Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T11:16:18.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Regeneration in tandem queues

Published online by Cambridge University Press:  01 July 2016

E. Nummelin
E. Nummelin*
Affiliation:
Helsinki University of Technology
*
∗Postal address: Helsinki University of Technology, Institute of Mathematics, 02150 Espoo 15, Finland.
Get access Rights & Permissions [Opens in a new window]

Abstract

Consider a tandem queue with renewal input process and i.i.d. service times (at each server). This paper is concerned with the construction of regeneration times for the multivariate Markov chain formed by the interarrival times, waiting times and service times of the customers.

Keywords

QUEUETANDEM QUEUEREGENERATION TIMEMARKOV CHAIN
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 1 , March 1981 , pp. 221 - 230
Copyright
Copyright © Applied Probability Trust 1981 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Charlot, F., Ghidouche, M. and Hamami, M. (1978) Irréductibilité et récurrence au sens de Harris des “Temps d'attente” des files GI/G/q. Z. Wahrscheinlichkeitsth. 43, 187–203.Google Scholar
[2] Cohen, J. W. (1976) On Regenerative Processes in Queuing Theory. Lecture Notes in Economics and Mathematical Systems, 121, Springer-Verlag, Heidelberg.Google Scholar
[3] Nummelin, E. (1979) A conservation property for general GI/G/1 queues with an application to tandem queues. Adv. Appl. Prob. 11, 660–672.CrossRefGoogle Scholar
[4] Orey, S. (1971) Lecture Notes on Limit Theorems for Markov Chain Transition Probabilities. Van Nostrand, New York.Google Scholar
[5] Revuz, D. (1975) Markov Chains. North-Holland, Amsterdam.Google Scholar
[6] Whitt, W. (1972) Embedded renewal processes in the GI/G/s queue. J. Appl. Prob. 9, 650–658.Google Scholar