Exploiting a Mobile Node for Fast Discrete Time Average Consensus

Discrete time average consensus has been attracting lots of research attentions due to its wide spectrum of applications in various networks. In these networks, it is also common and useful for mobile nodes serving as data collector or packet relayers. Hence, it is of great interest to investigate whether and how the design of mobile nodes can accelerate the discrete time average consensus while preserving the consensus value. This paper exploits a mobile node to reach fast discrete time average consensus. First, we give a sufficient condition of the mobile node's state, which guarantees the step-by-step convergence of consensus. Based on the condition, we propose a protocol for the mobile node to cope with information exchange without introducing much communication overhead for the static nodes. Then, we also provide rigorous proof that under our proposed protocol, the introduction of mobile node can increase the convergence rate of discrete time average consensus in expectation. Furthermore, a scheme to preserve the average value is provided. Extensive simulations demonstrate the effectiveness of the proposed protocol and validate the theoretical results.