Performance of Averaging Algorithms in Time-Varying Networks

We study averaging algorithms in time-varying networks, and means tomeasure their performance. We present sufficient conditions on these algorithms, which ensure they lead to computation at each node, of the global average of measurements provided by each node in the network. Further, we present and use results from ergodic theory to define an accurate performance metric for averaging algorithms. This metric, the contraction coefficient, differs from previously used metrics such as the second largest eigenvalue of the expected weighting matrix, which gives an approximation of the real convergence rate only in some special cases which are hard to specify. On the other hand, the contraction coefficient as set forth herein characterizes exactly the actual asymptotic convergence rate of the system. Additionally, it may be bounded by a very concise formula, and simulations show that this bound is, at least in all studied cases, reasonably tight so as to be used as an approximation to the actual contraction coefficient. Finally, we provide a few results and observations which make use of the derived tools. These observations may be used to find new optima for design parameters of some averaging algorithms, and also open the door to new problems in the study of the underlying mathematical models.