Fast mean square convergence of consensus algorithms in WSNs with random topologies

The average consensus in wireless sensor networks is achieved under assumptions of symmetric or balanced topology at every time instant. However, communication and/or node failures, as well as node mobility or changes in the environment make the topology vary in time, and instantaneous symmetry of the links is not guaranteed unless an acknowledgment protocol or an equivalent approach is implemented. In this paper, we evaluate the convergence in the mean square sense of a well-known consensus algorithm assuming a random topology and asymmetric communication links. A closed form expression for the mean square error of the state is derived as well as the optimum choice of parameters to guarantee fastest convergence of the mean square error.