Abstract
A single server fuzzy queue with modified Bernoulli vacation is analyzed using a technique which is a fusion of Zadeh's extension principle (L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1 (1978), 3–28), α-cut approach and parametric non-linear programming. Batches of customers arrive at the system according to a compound Poisson process. But all arriving batches are not allowed to enter into the system. The restriction policy depends on availability or otherwise of the server. The system is analyzed in Fuzzy environment. Some special cases are discussed. A numerical study is also carried out.