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

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

Authors

  • Baudouin Adia Leti Mawa Institut Supérieur Pédagogique et Technique de Kinshasa, Kinshasa, D.R.Congo
  • Rostin Mabela Makengo Matendo Faculty of Science and Technology, University of Kinshasa, Kinshasa, D.R.Congo
  • Jean Pierre Mukeba Kanyinda Département de Mathématique et Informatique, Institut Supérieur Pédagogique de Mbujimayi, Mbuji-Mayi, D.R.Congo
  • Bopatriciat Boluma Mangata Faculty of Science, Department of Mathematics, Statistics and Computer Science, University of Kinshasa, Kinshasa, D.R.Congo

DOI:

https://doi.org/10.24191/jcrinn.v7i2.323

Keywords:

Fuzzy Laplace Transforms, Fuzzy Arithmetic, Defuzzification

Abstract

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.

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References

Babu, P. S., Kumar, K. S., & Chandan, K. (2022). A Study on Optimal Strategy N-Policy Fuzzy Vacation Queueing System with Server Start Up And Time Out Using Lr Method. International Journal of Advanced Research in Computer Science, 13(2).

Fatoumata, Y., Adnane, A., & Ataoua, Z. (2021). Machine Learning Pour La Maintenance Prédictive.

Al-Kridi, K., Anan, M. T., & Zeina, M. B. (2018). New Approach to FM/FM/1 Queue and its Performance Measures. Journal of King Abdulaziz University: Science, 30(1).

Patel, K. R., & Desai, N. B. (2017). Solution of fuzzy initial value problems by fuzzy Laplace transform. Kalpa Publications in Computing, 2, 25-37.

Çitil, H. G. (2019). Investigation of a fuzzy problem by the fuzzy Laplace transform. Applied Mathematics and Nonlinear Sciences, 4(2), 407-416.

Gong, Z., & Hao, Y. (2019). Fuzzy Laplace transform based on the Henstock integral and its applications in discontinuous fuzzy systems. Fuzzy Sets and Systems, 358, 1-28.

Chen, G., Liu, Z., & Zhang, J. (2020). Analysis of strategic customer behavior in fuzzy queueing systems. Journal of Industrial & Management Optimization, 16(1), 371.

Fazlollahtabar, H., & Gholizadeh, H. (2019). Economic analysis of the M/M/1/N queuing system cost model in a vague environment. International Journal of Fuzzy Logic and Intelligent Systems, 19(3), 192-203.

Ritha, W., & Rajeswari, N. (2021). An Analytical Study Of The M/M/1/N Imprecise Queuing System With Encouraged Arrivals. Int. J. of Aquatic Science, 12(2), 1349-1359.

Panta, A. P., Ghimire, R. P., Panthi, D., & Pant, S. R. (2021). Optimization of M/M/s/N Queueing Model with Reneging in a Fuzzy Environment. American Journal of Operations Research, 11(03), 121.

Wang, F. F. (2022). Joint replacement and production control for a queueing system with different failures. Journal of Industrial and Production Engineering, 39(3), 196-209.

Zhang, Q., Sun, H., Gao, X., Wang, X., & Feng, Z. (2022). Time-division ISAC enabled connected automated vehicles cooperation algorithm design and performance evaluation. IEEE Journal on Selected Areas in Communications.

Kannadasan, G., & Sathiyamoorthi, N. (2018). The FM/FM/1 queue with single working vacation and set-up times. International Journal of Pure and Applied Mathematics, 118(6), 115-126.

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Published

2022-09-01

How to Cite

Adia Leti Mawa, B., Mabela Makengo Matendo, R., Mukeba Kanyinda, J. P., & Boluma Mangata, B. (2022). Analysis of the Performance Measures of a Non-Markovian Fuzzy Queue via Fuzzy Laplace Transforms Method. Journal of Computing Research and Innovation, 7(2), 304–315. https://doi.org/10.24191/jcrinn.v7i2.323

Issue

Section

General Computing

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