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.