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Tandem queues with bulk arrivals, infinitely many servers and correlated service times

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Ushio Sumita  and
Yasushi Masuda
Ushio Sumita*
Affiliation:
International University of Japan
Yasushi Masuda*
Affiliation:
Keio University
*
∗Postal address: International University of Japan, Yamato-machi, Minamiuonuma-gun, Niigata-ken, 949–72, Japan.
∗∗Postal address: Faculty of Science and Technology, Keio University, 3–14–1, Hiyoshi, Kohoku-ku, Yokohama 223, Japan.
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Abstract

A system of GIx/G/∞ queues in tandem is considered where the service times of a customer are correlated but the service time vectors for customers are independently and identically distributed. It is shown that the binomial moments of the joint occupancy distribution can be generated by a sequence of renewal equations. The distribution of the joint occupancy level is then expressed in terms of the binomial moments. Numerical experiments for a two-station tandem queueing system demonstrate a somewhat counterintuitive result that the transient covariance of the joint occupancy level decreases as the covariance of the service times increases. It is also shown that the analysis is valid for a network of GIx/SM/∞ queues.

Keywords

TANDEM QUEUESBULK ARRIVALSINFINITELY MANY SERVERSCORRELATED SERVICE TIMES

MSC classification

Primary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 248 - 257
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

This paper has been partially supported by the NTT research fund.

References

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