Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-30T23:38:03.107Z Has data issue: false hasContentIssue false
  • English
  • Français

A queueing process with the possibility of customers becoming servers

Published online by Cambridge University Press:  01 July 2016

Wen-Jang Huang  and
Prem S. Puri
Wen-Jang Huang*
Affiliation:
National Sun Yat-sen University
Prem S. Puri*
Affiliation:
Purdue University
*
∗Postal address: Institute of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, 80424, ROC.
∗∗Professor Puri died unexpectedly on 12 August 1989, less than a month after this paper had been submitted.
Get access Rights & Permissions [Opens in a new window]

Abstract

A new queueing system called G/G/{p} is introduced and studied. In this queue, unlike standard queues, the customers after being served are allowed to become servers themselves. More precisely, at the completion of his service each customer is assumed to become a server with probability p or leave the system with probability 1 – p, independent of everything else. We make some comparisons about the waiting times and queue sizes among different queueing systems. We also study the joint distribution of the queue size, the number of servers and the number of departures at time t for exact and asymptotic behavior for large t.

Keywords

EMBEDDED MARKOV CHAING/G/{p} QUEUEG/G/m QUEUEG/G/∞ QUEUEINEQUALITYLIMITING BEHAVIOURPOISSON PROCESS
Type
Research Article
Information
Advances in Applied Probability , Volume 23 , Issue 4 , December 1991 , pp. 957 - 971
Copyright
Copyright © Applied Probability Trust 1991 

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

This research was supported in part by U.S. National Science Foundation Grant No. DMS-8504319.

References

Bartholomy, A. F. (1964) The general catalytic queue process. In Stochastic Models in Medicine and Biology , ed. Gurland, J., pp. 101–145. University of Wisconsin Press, Madison.Google Scholar
Borovkov, A. A. (1976) Stochastic Process in Queueing Theory. Springer-Verlag, New York.Google Scholar
Doob, J. L. (1953) Stochastic Processes. Wiley and Sons, New York.Google Scholar
Isaacson, D. L. and Madsen, R. W. (1976) Markov Chains: Theory and Applications. Wiley, New York.Google Scholar
Kiefer, J. and Wolfowitz, J. (1955) On the theory of queues with many servers. Trans. Amer. Math. Soc. 78, 1–18.CrossRefGoogle Scholar
Loynes, R. M. (1962) The stability of queue with non-independent inter-arrival and service times. Proc. Camb. Phil. Soc. 58, 497–520.CrossRefGoogle Scholar
Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar