ARQ-based Average Consensus over Directed Network Topologies with Unreliable Communication Links

Abstract: In this paper, we address the discrete-time average consensus problem in strongly connected directed graphs, where nodes exchange information over unreliable error-prone communication links. We enhance the Robustified Ratio Consensus algorithm by exploiting features of the (Hybrid) Automatic Repeat ReQuest - (H)ARQ protocol used for error control of data transmissions, in order to allow the nodes to reach asymptotic average consensus even when information is exchanged over error-prone directional networks. This strategy, apart from handling time-varying information delays induced by retransmissions of erroneous packets, can also handle packet drops that occur when exceeding a predefined packet retransmission limit. Invoking the (H)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 (H)ARQ Ratio Consensus algorithm can reach asymptotic average consensus over unreliable networks, while improving their convergence speed and maintaining low values in their local buffers compared to the current state-of-the-art.