Asymptotic analysis of quadratic error of consensus in large-scale random directed networks

Authors:
Victor M. Preciado;Alireza Tahbaz-Salehi;Ali Jadbabaie
Affiliations:
Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA;Department of Economics and Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA;General Robotics, Automation, Sensing and Perception Laboratory, Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA
Venue:
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Year:
2009

Citing 2
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IEEE/ACM Transactions on Networking (TON) - Special issue on networking and information theory
Randomized consensus algorithms over large scale networks

IEEE Journal on Selected Areas in Communications

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Abstract

We analyze the asymptotic variance of distributed consensus algorithms over large-scale switching random networks. Our analysis is focused on consensus algorithms over large, i.i.d., and directed Erdös-Rényi random graphs. We assume that every agent can communicate with any other agent with some fixed probability c/n, where c is the expected number of neighbors of each agent and n is the size of the network. We compute the variance of the random consensus value and show that it converges to zero at rate 1/n as the number of agents grows. We provide numerical simulations that illustrate our results.