Article ID: | iaor1997402 |
Country: | United States |
Volume: | 5 |
Issue: | 1 |
Start Page Number: | 83 |
End Page Number: | 98 |
Publication Date: | Jan 1992 |
Journal: | Journal of Applied Mathematics and Stochastic Analysis |
Authors: | Abolnikov Lev, Dshalalow Jewgeni H. |
Keywords: | queues: theory |
A problem of the first passage of a cumulative random process with generally distributed discrete or continuous increments over a fixed level is considered in the article as an essential part of the analysis of a class of stochastic models (bulk queueing systems, inventory and control and dam models). Using direct probability methods the authors find various characteristics of this problem: the magnitude of the first excess of the process over a fixed level, the shortage before the first excess, the levels of the first and pre-first excesses, the index of the first excess and others. The results obtained are illustrated by a number of numerical examples and then are applied to a bulk queueing system with a service delay discipline.