Fuzzy Cost Computations of M/M/1 and M/G/1 Queueing Models

Abstract

In this paper two models of planning queuing system and its effect on the cost of the each system by using two fuzzy queuing models of M/M/1 and M/G/1 are studied. These two fuzzy queuing models based on the cost of each model are compared and fuzzy ranking methods are used to select the optimal model due to the resulted complexity. Fuzzy queuing is more practical and realistic than deterministic queuing models. The basic idea is to transform a fuzzy queuing cost problem to a family of conventional crisp queue cost problem by applying the α-cut approach and Zadeh’s extension principle. A set of parametric nonlinear programs are developed to calculate the lower and upper bound of the minimal expected total cost per unit time at α, through which the membership function of the total cost is constructed. Numerical example is illustrated to check the validity of the proposed method.