On the level crossing of multi-dimensional delayed renewal processes. (1997)

• Record Type: Journal Article
• Authors: Dshalalow, Jewgeni H.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 10:Number 4(1997)
• Page Start: 355
• Page End: 361
• Publication Date: 1997
• Subjects: fluctuations -- first excess level -- first passage time -- termination index -- renewal process -- marked point process -- N-policy queues -- D-policy queues -- queues with vacations; 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/S1048953397000415
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : The paper studies the behavior of an ( l + 3 ) th-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.