398 233
Full Length Article
Volume 6 , Issue 1, PP: 48-55 , 2020

Title

Neutrosophic Event-Based Queueing Model

Authors Names :   Mohamed Bisher Zeina   1 *  

1  Affiliation :  Dept. of Mathematical Statistics, Faculty of Sciences, University of Aleppo, Aleppo, Syria

    Email :  bisherzeina@alepuniv.edu.sy



Doi   :  10.5281/zenodo.3840771


Abstract :

In this paper we have defined the concept of neutrosophic queueing systems and defined its neutrosophic performance measures. An important application of neutrosophic logic in queueing systems we face in real life were discussed, that is the neutrosophic events accuring times, because of its wide applications in networking and simulating communication systems specialy when probability distribution is not known, and because it’s more realistic to consider and to not ignore the imprecise events times. Event-based table of a neutrosophic queueing system was presented and its neutrosophic performance measures were derived, i.e. neutrosophic mean waiting time in queue, neutrosophic mean waiting time in system, neutrosophic expected number of customers in queue and neutrosophic expected number of customers in system. Neutrosophic Little’s Formulas (NLF) were also defined which is a main tool in queueing systems problems to make it easier finding performance measures from each other.

Keywords :

Neutrosophic Logic; Queueing Theory; Performance Measures; Little’s Formula

References :

[1]    Smarandache.F., “Introduction to Neutrosophic Measure, Neutrosophic Integral, and Neutrosophic Probability”, Sitech-Education Publisher, Craiova – Columbus, 2013

[2]    Atanassov .k, “Intuitionistic fuzzy sets,” In V. Sgurev, ed., ITKRS Session, Sofia, June 1983, Central Sci. and Techn. Library, Bulg. Academy of Sciences, 1984.

[3]    Salama, A. A. and Smarandache, F. "Neutrosophic crisp probability theory & decision making process." Critical Review: A Publication of Society for Mathematics of Uncertainty, vol. 12, p. 34-48, 2016.

[4]    Alhabib, R., A. A. Salama, “Using Moving Averages To Pave The Neutrosophic Time Series”, International Journal of Neutrosophic Science, Vol. 3, 2020

[5]    Alhabib, R., Ranna, M., Farah, H. and Salama, A. “ Some neutrosophic probability distributions,” Neutrosophic Sets and Systems, 22, pp.30-38, 2018.

[6]    Sapan Kumar Das; S.A. Edalatpanah, “A new ranking function of triangular neutrosophic number and its application in integer programming”, International Journal of Neutrosophic Science, Vol. 4, No. 2, 02020

[7]    Christianto.V. ,Boyd. R.N. , Smarandach.F. , “Three possible applications of Neutrosophic Logic in Fundamental and Applied Sciences,” International Journal of Neutrosophic Science, Volume 1 , Issue 2, PP: 90-95 , 2020.

[8]    Smarandache. F, “Neutrosophic set a generalization of the intuitionistic fuzzy sets”, Inter. J. Pure Appl. Math., 24, 287 – 297, 2005

[9]    Smarandache, F.,  “A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability”, American Research Press, Rehoboth, NM, 1999

[10] Smarandache, F.” Introduction to Neutrosophic statistics,” Sitech & Education Publishing, 2014

[11] Hatip.A., “The Special Neutrosophic Functions” , International Journal of Neutrosophic Science,Vol. 4, 2020

[12] A. Chakraborty, A “New Score Function of Pentagonal Neutrosophic Number and its Application in Networking Problem”, International Journal of Neutrosophic Science, Volume 1 , Issue 1, pp. 40-51 , 2020

[13] Erlang, Agner Krarup, "The theory of probabilities and telephone conversations" . NYT Tidsskrift for Matematik B. 20: 33–39, 1909. 

[14] F Shortle J.; M Thompson J.; Gross D.; M Harris C., “Fundamentals of Queueing Theory”, 5th ed.; Wiley: United States of America, 2018

[15] Nick T. Thomopoulos; “Fundamentals of Queuing Systems”, 1st ed.; Springer: United States of America, 2012

[16] Balter. M.H., “Performance Modeling and Design of Computer Systems: Queueing Theory in Action”, Cambridge, 2013

[17] Robertazzi T.G., “Computer Networks and Systems: Queueing Theory and Performance Evaluation”, 2nd Edition, Springer, 1994

[18] Salama.A.A, Smarandache. F, Neutrosophic Crisp Set Theory. Education Publishing, Columbus, 2015.

[19] Patro.S.K, Smarandache. F., “The Neutrosophic Statistical Distribution, More Problems, More Solutions”,  Neutrosophic Sets and Systems, Vol. 12, 2016

[20] Kawther Fawzi Hamza Alhasan, F. Smarandache, “Neutrosophic Weibull distribution and Neutrosophic Family Weibull Distribution”, Neutrosophic Sets and Systems, vol. 28, pp. 191-199, 2019