ARQ-based Average Consensus over Unreliable Directed Network Topologies

In this paper, we address the discrete-time average consensus problem, where nodes exchange information over unreliable communication links. We enhance the Robustified Ratio Consensus algorithm by exploiting features of the Automatic Repeat ReQuest (ARQ) protocol used for error control of data transmissions, in order to allow the nodes to reach asymptotic average consensus even when operating within unreliable directed networks. This strategy, apart from handling time-varying delays induced by retransmissions of erroneous packets, can also handle packet drops that occur when exceeding a predefined packet retransmission limit imposed by the ARQ protocol. Invoking the ARQ protocol allows nodes to: (a) exploit the incoming error-free acknowledgement feedback to initially acquire or later update their out-degree, (b) know whether a packet has arrived or not, and (c) determine a local upper-bound on the delays imposed by the retransmission limit. By augmenting the network's corresponding weight matrix, we show that nodes utilizing our proposed ARQ-based Ratio Consensus algorithm can reach asymptotic average consensus over unreliable networks, while maintaining low running sum values

Distributed Averaging via Lifted Markov Chains

Motivated by applications of distributed linear estimation, distributed control and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average of numbers in a network. Specifically, our interest is in designing such an algorithm with the fastest rate of convergence given the topological constraints of the network. As the main result of this paper, we design an algorithm with the fastest possible rate of convergence using a non-reversible Markov chain on the given network graph. We construct such a Markov chain by transforming the standard Markov chain, which is obtained using the Metropolis-Hastings method. We call this novel transformation pseudo-lifting. We apply our method to graphs with geometry, or graphs with doubling dimension. Specifically, the convergence time of our algorithm (equivalently, the mixing time of our Markov chain) is proportional to the diameter of the network graph and hence optimal. As a byproduct, our result provides the fastest mixing Markov chain given the network topological constraints, and should naturally find their applications in the context of distributed optimization, estimation and control