Title:ARQ-based Average Consensus over Unreliable Directed Network Topologies

Abstract: In this paper, we address the problem of discrete-time average consensus, where agents (nodes) exchange information over unreliable communication links. We enhance the Robustified Ratio Consensus algorithm by embedding the Automatic Repeat ReQuest (ARQ) protocol used for error control of data transmissions, in order to allow the agents 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 (that can be captured by the Robustified Ratio Consensus as well), it is also possible to handle packet drops that occur due to excess of 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 signals 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 which is imposed by the retransmission limit. By augmenting the network's corresponding weighted adjacency matrix, to handle time-varying (yet bounded) delays and possible packet drops, we show that nodes can make use of the proposed algorithm, herein called the ARQ-based Ratio Consensus algorithm, to reach asymptotic average consensus, despite the fact that the communication links are unreliable. To the best of the authors' knowledge, this is the first consensus algorithm that incorporates a communication protocol for error control used in real communication systems with feedback.