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

Lev Abolnikov and Jewgeni H. Dshalalow

International Journal of Stochastic Analysis, 1992, vol. 5, 1-15

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 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.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:582154

DOI: 10.1155/S1048953392000066

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