On applications of excess level processes to (N, D)-policy bulk queueing systems. (1996)

• Record Type: Journal Article
• Authors: Dshalalow, Jewgeni H.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 9:Number 4(1996)
• Page Start: 551
• Page End: 562
• Publication Date: 1996
• Subjects: queueing -- queueing process -- vacations -- N-policy -- D-policy -- (N -- D)-policy -- Kendall's formula -- fluctuation theory -- first excess level theory -- semi-regenerative techniques -- embedded Markov chain; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953396000457
• Languages: English
• ISSNs: 1048-9533

Abstract

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.