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The cyclic queue with one general and one exponential server

Published online by Cambridge University Press:  01 July 2016

O. J. Boxma
O. J. Boxma*
Affiliation:
University of Utrecht
*
∗Postal address: Mathematical Institute, State University of Utrecht, Budapestlaan 6, P.O. Box 80.010, 3508 TA Utrecht, The Netherlands.
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Abstract

This paper considers the two-stage cyclic queueing model consisting of one general (G) and one exponential (M) server. The strong connection between the present model and the M/G/1 model (with finite waiting room) is exploited to yield the joint distribution of the successive response times of a customer at the G queue and the M queue. This result reveals a surprising phenomenon: in general there is a difference between the joint distribution of the two successive response times at (first) the G queue and (then) the M queue, and the joint distribution of the two successive response times at (first) the M queue and (then) the G queue.

Another associated result is an expression for the cycle-time distribution. Special consideration is given to the case that the number of customers in the system tends to ∞, while the mean service times tend to 0 at an inversely proportional rate.

Keywords

M/G/1 QUEUERESPONSE TIMEJOINT DISTRIBUTIONCYCLE TIME
Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 4 , December 1983 , pp. 857 - 873
Copyright
Copyright © Applied Probability Trust 1983 

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References

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