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...

Full description

Saved in:
Bibliographic Details
Published in:Communications in statistics. Theory and methods 2021-07, Vol.50 (13), p.3137-3158
Main Authors: Kumar, Nitin, Gupta, U. C.
Format: Article
Language:English
Subjects:
Batch Markovian arrival process
catastrophes
Eigenvalues
Eigenvectors
geometric
Population
Size distribution
State vectors
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
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.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2019.1682166