Sequential Stopping Rules for the Regenerative Method of Simulation

We consider the estimation via simulation of confidence intervals for steady-state response variables for stochastic systems which have a regenerative stochastic structure. Sequential stopping rules are investigated which allow the ratio of the width to the mid-point of an estimated confidence interval to be specified ahead of time. We prove that the resulting confidence intervals are valid asymptotically as the relative width decreases to zero. For various relative widths we empirically investigate the validity of the confidence intervals obtained when the stopping rules are applied to the simulation of queuing systems having a regenerative stochastic structure. For the queuing systems and response variables considered, a relative width of 0.05 is found to be sufficiently small to yield valid confidence intervals in almost all cases. In addition, we empirically compare the sequential stopping rules with a fixed stopping rule.