On single-server closed queues with priorities and state dependent parameters |
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Authors: | Jewgeni Dshalalow |
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Institution: | (1) Department of Mathematics, Florida Institute of Technology, 32901 Melbourne, FL, USA |
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Abstract: | A wide class of closed single-channel queues is considered. The more general model involvesm +w + 1 “permanent” customers that occasionally require service. Them customers are of the first priority and the rest are of the second priority. The input rate and service of customers depend
upon the total number of customers waiting for service. Such a system can also be described in terms of servicing machines
processes with reserve replacement and multi-channel queues with finite waiting room. Two dual models, with and without idle
periods, are treated. An explicit relation between the servicing processes of both models is derived. The semi-regenerative
techniques originally developed in the author's earlier work 4] are extended and used to derive the probability distribution
of the processes in equilibrium. Applications and examples are discussed.
This paper is a part of work supported by the National Science Foundation under Grant No. DMS-8706186. |
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Keywords: | Closed queues single-server queue servicing machines reserve replacement multi-channel queue double control duality semi-regenerative process Markov chain semi-Markov process weak Markov process |
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