Abstract: Here arrivals of the customer follow poisson distribution and there is single server who is providing service to the customer. Also server serve the customer on first come first serve basis. The vacation queues have been extended to computer networks, communications systems, as well as production management, inventory management and other fields (Doshi B.T., 1990). For the classical single-server vacation model, a server stops working completely during the vacation periods. However, the server can be generalized to work at a different rate during the vacation periods. This type of queueing models are useful to analyze a variety of multi-queue systems that frequently arise in computer and communication networks. Different parameter is used for finding expected busy period and queueing length.