A first passage problem and its applications to the analysis of a class of stochastic models. (1992)

• Record Type: Journal Article
• Authors: Abolnikov, Lev; Dshalalow, Jewgeni H.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 5:Number 1(1992)
• Page Start: 83
• Page End: 97
• Publication Date: 1992
• Subjects: first passage problem -- fluctuation theory -- delayed renewal process -- first excess level -- pre-first excess level -- shortage before the first excess -- index of the first excess -- bulk queues -- inventory control -- dam; 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/S1048953392000066
• Languages: English
• ISSNs: 1048-9533

Abstract

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.