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Time dependent analysis of multivariate marked renewal processes

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Jewgeni H. Dshalalow
Jewgeni H. Dshalalow*
Affiliation:
Florida Institute of Technology
*
∗ Postal address: Applied Mathematics Program, Division of Mathematical Sciences, College of Science and Liberal Arts, Florida Institute of Technology, Melbourne, FL 32901, USA. Email address: eugene@fit.edu
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Abstract

The paper examines multivariate delayed marked renewal processes, of which one component is formed by a delayed compound Poisson process observed at epochs of some point process. In addition, the values of these observations (and other components) are watched when crossing their respective thresholds and the value of the original Poisson process at any moment of time, past the first passage time, is the objective of this investigation. The results (which are imperative for classes of semiregenerative processes) are given in closed analytical forms and illustrated on various stochastic models.

Keywords

Point processmarked renewal processPoisson compound processfluctuationsfirst excess level theoryfirst passage timesemiregenerative processqueueing processvacations

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.) 60K15: Markov renewal processes, semi-Markov processes 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 3 , September 2001 , pp. 707 - 721
Copyright
Copyright © by the Applied Probability Trust 2001 

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