Transient Markov arrival processes

Guy Latouche · Marie-Ange Remiche · Peter G. Taylor

27 citations0/0 files storedThe Annals of Applied Probability

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Advanced Queuing Theory Analysis Probability and Statistical Research Point processes and geometric inequalities

Abstract

We define the family of transient Markov arrival processes (transient MAPs) which combine features of transient (or terminating) renewal processes and of the well-known MAPs: transient MAPs are point processes on the line, controlled by a finite Markov chain, which almost surely comprise a finite number of points. We analyze their basic properties.

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1999Introduction to Matrix Analytic Methods in Stochastic Modeling 1984Matrix-Geometric Solutions to Stochastic Models 1991Structured Stochastic Matrices of M/G/1 Type and Their Applications.1990A single-server queue with server vacations and a class of non-renewal arrival processes 1992The first two moment matrices of the counts for the markovian arrival process 1990Proc symp on congestion theory 2023Markov-additive processes of arrivals

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