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International Journal of Stochastic Analysis

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International Journal of Stochastic Analysis / 1996 / Article

Open Access

Volume 9 |Article ID 549724 | https://doi.org/10.1155/S1048953396000457

Jewgeni H. Dshalalow, "On applications of excess level processes to (N,D)-policy bulk queueing systems", International Journal of Stochastic Analysis, vol. 9, Article ID 549724, 12 pages, 1996. https://doi.org/10.1155/S1048953396000457

On applications of excess level processes to (N,D)-policy bulk queueing systems

Jewgeni H. Dshalalow1

1Department of Applied Mathematics, Florida Institute of Technology, USA

Received01 Jul 1996
Revised01 Nov 1996

Abstract

The paper deals with queueing systems in which N- and D-policies are combined into one. This means that an idle or vacationing server will resume his service if the queueing or workload process crosses some specified fixed level N or D, respectively. For the proposed (N,D)-policy we study the queueing processes in models with and without server vacations, with compound Poisson input, and with generally distributed service and vacation periods. The analysis of the models is essentially based on fluctuation techniques for two-dimensional marked counting processes newly developed by the author. The results enable us to arrive at stationary distributions for the embedded and continuous time parameter queueing processes in closed analytic forms, enhancing the well-known Kendall formulas and their modifications.This article is dedicated to the memory of Roland L. Dobrushin.

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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