Computing queue length distributions in MAP/G/1/N queue under single and multiple vacation

This paper studies a single server queue with finite waiting room in which the server takes vacation(s) whenever the system becomes empty and we consider both single and multiple vacation(s). Whereas the input process is a Markovian Arrival Process (MAP), the service and vacation times are arbitrarily distributed. The distributions of number of customers in the queue at service completion, vacation termination, departure, arbitrary and pre-arrival epochs have been obtained. Computational procedure has been given when the service- and vacation-time distributions are of phase type (PH-distribution).