Variance Reduction Techniques for the Simulation of Markov Processes, I: Multiple Estimates

A method for reducing the variance of simulation-generated estimates is proposed and discussed. The method may be applied to the estimation of steady state parameters of discrete and continuous time Markov chains, semi-Markov processes, and regenerative discrete time Markov processes on a general state space (such as the waiting time process in a multiple-server queue). The method is similar to the technique of control variables, but differs in that the means of the controls need not be explicitly known. Numerical results for a variety of simple queueing models are presented.