Analysis of MAP/G/1/N queue with two phases of service under single (multiple) vacation(s)

This paper deals with a finite buffer MAP/G/1 queue with an additional second phase of optional service with single and multiple vacation policies. Arrival of customers follows a Markovian arrival process (MAP). After completion of the first phase of essential service, the customer may or may not opt for second phase of service. If the server finds an empty system at a service completion epoch, he goes for single or multiple vacations. The queue length distributions at various epochs, such as pre‐arrival, arbitrary and departure have been obtained using embedded Markov chain technique and supplementary variable technique. Waiting time of a customer in the queue is also obtained. Numerical illustrations are presented.