A Sequential Procedure for Determining the Length of a Steady-State Simulation

A common problem faced by simulators is that of constructing a confidence interval for the steady-state mean of a stochastic process. We have reviewed the existing procedures for this problem and found that all but one either produce confidence intervals with coverages which may be considerably lower than desired or have not been adequately tested. Thus, in many cases simulators will have more confidence in their results than is justified. In this paper we present a new sequential procedure based on the method of batch means for constructing a confidence interval with coverage close to the desired level. The procedure has the advantage that it does not explicitly require a stochastic process to have regeneration points. Empirical results for a large number of stochastic systems indicate that the new procedure performs quite well.