A first passage problem and its applications to the analysis of a class of stochastic models

A first passage problem and its applications to the analysis of a class of stochastic models

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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: ,
Keywords: queues: theory
Abstract:

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.

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