| Many stochastic processes may be approximated by another mathematically more tractable Markov process. For example, the waiting time sequence in a single-server queue may be approximated by a reflected Brownian motion. It seems reasonable that knowledge of the approximation might enable a simulator to increase the efficiency of a simulation of the original process. The method of external control variates is one possible approach in which the approximating process is simulated in parallel with the original process. In this thesis, we present a new method of exploiting the approximation that does not require the simulation of the approximating process.;To be specific, suppose that X is a Markov process living on state space S. Let f be a real-valued function on S that represents the rate at which cost accrues. The typical estimator for long-term average cost is simply;In this thesis we present the general methodology behind the AMP method, and then discuss applications to the waiting time sequence and queue size process in the single-server queue. In particular, we demonstrate that if heavy-traffic approximations are used for these processes, then order of magnitude variance reductions are possible when estimating steady-state moments and tail probabilities. |
