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The batch Markovian arrival process subject to renewal generated geometric catastrophes

Economou, A. and Gómez Corral, Antonio (2007) The batch Markovian arrival process subject to renewal generated geometric catastrophes. Stochastic Models, 23 (2). pp. 211-233. ISSN 1532-6349

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Abstract

We deal with a population of individuals that grows stochastically according to a batch Markovian arrival process and is subject to renewal generated geometric catastrophes. Our interest is in the semi-regenerative process that describes the population size at arbitrary times. The main feature of the underlying Markov renewal process is the block structure of its embedded Markov chain. Specifically, the embedded Markov chain at post-catastrophe epochs may be thought of as a Markov chain of GI/G1-type, which is indeed amenable to be studied through its R- and G-measures, and a suitably defined Markov chain of M/G/1-type. We present tractable formulae for a variety of probabilistic descriptors of the population, including the equilibrium distribution of the population size and the distribution of the time to extinction for present units at post-catastrophe epochs.


Item Type:Article
Uncontrolled Keywords:Batch Markovian arrival process; Extinction time; Geometric catastrophes; Markov chain of GI /G/1-type; Markov chain of M/G/1-type; Population processes; RG-factorization; Stationary distribution
Subjects:Sciences > Mathematics > Stochastic processes
ID Code:15599
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