Analysis of a population model with batch Markovian arrivals influenced by Markov arrival geometric catastrophes

We consider a population model in which individuals arrive as per the batch Markovian arrival process. The population is influenced by catastrophes which occur according to Markovian arrival process and it eliminates each individual of the population in a sequential order with probability p until th...

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Published inCommunications in statistics. Theory and methods Vol. 50; no. 13; pp. 3137 - 3158
Main Authors Kumar, Nitin, Gupta, U. C.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.07.2021
Taylor & Francis Ltd
Subjects
Batch Markovian arrival process
catastrophes
Eigenvalues
Eigenvectors
geometric
Population
Size distribution
State vectors
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Summary:We consider a population model in which individuals arrive as per the batch Markovian arrival process. The population is influenced by catastrophes which occur according to Markovian arrival process and it eliminates each individual of the population in a sequential order with probability p until the one individual survives or the entire population is annihilated. We first obtain the steady-state vector generating function of the population size distribution at arbitrary epoch and then the distribution is extracted in term of roots of the associated characteristic equation. Further, we obtain the population size distribution at post-catastrophe and pre-arrival epochs. Finally, a few numerical results are given.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2019.1682166