Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-13T05:33:20.236Z Has data issue: false hasContentIssue false
  • English
  • Français

A correlated queue with infinitely many servers

Published online by Cambridge University Press:  14 July 2016

C. Langaris
C. Langaris*
Affiliation:
University of Ioannina
*
∗Postal address: Department of Mathematics, University of Ioannina, Ioannina 45332, Greece.
Get access Rights & Permissions [Opens in a new window]

Abstract

This work analyses a queueing mechanism with infinitely many servers in which the interarrival interval T preceding the arrival of a customer and his service time S are assumed correlated. A bivariate distribution with negative exponential marginals is used and the Laplace transforms pn (z) of the system probabilities in transient state are obtained. Closed-form expressions for the steady-state probabilities pn and their moments are given too. Finally the output process is investigated and conclusions are drawn from numerical calculations.

Keywords

SYSTEM STATE PROBABILITIESOUTPUT
Type
Research Papers
Information
Journal of Applied Probability , Volume 23 , Issue 1 , March 1986 , pp. 155 - 165
Copyright
Copyright © Applied Probability Trust 1986 

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] Conolly, B. W. (1975) Queueing Systems. Ellis Horwood, Chichester.Google Scholar
[2] Conolly, B. W. (1968) The waiting time of a certain correlated queue. Operat. Res. 16, 1006–1015.CrossRefGoogle Scholar
[3] Conolly, B. W. and Choo, Q. H. (1979) The waiting time process for a generalized correlated queue with exponential demand and service. SIAM J. Appl. Math. 37, 263–275.CrossRefGoogle Scholar
[4] Conolly, B. W. and Hadidi, N. (1969) A correlated queue. J. Appl. Prob. 6, 122–136.CrossRefGoogle Scholar
[5] Mitchell, C. R. and Paulson, A. S. (1976) M/M/1 queues with inter-dependent arrival and service processes. Research Report No. 37-76-P7, Rensselaer Polytechnic Institute, New York.Google Scholar
[6] Widder, D. V. (1946) The Laplace Transform. Princeton University Press, Princeton, NJ.Google Scholar