Stationary and transient analysis of M/M/1/N queue subject to disasters and subsequent repair

A single server Markovian queuing model with finite capacity subject to disaster is considered. When the system is met with disasters, all customers (including those waiting) are lost forever and the system transits to the repair state. However, the customers are allowed to join the queue even when the system is under repair, but at a slower arrival rate. Repair times are also assumed to follow exponential distribution. In this paper, we obtain the stationary and time dependent system size probabilities of such a model using Laplace transform and generating function techniques. Certain performance measures of interest are also obtained in closed form.