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Level Crossing Ordering of Skip-Free-to-the-Right Continuous-Time Markov Chains

Part of: Distribution theory - Probability Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Fátima Ferreira  and
António Pacheco
Fátima Ferreira*
Affiliation:
CEMAT and Universidade de Trás os Montes e Alto Douro
António Pacheco*
Affiliation:
CEMAT and Instituto Superior Técnico, Universidade Técnica de Lisboa
*
∗Postal address: Departamento de Matemática, Universidade de Trás os Montes e Alto Douro, Quinta dos Prados, Apartado 1013, 5001-911 Vila Real, Portugal. Email address: mmferrei@utad.pt
∗∗Postal address: Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa, Portugal. Email address: apacheco@math.ist.utl.pt
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Abstract

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As proposed by Irle and Gani in 2001, a process X is said to be slower in level crossing than a process Y if it takes X stochastically longer to exceed any given level than it does Y. In this paper, we extend a result of Irle (2003), relative to the level crossing ordering of uniformizable skip-free-to-the-right continuous-time Markov chains, to derive a new set of sufficient conditions for the level crossing ordering of these processes. We apply our findings to birth-death processes with and without catastrophes, and M/M/s/c systems.

Keywords

Birth-death process with catastrophecontinuous-time Markov chainlevel crossing orderingM/M/s/c systemstochastic ordering

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 60J27: Continuous-time Markov processes on discrete state spaces 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 42 , Issue 1 , March 2005 , pp. 52 - 60
Copyright
© Applied Probability Trust 2005 

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