Time dependent probabilities of M/M/1 queue with working vacation subject to disasters and repair

Abstract

A single server Markovian queueing model with working vacation subject to disaster and repair is considered. Whenever the server finds nobody in the system, the server is allowed to take a working vacation where, the server provides service at a slower rate than usual. Also disaster can occur either during busy state or during working vacation state. Whenever the system met with disaster all customers are flushed out and the system transits to repair state. Customers are allowed to join the queue even during repair time. After repair, if the server finds customer then the server moves to busy state otherwise the server moves to working vacation state. Using generating function and Laplace transform techniques explicit time dependent probabilities for various states have been obtained.