Random Symmetric Gossip Consensus with Overhearing Nodes in Wireless Networks

This paper considers consensus in wireless networks with random symmetric gossip. During each timeslot, a pair of nodes is randomly selected. These nodes then exchange messages and adjust their states to reduce the distance from consensus in the network. Since only two messages are exchanged and only two nodes adjust their states in each timeslot, the convergence rate of symmetric gossip to a consensus state is often prohibitively slow (especially for networks with a large number of nodes). This paper proposes an extension to the symmetric gossip consensus model which takes advantage of the broadcast nature of wireless transmissions. Specifically, this paper considers a scenario in which some nodes can "overhear" the transmissions of the randomly selected node pair in each timeslot. These nodes can use this overheard information to adjust their states for "free", i.e., without any additional messaging in each timeslot, consequently improving convergence rates. This paper analyzes the performance of random symmetric gossip with overhearing nodes under several different network topologies. Numerical results are also provided for consensus synchronization scenario. These results show that overhearing nodes can significantly improve the convergence rate of symmetric gossip systems without increasing messaging overhead.