In this paper, we compare six known linear distributed average consensus algorithms on a sensor network in terms of convergence time (and therefore, in terms of the number of transmissions required). The selected network topologies for the analysis (comparison) are the cycle and the path. Specifically, in the present paper, we compute closed-form expressions for the convergence time of four known deterministic algorithms and closed-form bounds for the convergence time of two known randomized algorithms on cycles and paths. Moreover, we also compute a closed-form expression for the convergence time of the fastest deterministic algorithm considered on grids.
Keywords: average consensus algorithms; convergence time; distributed computation; number of transmissions; sensor networks.