Approximation on MAP/G/1 queue with N-policy working vacation

MAP/G/1 Queue with N-Policy Working Vacation (N-PWV) is investigated. The input process of the queue model is markovian arrival process (MAP), and server has working vacation with N-Policy. The server starts a vacation only when the system is empty, and the busy period stars on the point just when there are N customers in the queuing system, furthermore the service rate in the vacation is not zero. Using the good character of PH distribution, which is dense in the set of all probability distribution on(0,+∞), which can be used to approximate any probability distribution, we simplify the MAP/G/1 Queue with N-PWV into a quasi-birth-death process (QBD). By matrix-geometric theory of Neuts, the stationary performance measures are got. Finally, we give a table with the change of system parameters by numerical example.