published online: 23 Jan 2010 *

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