This paper studied and investigated about the N-policy queueing system with server timeout, using Triangular Trapezoidal and Pentagon Fuzzy numbers with the application of fuzzy set. We consider single server vacation queueing system that operates in the following manner; when the system is empty, the server waits for fixed time c. At this time if n-customers are waiting in the queue then server return to the system and do the service. At the expiration of the time, if no customer arrives server goes on vacation. Similarly in vacation also if n-customers are waiting in queue serve return to the system and commence service exhaustively. By the approach of DSW algorithm, we develop the membership function of the system performance are of fuzzy nature. Based on the α-cut approach the fuzzy queues are reduced to a family of a crisp set. The numerical examples are also studied in this model.