Distributed Binary Consensus in Networks with Disturbances

Abstract

This article evaluates convergence rates of binary majority consensus algorithms in networks with different types of disturbances and studies the potential capacity of randomization to foster convergence. Simulation results show that (a) additive noise, topology randomness, and stochastic message loss may improve the convergence rate; (b) presence of faulty nodes degrades the convergence rate; and (c) explicit randomization of consensus algorithms can be exploited to improve the convergence rate. Watts-Strogatz and Waxman graphs are used as underlying network topologies. A consensus algorithm is proposed that exchanges state information with dynamically randomly selected neighbors and, through this randomization, achieves almost sure convergence in some scenarios. ACM Reference Format:Alexander Gogolev, Nikolaj Marchenko, Lucio Marcenaro, and Christian Bettstetter. 2015. Distributed binary consensus in networks with disturbances.

Randomized Binary Consensus with Faulty Agents

“…Due to this, SM indicates a low convergence rate in ordered and noiseless systems, but in strongly randomized setups, it can show a high convergence rate [15,17,32] and outperform GKL.…”

“…Specific cases of BMC with faulty nodes have been previously studied in [32] and [17]. Thus, [32] reports that simple majority (SM) consensus is more strongly inhibited by faulty nodes with persistent failure than by faulty nodes with random failure in some networks.…”

“…Thus, [32] reports that simple majority (SM) consensus is more strongly inhibited by faulty nodes with persistent failure than by faulty nodes with random failure in some networks. Another affect is reported in [17], where it is shown that Gacs-Kurdyumov-Levin (GKL) and SM consensus inhibited by a low number of faulty nodes with persistent failure can restore the convergence rate with randomization.…”

“…One can see that, essentially, GKL is a modification of SM consensus with a built-in state-direction bias. This bias provides for the high efficiency of GKL in ring lattices, but it can lead to low efficiency if the network structure or the update sequence are disturbed [15,17].…”

“…Studies show that randomization can be beneficial for consensus, both in terms of efficiency [14,15] and fault tolerance [14,16]. Recent studies show that such beneficial randomization can sometimes be provided explicitly by noise [17,18] or errors [15].…”