Journal of Applied Mathematics and Stochastic Analysis
Volume 9 (1996), Issue 4, Pages 551-562

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

Jewgeni H. Dshalalow

Department of Applied Mathematics, Florida Institute of Technology, Melbourne 32901, FL, USA

Received 1 July 1996; Revised 1 November 1996

Copyright © 1996 Jewgeni H. Dshalalow. 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.


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.