Analysis of the Performance Measures of a Non-Markovian Fuzzy Queue via Fuzzy Laplace Transforms Method

Journal of computing research and innovation

article

Baudouin Adia Leti Mawa¹  Rostin Mabela Makengo Matendo²  Jean Pierre Mukeba Kanyinda³  Bopatriciat Boluma Mangata⁴ 

[1] Institut Supérieur Pédagogique et Technique de Kinshasa;Faculty of Science and Technology, University of Kinshasa;Departement de Mathématique et Informatique, Institut Supérieur Pédagogique de Mbujimayi;Faculty of Science, Department of Mathematics, Statistics and Computer Science, University of Kinshasa

关键词: Fuzzy Laplace Transforms;    Fuzzy Arithmetic;    Defuzzification;   

DOI  :  10.24191/jcrinn.v7i2.323

学科分类：社会科学、人文和艺术（综合）

来源: Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Perlis

【 摘 要 】

Laplace transforms play an essential role in the analysis of classical non-Markovian queueing systems. The problem addressed here is whether the Laplace transform approach is still valid for determining the characteristics of such a system in a fuzzy environment. In this paper, fuzzy Laplace transforms are applied to analyze the performance measures of a non-Markovian fuzzy queueing system FM/ FG/1. Starting from the fuzzy Laplace transform of the service time distribution, we define the fuzzy Laplace transform of the distribution of the dwell time of a customer in the system. By applying the properties of the moments of this distribution, the derivative of this fuzzy transform makes it possible to obtain a fuzzy expression of the average duration of stay of a customer in the system. This expression is the fuzzy formula of the same performance measure that can be obtained from its classical formula by the Zadeh extension principle. The fuzzy queue FM/ FE_k /1 is particularly treated in this text as a concrete case through its service time distribution. In addition to the fuzzy arithmetic of L-R type fuzzy numbers, based on the secant approximation, the properties of the moments of a random variable and Little's formula are used to compute the different performance measures of the system. A numerical example was successfully processed to validate this approach. The results obtained show that the modal values of the performance measures of a non-Markovian fuzzy queueing system are equal to the performance measures of the corresponding classical model computable by the Pollaczeck-Khintchine method. The fuzzy Laplace transforms approach is therefore applicable in the analysis of a fuzzy FM/FG/1 queueing system in the same way as the classical M/G/1 model.

【 授权许可】

CC BY-SA