A population model with Markovian arrival process and binomial correlated catastrophes

Abstract

Stochastic population models with mild catastrophes have gained much attention in recent years due to their wide application in a variety of areas including computer-communications systems. This article considers a population model in which both the arrival process of individuals and catastrophes occur as per the Markovian arrival process (MAP) and are independent of each other. The killing mechanism takes place according to the binomial distribution. The steady-state analysis of the model is carried out using the vector generating function approach and the population size distributions at an arbitrary, post-catastrophe, and pre-arrival epochs are presented in terms of the roots of the characteristic equation. Several performance measures of the system are studied in detail, and the impact of critical parameters is duly investigated.