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On the busy-period distributions of M/G/1/K queues by state-dependent arrivals and FCFS/LCFS-P service disciplines

Published online by Cambridge University Press:  14 July 2016

J. George Shanthikumar  and
Ushio Sumita
J. George Shanthikumar*
Affiliation:
University of California, Berkeley
Ushio Sumita*
Affiliation:
University of Rochester
*
∗ Postal address: Management Science Group, School of Business Administration, University of California, Berkeley, CA 94720, USA.
∗ Postal address: Management Science Group, School of Business Administration, University of California, Berkeley, CA 94720, USA.
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Abstract

The busy-period distributions of M/G/1/K queues with state-dependent arrival rates are considered. Two recursion formulas for the Laplace–Stieltjes transforms of the busy periods under the FCFS and preempt resume LCFS service disciplines are obtained. It is shown that the busy-period distributions for the two service disciplines are, in general, different, in contrast to the fact that they coincide for ordinary M/G/1 queues. For deterministic service times and arrival rates non-increasing in the number of customers in the system, stochastic ordering between these two busy periods is also established.

Keywords

FINITE QUEUESRECURSION FORMULASTOCHASTIC ORDERING
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 912 - 919
Copyright
Copyright © Applied Probability Trust 1985 

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References

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