Computing Statistical Functions in Wired Networks

For applications in which a node is interested in a function of the data generated at different sources, in-network computation is a promising approach to improve the network performance. In this paper, we study the problem of computing the first M moments of the data using in-network computation in an arbitrary wired communication network. We are interested in finding a routing and queue management strategy that maximizes the data rate at which the sources could generate new data. We first propose a very simple tractable flow model that computes an upper bound on the maximum data generation rate that could be supported in a given network for a given M. To validate the tightness of this upper bound and to provide a practical feasible solution, we then propose a heuristic strategy involving the generation of multiple trees and effective queue management that achieves data generation rates close to this upper bound. This cross-validates the tightness of the upper bound and the goodness of our heuristic strategy. Finally, using the flow model, we provide engineering insights on what in-network computation can achieve.