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

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  • Jewgeni H. Dshalalow

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.

Suggested Citation

  • Jewgeni H. Dshalalow, 1996. "On applications of excess level processes to (N,D)-policy bulk queueing systems," International Journal of Stochastic Analysis, Hindawi, vol. 9, pages 1-12, January.
    • Handle: RePEc:hin:jnijsa:549724
    DOI: 10.1155/S1048953396000457
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    Cited by:

    1. Renbin Liu & Attahiru Sule Alfa & Miaomiao Yu, 2019. "Analysis of an ND-policy Geo/G/1 queue and its application to wireless sensor networks," Operational Research, Springer, vol. 19(2), pages 449-477, June.

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