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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.
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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 

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Footnotes

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

References

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