Time dependent analysis of an M/M/1/N queue with catastrophes and a repairable server

Abstract

In this paper, we consider a single server Markovian queueing system with a finite buffer. In addition to a Poisson stream of positive arrivals we assume that there is a also a Poisson stream of negative arrivals into the system. These negative arrivals which may be called as catastrophes may occur at any instant of time, whether the server is idle or busy. The time dependent performance measures and the busy period of the system are discussed. The corresponding steady state results are derived. We present a few numerical examples to illustrate the behavior of the time dependent probabilities, the time dependent expected system size and the time dependent variance of the system size distribution.