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Distribution of the busy period in a controllable M/M/2 queue operating under the triadic (0, K, N, M) policy

Published online by Cambridge University Press:  14 July 2016

Hahn-Kyou Rhee  and
B. D. Sivazlian
Hahn-Kyou Rhee
Affiliation:
University of Florida
B. D. Sivazlian*
Affiliation:
University of Florida
*
∗Postal address for both authors: Department of Industrial and Systems Engineering, University of Florida, Gainesville FL 32611, USA.
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Abstract

We consider an M/M/2 queueing system with removable service stations operating under steady-state conditions. We assume that the number of operating service stations can be adjusted at customers' arrival or service completion epochs depending on the number of customers in the system. The objective of this paper is to obtain the distribution of the busy period using the theory of the gambler's ruin problem. As special cases, the distributions of the busy periods for the ordinary M/M/2 queueing system, the M/M/1 queueing system operating under the N policy and the ordinary M/M/1 queueing system are obtained.

Keywords

MARKOVIAN QUEUEING SYSTEMGAMBLER'S RUIN PROBLEMLAPLACE TRANSFORMBUSY PERIOD
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 2 , June 1990 , pp. 425 - 432
Copyright
Copyright © Applied Probability Trust 1990 

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