A central-limit-theorem version of \(L=\lambda W\)
type: Item
instance of: scholarly article
title: A central-limit-theorem version of \(L=\lambda W\)
zbMATH Open document ID: 0676.60088
DOI: 10.1007/BF01536188
author: Peter W. Glynn
author: Ward Whitt
published in: Queueing Systems
publication date: 1986-01-01T00:00:00Z
review text: The authors have shown that in the well-known queueing formula \(L=\lambda W\) the customer-average wait (W) obeys a CLT (central limit theorem) iff the time average queue length (L) obeys a CLT. The authors have further related the two limits. Just as the classical CLTs can be regarded as refinements of the classical LLNs (laws of large numbers), so the authors have shown that their result is a refinement of the standard relation between the limits of the averages w.p. 1 (with probability one). To relate the CLT behaviour of the time averages and customer averages, the authors have worked with FCLTs (functional central limit theorems) instead of ordinary CLTs, using the theory of weak convergence of probability measures on the function space \(D\equiv D[0,\infty)\). The FCLTs have also been used for estimation of queueing system parameters by computer simulation.
reviewed by: L.R.Goel
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 4107894
zbMATH Keywords: queueing theory
zbMATH Keywords: central limit theorem
zbMATH Keywords: functional central limit theorems
zbMATH Keywords: estimation of queueing system parameters
zbMATH Keywords: computer simulation
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01536188
OpenAlex ID: W1481778483
description: scientific article; zbMATH DE number 4107894