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Concavity of the throughput of tandem queueing systems with finite buffer storage space

Published online by Cambridge University Press:  01 July 2016

Ludolf E. Meester  and
J. George Shanthikumar
Ludolf E. Meester*
Affiliation:
University of California, Berkeley
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
*
∗Postal address: Department of Statistics, University of California, Berkeley, CA 94720, USA.
∗∗Postal address: Walter A. Haas School of Business, University of California, Berkeley, CA 94720, USA.
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Abstract

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We consider a tandem queueing system with m stages and finite intermediate buffer storage spaces. Each stage has a single server and the service times are independent and exponentially distributed. There is an unlimited supply of customers in front of the first stage. For this system we show that the number of customers departing from each of the m stages during the time interval [0, t] for any t ≧ 0 is strongly stochastically increasing and concave in the buffer storage capacities. Consequently the throughput of this tandem queueing system is an increasing and concave function of the buffer storage capacities. We establish this result using a sample path recursion for the departure processes from the m stages of the tandem queueing system, that may be of independent interest. The concavity of the throughput is used along with the reversibility property of tandem queues to obtain the optimal buffer space allocation that maximizes the throughput for a three-stage tandem queue.

Keywords

BLOCKINGSAMPLE PATH CONSTRUCTIONSTOCHASTIC CONCAVITYBUFFER ALLOCATION
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 3 , September 1990 , pp. 764 - 767
Copyright
Copyright © Applied Probability Trust 1990 

References

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