Empirical convergence rates for continuous-time Markov chains

We consider the problem of estimating the rate of convergence to stationari ty of a continuous-time, finite-state Markov chain. This is done via an est imator of the second-largest eigenvalue of the transition matrix, which in turn is based on conventional inference in a parametric model. We obtain a limiting distribution for the eigenvalue estimator. As an example we treat an M/M/c/c queue, and show that the method allows us to estimate the time t o stationarity tau within a time comparable to tau.