Computing The Performance Parameters of A Fuzzy Markovian Queueing System Fm/Fm/1 In Transient Regime By The Flexible Alpha-Cuts Method

Jean Alonge w'Omatete; Rostin Mabela Makengo Matendo; Daniel Lama Okenge; Claude Mfumu Mbikudi; Bopatriciat Boluma Mangata

doi:10.24191/jcrinn.v8i1.347

Computing The Performance Parameters of A Fuzzy Markovian Queueing System Fm/Fm/1 In Transient Regime By The Flexible Alpha-Cuts Method

Authors

Jean Alonge w'Omatete Department of Mathematics and Physics, Higher Pedagogical Institute of Wembo Nyama , D.R.Congo
Rostin Mabela Makengo Matendo Faculty of Science and Technology, University of Kinshasa, Kinshasa, D.R.Congo
Daniel Lama Okenge Department of Mathematics and Physics Pedagogical Institute of Kindu, D.R.Congo
Claude Mfumu Mbikudi Kimwenza High School in Kinshasa, D.R.Congo
Bopatriciat Boluma Mangata University of Kinshasa

DOI:

https://doi.org/10.24191/jcrinn.v8i1.347

Keywords:

Performance parameters, fuzzy markovian queuing system, flexible α-cuts method, Zadeh's extension principle, α-cuts intervals arithmetic

Abstract

This scientific article sets out to solve the following fundamental problem to calculate the performance parameters of the FM/FM/1 queuing system in transient state. To resolve this problem the fuzzy arithmetic of cuts and intervals was used in transient state (TS). To achieve the expected results of our work, we used the analytical method with its different stages which are : selecting textual or visual documents ( books, articles, conferences, seminars,... with or without internet); read and analyze the content of these documents; record selected documents related to our research topic; interpret during the reading and the classification, the data obtained. This method helped us to identify the appropriate mathematical approach to evolve the performance of the queuing system under study. This is precisely the relaxed a-cuts and intervals. To illustrate this approach, a numerical example is given in the sixth section. The membership function enabled us to represent the graphs of the performance parameters of the FM/FM/1 queuing system in the three-dimensional space in the transient regime in a fuzzy environment.

Downloads

Download data is not yet available.

References

Allahviranlov T., Gouyandechz Z., Armand A. and Haranoglie A. (2015). On Fuzzy Solution For Heat Equation Based On Generalized Hukuhara Differentiability, Fuzzy Sets and systems, 265, 1-23.

Alonge W’Omatete J. (2019). Analysis of the Performance Parameters of Markovian queuing systems in Transient Regime, Master dissertation in mathematical sciences, unpublished, UPN/ Kinshasa, DRC.

Barak S. and Fallahnezhad MS. (2017). Cost analysis of fuzzy Queuing Systems. International journal of Applied Operation Research, 12.

Bede B. (2015.). Mathematics of Fuzzy Sets and Fuzzy Logic Springer-Verlag, Berlin.

Buckley J.J and Eslami E. (2015). An introduction to Fuzzy logic and fuzzy Sets. Springer-Verlag, Berlin Heidelberg.

Buckley J.J, Eslami E. and Feuring T. (2016). Fuzzy Mathematics in Economics and Engineering. Physica-Verlag, Heidelberg.

Dervaraj J. and Jayalakshmi D. (2015). A fuzzy Approach to Non-Preempted priority Queues. International Journal of mathematical archive, 3(7) : 2704-2712.

Gani A. N. and Kumar V.A. (2017). A Bulk Arrival Queueing Model with Fuzzy parameters and Fuzzy varying Batch sizes. International Journal of Algorithms, Computing and Mathematical, 2 (3) : 1-8.

Gani A. N and Manikandan A.R. (2016). On fuzzy det-norm matrix. J. Math. Comput. Sci. , 3 :233-241.

Jeeva M. and Rathnakumari E. (2015). Fuzzy Cost computations of M/M1 and M/G/1 queuing Models. British Journal of Mathematics and computer Science, 4(1) :120-132.

Kalayanaraman R., Thillaigovindan N. and Kannadasa, G. (2015). A Single Server fuzzy Queue with Unreliable Server. International Journal of computational Cognition, 8 (1) : 1-4.

Mary K.J.R., Monica P. and Mythili S. (2018). Performance Measures of FM/FM/1 Queuing System with N-Policy. Internal journal of Physics and Mathematical Sciences, 4 (3).

Mukeba J.P. (2016). Analysis of fuzzy Queue characteristics by Flexible Alpha-Cuts Method. Journal of Fuzzy Sets Valued Nalaysuis, pages 1-12.

Mukeba J.P., Mabela, R. and Ulungu B. (2015). Performance Measures of a Product from Queueing network with fuzzy Parameters. Journal of Fuzzy Sets valued Analysis, 2015 (1) : 68-77. http://dx.doi.org/10.5899/2015/jfsva-00228

Noora A.A., Jahanshahloo G.R., Rashidi S.F and Godari M.M. (2017). A study of Discrete-Time Multi Server Retrial Queue with Finite Population And Fuzzy Parameters. African Journal of Business management, 5(6) : 2426-2431.

Palpandi B. and Gectharamani G. (2016). Computing Performance Measures of Fuzzy Non-preemptive Priority Queues Using Robust Ranking Technique. Applied mathematical sciences, 7 (102) : 5095-5102.

Vincent G.S. ans Bhuvaneswari S. (2017). On Fuzzy Retrial Queue with priority Subscribers. International Journal of Algorithms, Computing and mathematics, 4(1) : 9-20.

Wang T.Y., Yang D.Y and Li M.J. (2016). Fuzzy Analysis for the N-Policy Queues with Infinite Capacity. International Journal of Information and Management Sciences, 21 : 41-45.

Zadeh L.A. (2015). Outline of a new Approach to the Analysis of complex Systems. Man and Cybernetics, 3 :28-44.