Measuring the mixing time of a network

Abstract

Mixing time is a global property of a network that indicates how fast a random walk gains independence from its starting point. Mixing time is an essential parameter for many distributed algorithms, but especially those based on gossip. We design, implement, and evaluate a distributed protocol to measure mixing time. The protocol extends an existing algorithm that models the diffusion of information seen from each node in the network as the impulse response of a particular dynamic system. In its original formulation, the algorithm was susceptible to topology changes (or “churn”) and was evaluated only in simulation. Here we present a concrete implementation of an enhanced version of the algorithm that exploits multiple parallel runs to obtain a robust measurement, and evaluate it using a network testbed (Emulab) in combination with a peer-to-peer system (FreePastry) to assess both its performance and its ability to deal with network churn.