The Queue Model with Policy Set-Up Time, Multiple Vacation and Disasters

This paper studies the queue model with policy set-up time, multiple vacation and disasters. The server will start up the random set-up period with the probability if the customer number is at least at the end of a random length of the holiday. Otherwise, the server takes vacation repeatedly with the probability. Using embedded Markov chain and supplemental variable method, we derive the probability generating function (PGF) of the number of customers waiting in the system. From the process of the proof and the results, we also obtain the probabilities that the server is in vacations, set-up time, and busy period, respectively.