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

Abstract

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.

Keywords:

• Batch Markovian arrival process
• catastrophes
• geometric
• population

Acknowledgments

The authors would like to thank the editor and two anonymous referees for their valuable remarks and suggestions which led to the paper in current form.