Mathematics and System Engineering Faculty Publications

Document Type

Article

Publication Title

Symmetry

Abstract

This article is a study of vector-valued renewal-reward processes on Rd . The jumps of the process are assumed to be independent and identically distributed nonnegative random vectors with mutually dependent components, each of which may be either discrete or continuous (or a mixture of discrete and continuous components). Each component of the process has a fixed threshold. Operational calculus techniques and symmetries with respect to permutations are used to find a general result for the probability of an arbitrary weak ordering of threshold crossings. The analytic and numerical tractability of the result are demonstrated by an application to the reliability of stochastic networks and some other special cases. Results are shown to agree with empirical probabilities generated through simulation of the process. © 2022 by the author. Licensee MDPI, Basel, Switzerland.

DOI

10.3390/sym14061167

Publication Date

2022

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