Parametric Nonlinear Programming Approach with Fuzzy Queues Using Hexagonal Membership Functions

摘要

In this paper, a procedure is proposed for adopting parametric nonlinear programming approach through the derivation of new constraints with consideration of the hexagonal fuzzy number states of the arrival and service rates. In queueing systems, hexagonal fuzzy numbers obtain morerealistic crisp values as the membership functions of the fuzzy numbers covers a wider area than other linear membership functions with fewer points. The presence of more points in the hexagonal membership functions defines the system better because arrival of customers is multi-dimensional,although it involves more computations in the mathematical procedures, hence less used. The proposed method reduces the hexagonal fuzzy values into a family of conventional crisp values using the α-cut approach. To validate the method using hexagonal arrival- and service-rate fuzzy numbers,it was implemented on both single- and multiple-channel fuzzy queues. The results showed the suitability of the procedure for adequately estimating real-life scenarios, especially when the serving channels are improved. Furthermore, convergence was apparent between the proposed approach ofintroducing a new fuzzy number family and trapezoidal membership functions. Therefore, this procedure can be effectively applied to real-life scenarios that are modelled as queueing models.