An Identification Problem for Multiterminal Networks: Solving for the Traffic Matrix from Input-Output Measurements

Abstract

We consider the problem of determining the unknown characteristics of a random routing strategy from end-to-end measurements. More specifically, we construct a Markov chain that models the traffic of messages in a multiterminal network consisting of input, intermediate, and output terminals. The topology of the network is assumed to be known, but the Markovian routing strategy is not known. We solve the problem of determining the unknown one-step transition probability matrix of our random walk from input-output measurements of ``travel time.'' We give explicit inversion formulas (up to a natural gauge) in a nontrivial example. The result holds for a large (but not arbitrary) class of multiterminal networks, many of which are indicated here. The networks that we display here are constructed in a canonical fashion from certain graphs. Some of these graphs as well as the way to go from graphs to networks are also displayed. One example of a graph for which our method works is the edge graph of a hypercube in any dimension.