Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-29T05:37:27.338Z Has data issue: false hasContentIssue false
  • English
  • Français

An invariance relationship for the G/G/1 queue

Published online by Cambridge University Press:  01 July 2016

Bhaskar Sengupta
Bhaskar Sengupta*
Affiliation:
AT & T Bell Laboratories
*
∗Postal address: Room HO 3L-309, AT & T Bell Laboratories, Holmdel, NJ 07733, USA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this note, we show that for a stationary FCFS G/G/1 queue, the virtual waiting time and the time spent in the system by the customer in service have the same distribution. We assume that the latter is zero if the queue is empty.

Keywords

VIRTUAL WAITING TIMETIME IN SYSTEM BY CUSTOMER IN SERVICEFCFS
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 956 - 957
Copyright
Copyright © Applied Probability Trust 1989 

References

Asmussen, S. (1988) Matrix representations of ladder height distributions. Submitted for publication.Google Scholar
Miyazawa, M. (1979) A formal approach to queueing processes in the steady state and their applications. J. Appl. Prob. 16, 332–346.CrossRefGoogle Scholar
Miyazawa, M. (1983) The derivation of invariance relations in complex queueing systems with stationary inputs. Adv. Appl. Prob. 15, 874–885.Google Scholar
Prabhu, N. U. (1965) Queues and Inventories: A Study of their Basic Stochastic Processes. Wiley, New York.Google Scholar
Ramaswami, V. (1989) From the matrix-geometric to the matrix-exponential. In preparation.Google Scholar
Sengupta, B. (1988) The semi-Markovian queue: theory and applications. To appear.Google Scholar
Sengupta, B. (1989) Markov processes whose steady state distribution is matrix-exponential with an application to the GI/PH/1 queue. Adv. Appl. Prob. 21, 159–180.CrossRefGoogle Scholar