Computational and Numerical Investigation of the Batch Markovian Arrival Process Subject to Renewal Generated Geometric Catastrophes

Abstract

In this paper, we consider a stochastic model in which the population grows according to the batch Markovian arrival process and is subjected to renewal generated geometric catastrophes. Our analytical work starts from the vector generating function (VGF) of the population size at post-catastrophe epoch. We develop a methodology for extracting the population size distribution at post-catastrophe epoch from the VGF, which is based on the inversion of VGF using the roots method. The method is analytically quite simple and easy to implement. Further, we obtain the population size distribution at arbitrary, pre-catastrophe and pre-arrival epochs along with their factorial moments. To show the applicability and correctness of the proposed methodology, we match our results with the available ones in special cases and present several numerical examples for different inter-catastrophe time distributions. Moreover, we investigate the effect of key parameters on the system performance and display the results in the form of graphs along with a detailed description.