Empirical Comparison of Replications and Batch-based Approaches for Mean, Variance and Quantile Estimation in Steady-State Simulations

摘要

In this article we present an empirical comparison among three methods (multiple replications, non-overlapping batches and spaced batches) to estimate the expectation, the variance and the 90%-quantile of the steady-state waiting time in an M/M/1 queue. Our comparison is based on the empirical coverage, bias and relative error of 90% asymptotic confidence intervals from 1000 independent replications of a simulation-based estimation. Experimental results show that all three methods provide similar (and valid) empirical coverage for the estimation of the expectation, variance and quantile; and the method of non-overlapping batches provided smaller bias and relative errors than the other two methods. In addition, we discuss an example of a continuous state-space Markov chain that is ergodic but non-geometric, for which we also obtained asymptotically valid confidence intervals by using the methods considered in this paper.