On the level crossing of multi-dimensional delayed renewal processes
type: Item
instance of: scholarly article
title: On the level crossing of multi-dimensional delayed renewal processes
zbMATH Open document ID: 0896.60056
DOI: 10.1155/S1048953397000415
author: Jewgeni H. Dshalalow
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1998-03-05T00:00:00Z
full work available at URL: https://eudml.org/doc/47976
review text: Summary: The paper studies the behavior of an \((l+3)\)-dimensional, delayed renewal process with dependent components, the first three (called active) of which are to cross one of their respective thresholds. More specifically, the crossing takes place when at least one of the active components reaches or exceeds its assigned level. The values of the other two active components, as well as the rest of the components (passive), are to be registered. The analysis yields the joint functional of the ``crossing level'' and other characteristics (some of which can be interpreted as the first passage time) in a closed form, refining earlier results of the author. A brief, informal discussion of various applications to stochastic models is presented.
Mathematics Subject Classification ID: 60K10
Mathematics Subject Classification ID: 60K05
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 60G25
Mathematics Subject Classification ID: 68M20
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 1124518
zbMATH Keywords: fluctuations
zbMATH Keywords: first excess level
zbMATH Keywords: first passage time
zbMATH Keywords: termination index
zbMATH Keywords: renewal process
zbMATH Keywords: marked point process
zbMATH Keywords: \(N\)-policy queues
zbMATH Keywords: \(D\)-policy queues
zbMATH Keywords: queues with vacations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1124518