A Study of the Dynamics of the Average in a Residual Gossip Protocol

Gossip protocols are appreciated tools to achieve consensus in large and decentralized multi-agent systems. Residual gossip protocols have been proposed to use the gossip approach to solve the distributed averaging problem in multi-agent systems with asymmetric links. A residual gossip protocol is studied in this paper using an atypical method and obtaining two results. First, it is confirmed that the studied protocol can be used to solve the distributed averaging problem. Second, a closed-form expression of the time evolution of the studied average is obtained, thus addressing a gap in the literature on residual gossip protocols. These analytic results are confirmed by a few illustrative simulations discussed in the last part of this paper primarily for illustrative purposes.