Performance Measure of Fuzzy Simple Queue with Balking and Feedback Customers using Symmetric Heptagonal Fuzzy Numbers

Abstract

This paper investigates the simple queue with balking and feedback customers by using the fuzzy set theory. The main proposal is a mathematical programming approach to develop the membership function of the performance measures of the model, in which the arrival rate and service rate are defined as fuzzy numbers. The Zadeh's extension principle and cut approach are used to transform fuzzy queue into a family of crisps queue. To illustrate the approach, a numerical example is presented for heptagonal fuzzy numbers. Also, economic analysis of system is carried out by developing a cost model when some of parameters of the system are fuzzy numbers.