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The Busy Period of an M/G/1 Queue with Customer Impatience

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Onno Boxma ,
David Perry ,
Wolfgang Stadje  and
Shelley Zacks
Onno Boxma*
Affiliation:
EURANDOM and Eindhoven University of Technology
David Perry*
Affiliation:
University of Haifa
Wolfgang Stadje*
Affiliation:
University of Osnabrück
Shelley Zacks*
Affiliation:
Binghamton University
*
∗Postal address: Department of Mathematics and Computer Science, Eindhoven University of Technology, HG 9.14, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: boxma@win.tue.nl
∗∗Postal address: Department of Statistics, University of Haifa, Haifa 31909, Israel. Email address: dperry@haifa.ac.il
∗∗∗Postal address: Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany. Email address: wolfgang@mathematik.uni-osnabrueck.de
∗∗∗∗Postal address: Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902-6000, USA. Email address: shelly@math.binghamton.edu
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Abstract

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We consider an M/G/1 queue in which an arriving customer does not enter the system whenever its virtual waiting time, i.e. the amount of work seen upon arrival, is larger than a certain random patience time. We determine the busy period distribution for various choices of the patience time distribution. The main cases under consideration are exponential patience and a discrete patience distribution.

Keywords

Busy periodM/G/1 queueimpatiencevirtual waiting time

MSC classification

Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 60J27: Continuous-time Markov processes on discrete state spaces 60J75: Jump processes
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 130 - 145
Copyright
Copyright © Applied Probability Trust 2010 

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