Second Optional Service Queuing Model with Fuzzy Parameters

The aim of this paper is to analyze Bi-level threshold policy of M/(G1, G2)/1 with single vacation (SV) queue in a fuzzy environment. A mathematical Non linear programming (NLP) method is used to construct the membership function of the system characteristic in which the batch arrival-rate, expected group size, setup time, vacation time, service time for first essential service(FES), service time for second optional service(SOS) and probability for opting second channel are all fuzzy numbers. The α-cut and zadeh’s extension principle are used to transform a fuzzy queue into a family of conventional crisp queue. By means of the membership functions of the system characteristic, a set of parametric NLP is developed to calculate the lower and upper bound of the system characteristics function at α. Moreover a numerical example is also illustrated to check the validity of the proposed approach.