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.

This paper investigates distributed consensus for density classification in asynchronous random networks with faulty nodes. We compare four different models of faulty behavior under randomized topology. Using computer simulations, we show that (a) faulty nodes' impact depends on their location and (b) faulty nodes with persistent failures inhibit consensus stronger than commonly-used Byzantine faulty nodes with random failures. We also show that (c) randomization by Byzantine faulty nodes can be strongly beneficial for binary consensus and (d) topology randomization can increase robustness towards faulty node behavior

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Abstract. This short paper studies distributed consensus algorithms with focus on their robustness against communication errors. We report simulation results to verify and assess existing algorithms. GacsKurdyumov-Levin and simple majority rule are evaluated in terms of convergence rate and speed as a function of noise and network topology.

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