Geometric-Moment Contraction of G/G/1 Waiting Times

Abstract

For asymptotically valid point and confidence-interval (CI) estimation of steady-state quantiles in dependent simulation output processes, two recent outputanalysis procedures assume that those processes satisfy the geometric-moment contraction (GMC) condition. Moreover, the GMC condition ensures satisfaction of most of the other assumptions underlying those procedures, which are based on the techniques of batch means and standardized time series, respectively. For performance evaluation of the associated point and CI estimators, the G/G/1 queueing system provides gold-standard test processes. We prove that the GMC condition holds for G/G/1 queue-waiting times obtained with a non-heavy-tailed service-time distribution (i.e., its moment generating function exists in a neighborhood of zero). This result complements earlier proofs that the GMC condition holds for many widely used time-series and Markov-chain processes. A robustness study illustrates empirical verification of the GMC condition for M/G/1 queue-waiting times obtained with non-heavy-tailed and heavy-tailed service-time distributions. © 2023 Elsevier B.V., All rights reserved.