Notes on Fisher Information-Based Measurement Design for Network Tomography

Let G = (V, L) denote a network with nodes V and links L. Each link l ∈ L is associated with a performance metric that varies stochastically according to a distribution with unknown parameter θl. Let P be a given set of candidate probing paths in G. Each path py ∈ P consists of one or more pairwise adjacent links in G. We assume that the monitoring system can inject probes on any selected paths in P and observe their endto-end performance. We also introduce a matrix A defined by P , called the measurement matrix, which is a |P |× |L| matrix with the (y, l)-th entry Ay,l ∈ {0, 1} indicating whether link l is on path py. Without loss of generality, we assume that each link is on at least one path in P . Additional constraints on A (and hence P ) will be introduced later when needed.