Hostname: page-component-848d4c4894-jbqgn Total loading time: 0 Render date: 2024-06-23T07:59:25.199Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the MX/GY/1, K bulk queueing system

Published online by Cambridge University Press:  14 July 2016

Tapan P. Bagchi  and
J. G. C. Templeton
Tapan P. Bagchi*
Affiliation:
Department of Industrial Engineering, University of Toronto
J. G. C. Templeton
Affiliation:
Department of Industrial Engineering, University of Toronto
*
*Now with Imperial Oil Ltd., Sarnia, Ontario, Canada.
Get access Rights & Permissions [Opens in a new window]

Abstract

Cohen (1969) has studied the transient and stationary queue length distributions for the M/G/1, K queue, with a fixed maximum number of customers, K, in the system at any time. The present note applies Cohen's method to generalize his results to the MX/GY/1, K queue.

Keywords

SINGLE SERVER BULK QUEUESFINITE WAITING SPACEBULK POISSON ARRIVALBULK GENERAL SERVICEIMBEDDED MARKOV CHAINQUEUE LENGTH PROCESSTRANSIENT AND STATIONARY SOLUTIONSINTEGRAL EQUATIONS OF QUEUEING THEORY
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 901 - 906
Copyright
Copyright © Applied Probability Trust 1973 

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.)

Footnotes

Research partially supported by the National Research Council of Canada, Grant no. A5639.

References

Bagchi, Tapan P. (1971) Contributions to the Theory of Bulk Queues. , University of Toronto.Google Scholar
Bagchi, Tapan P. and Templeton, J.G.C. (1973) Finite waiting space bulk queueing systems. J. Engineering Math. To appear.Google Scholar
Bhat, U. N. (1964) Imbedded Markov chain analysis of single server bulk queues. J. Austral. Math. Soc. 4, 244–263.Google Scholar
Cohen, J. W. (1967) On two integral equations of queueing theory. J. Appl. Prob. 4, 343–355.CrossRefGoogle Scholar
Cohen, J. W. (1969) The Single Server Queue. North-Holland, Amsterdam.Google Scholar
Kinney, J. R. (1962) A transient discrete time queue with finite storage. Ann. Math. Statist. 33, 130–136.CrossRefGoogle Scholar
Roes, P. B. M. (1970) The finite dam. J. Appl. Prob. 7, 316–326.CrossRefGoogle Scholar
Singh, V. P. (1971) Finite waiting space bulk service system. J. Engineering Math. 5, 241–248. Addendum, J. Engineering Math. 6, 85–88.Google Scholar