Average consensus in sensor networks via broadcast multi-gossip algorithms

Motivated by applications to wireless sensor, peer-to-peer, and ad hoc   networks, we propose a distributed algorithm called broadcast based multi-gossiping algorithm (BMGA), which is designed for exchanging information and computing in an arbitrarily connected network of nodes. Unlike traditional randomized gossip algorithms, push-sum mechanism based BMGA preserves the sums and weights, and admits stochastic diffusion matrices which need not be doubly stochastic. Based on the theory of weak ergodicity and message spreading, we derive a lower bound on the weight, and give an approximate value for this bound. By introducing a potential function, we show that BMGA converges almost surely to the average of initial node measurements with probability one. Specifically, we further provide the upper bounds on the diffusion speed, ϵ-convergenceϵ-convergence time and the number of radio transmissions. Finally, we present a numerical example to assess and compare the communication cost with several gossip-based algorithms to achieve a given performance.