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

Kemal Dinçer Dingeç (), Christos Alexopoulos (), David Goldsman (), Athanasios Lolos () and James R. Wilson ()
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Kemal Dinçer Dingeç: Gebze Technical University
Christos Alexopoulos: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
David Goldsman: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
Athanasios Lolos: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology
James R. Wilson: North Carolina State University, Edward P. Fitts Department of Industrial and Systems Engineering

A chapter in Advances in Modeling and Simulation, 2022, pp 111-130 from Springer

Abstract: Abstract For asymptotically valid point and confidence-interval (CI) estimation of steady-state quantiles in dependent simulation output processes, two recent output-analysis 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.

Keywords: Dependent simulation output processes; Geometric-moment contraction condition; Queue-waiting times; Single-server queue; Steady-state quantile estimation (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-10193-9_6

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DOI: 10.1007/978-3-031-10193-9_6

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