Markovian queueing model with single working vacation and catastrophic

Abstract

A markovian queueing system with a single working vacation and different service rates have been considered. Service times during the vacation period, service times during the service period as well as vacation times are all exponentially distributed. If the queue length is increasing, the server converts the service parameter from µv to µb, and a normal working time begins. According to the Poisson process, a catastrophe event with parameter α occurs only if there is a customer in the system. This type of queue model has been analysed using Matrix Geometric Method (MGM) to find steady state probability vectors. Using it some performance measure is also determined.