A Fixed-Sample-Size Method for Estimating Steady-State Quantiles

Abstract

We propose FQUEST, a fully automated fixed-sample-size procedure for computing confidence intervals (CIs) for steady-state quantiles. The user provides a (simulation-generated) dataset of arbitrary size and specifies the required quantile and nominal coverage probability of the anticipated CI. FQUEST incorporates the simulation analysis methods of batching, standardized time series (STS), and sectioning. Preliminary experimentation with the waiting-time process in a congested M/M/1 queueing system showed that FQUEST performed well by delivering CIs with estimated coverage probability close to the nominal level, even in unfavorable circumstances where the sample sizes were inadequate. In the latter cases and for very small samples for steady-state quantile estimation, the close conformance of the CI coverage probability typically came at the expense of loose CI precision. © 2024 Elsevier B.V., All rights reserved.