Analysis of a renewal arrival process subject to geometric catastrophe with random batch killing

Abstract

This paper considers a population model (system) which is prone to catastrophe that kills individuals in batches. Individuals enter the system in accordance with the renewal process and catastrophe occurs as per the Poisson process. The catastrophe attacks the population in a successive order in batches of random size, each batch of individuals dies with probability ξ. This successive process ends when the whole population is wiped out or a batch of individuals survives with probability 1 − ξ. This type of killing pattern is known as geometric catastrophe. The supplementary variable technique is used to develop the steady-state governing equations. Further using the difference operator, the distributions of population size are evaluated at arbitrary, pre-arrival, and post-catastrophe epochs. In addition to that, a few different measurements of the system’s performance are derived. In order to demonstrate the applicability of the model, a number of numerical and graphical outcomes are presented in the form of tables and graphs.