Analysis of performance measures with single channel fuzzy queues under two class by using ranking method

Abstract

In this paper, we propose a procedure to find different performance measurements under crisp value terms for new single fuzzy queue FM/F(H1,H2)/1 with two classes, where arrival rate and service rates are all fuzzy numbers which are represented by triangular and trapezoidal fuzzy numbers. The basic idea is to obtain exact crisp values from the fuzzy value, which is more realistic in the practical queueing system. This is done by adopting left and right ranking method to remove the fuzziness before computing the performance measurements using conventional queueing theory. The main advantage of this approach is its simplicity in application, giving exact real data around fuzzy values. This approach can also be used in all types of queueing systems by taking two types of symmetrical linear membership functions. Numerical illustration is solved in this article to obtain two groups of crisp values in the queueing system under consideration.