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Queueing processes in bulk systems under the D-policy

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Jewgeni H. Dshalalow
Jewgeni H. Dshalalow*
Affiliation:
Florida Institute of Technology
*
∗Postal address: Department of Applied Mathematics, Florida Institute of Technology, Melbourne, FL 32901, USA. Email address: [email protected]
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Abstract

This paper studies the queueing process in a class of D-policy models with Poisson bulk input, general service time, and four different vacation scenarios, among them a multiple vacation, single vacation and idle server. The D-policy specifies a busy period discipline, which requires an idle or vacationing server to resume his service when the workload process crosses some fixed level D. The analysis of the queueing process is based on the theory of fluctuations for three-dimensional marked counting processes presented in the paper. For all models, we derive the stationary distributions for the embedded and continuous time parameter queueing processes in closed analytic forms and illustrate the results by a number of examples and applications.

Keywords

Queueingqueueing processvacationsD-policyKendall's formulafluctuation theoryfirst excess level theoryfirst passage timesemi-regenerative techniquesembedded Markov chain

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.) 60K15: Markov renewal processes, semi-Markov processes 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 35 , Issue 4 , December 1998 , pp. 976 - 989
Copyright
Copyright © Applied Probability Trust 1998 

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