Calculation of the Mean and Variance in the Birth-Death Immigration process with Catastrophe for M\M\1 Queueing Mode

Abstract

This paper, delineates how catastrophe affect the Birth-Death and Immigration Process (BDI). To find the general solution for the population size distribution, the Probability Generating Function (PGF) is used. When the rates of birth, death, immigration, and catastrophe are remain's constant, the accurate solution of mean and variance is also obtained. In addition, the mean and variance are time dependent. The system's behavior, a numerical example is presented for investigated.