Note on a series for M/G/1 queues
type: Item
instance of: scholarly article
title: Note on a series for M/G/1 queues
zbMATH Open document ID: 1169.90336
DOI: 10.1504/IJOR.2009.025202
author: Percy H. Brill
published in: International Journal of Operational Research
publication date: 2009-09-13T00:00:00Z
review text: Summary: This paper provides a geometrical (physical) interpretation for a series representing of the steady-state probability density function (PDF) of wait in a standard M/G/1 queue. This series was called 'intriguing' by a prominent queueing theorist in 1975. The series converges geometrically fast, making it potentially useful for approximating the PDF. We provide an intuitive explanation in terms of sample-path upcrossings of a level of the virtual wait. We also consider a similar series for an M/G/1 variant with zero-wait customers receiving special service. This leads to a generalised explanation of both series in terms of sample-path upcrossings.
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 5603404
zbMATH Keywords: M/G/1 queues
zbMATH Keywords: M/G/1 variants
zbMATH Keywords: probability density function
zbMATH Keywords: waiting
zbMATH Keywords: series representation
zbMATH Keywords: renewal theory
zbMATH Keywords: excess service time
zbMATH Keywords: level crossings
zbMATH Keywords: PASTA
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5603404