Performance Analysis of a Fuzzy Markovian Queueing System with a Posteriori Impatience Using the L–R Method

The objective of this paper is to analyze the performance of a fuzzy Markovian queueing system FM / FM / C + FM with a posteriori impatience by the method L – R . We start by solving a system of fuzzy Kolmogorov differential equations, otherwise called equilibrium equations, allowing us to obtain the fuzzy state probabilities of the system in steady state by the recursive method. These probabilities are considered as probabilistic indicators of the system's performance. In addition, these fuzzy state probabilities will allow us to determine the system's performance indicators. In particular, the numerical results obtained show that the L – R method allows us to obtain more realistic performance indicators than those of the classical model, while maintaining high computational efficiency. The originality of this article lies in the analysis of the performance of the fuzzy Markovian queueing system FM / FM / C + FM with a posteriori impatience by the method L – R . This is a method based essentially on the arithmetic of fuzzy numbers of type L – R . Since the calculation of the product and the quotient is made possible by the use of two approximations called tangent approximation and secant approximation, only the secant approximation will be used in this article, because it provides the same results as the other methods concerning supports and modes. It is a method that seems short and efficient when the fuzzy variables that define the system are fuzzy numbers of the same type L – R and that provides exact values of the supports and modes of the performance indicators. A numerical application is proposed to illustrate the validity and feasibility of this method.