# ANALYSIS OF PRIORITY QUEUES WITH PENTAGON FUZZY NUMBER

• W. Ritha Department of Mathematics, Holy Cross College (Autonomous), Tiruchirappalli -2, Tamil Nadu, India
• S. Josephine Vinnarasi Department of Mathematics, Holy Cross College (Autonomous), Tiruchirappalli -2, Tamil Nadu, India
Keywords: Fuzzy Sets, Membership Functions, Priority Queues, Mathematical Programming, Pentagon and Trapezoidal Fuzzy Numbers, Performance Measures

### Abstract

Fuzziness is a sort of recent incoherence. Fuzzy set theory is asserted to depict vagueness. This study explores the queuing model of priority classes adopting pentagon fuzzy number with the inclusions of fuzzy set operations. A mathematical programming method is designed to establish the membership function of the system performance, in which the arrival rate and service rate of the system performance of two priority classes are utilized as fuzzy numbers. Based on  -cut approach and Zadeh’s extension principle, the fuzzy queues are scaled down to a family of ordinary queues. The potency of the performance measures of the characteristics of the queuing model is ensured with an illustration and its graph.

### References

Kao, C., Li, C.C., and Chen, S.P., Parametric programming to the analysis of fuzzy queues, Fuzzy queuer Fuzzy sets and Systems, Vol.017, 1999, 93-100. DOI: https://doi.org/10.1016/S0165-0114(97)00295-9

Devaraj. J. and Jayalakshmi. D., A fuzzy approach to priority Queues, International Journal of Fuzzy Mathematics and Systems, Volume 2, 2012, 479-488.

Kaufmann, A., Introduction to the Theory of Fuzzy subsets, Vol. 1, Academic Press, New York, 1975.

Li, R. J., and Lee, E.S., Analysis of fuzzy queues, Computers and Mathematics with Applications, vol. 17, 1989, 1143-1147. DOI: https://doi.org/10.1016/0898-1221(89)90044-8

Negi, D.S., and Lee, E.S., Analysis and simulation of Fuzzy Queue, Fuzzy sets and systems, Vol. 46, 1992, 321-330. DOI: https://doi.org/10.1016/0165-0114(92)90370-J

Zimmermann, H.J., Fuzzy set Theory and Its Applications, Klower Academic, Boston, 2001. DOI: https://doi.org/10.1007/978-94-010-0646-0

Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, Vol. 1, 1978, 3-28. DOI: https://doi.org/10.1016/0165-0114(78)90029-5

Usha Madhuri K., and Chandan. K., Study on FM/FM/1 queuing system with pentagon Fuzzy number using  cuts, International innovations in technology, Vol.3, Issue 4, 2017, Impact factor 4.295.

S. Thamotharan, A study on Multiserver Fuzzy Queuing Model in Triangular and Trapezoidal Fuzzy Numbers using  cuts, Volume 5, Issue 1, 2016, 226-230. DOI: https://doi.org/10.21275/v5i1.NOV152615

Chen. S.P., Parametric Nonlinear Programming Approach to Fuzzy queues with bulk service”, European Journal of Operations Research, 163, 2005, 434-444. DOI: https://doi.org/10.1016/j.ejor.2003.10.041

Chen. S.P., A mathematics Programming Approach to the Machine Interference Problem with Fuzzy Parameters, Applied Mathematics and Computation 174, 2006, 374-387. DOI: https://doi.org/10.1016/j.amc.2005.05.012

Ashok Kumar. V., Analysis of FM/FM/1 queuing system with Pentagon Fuzzy numbers and using DSW algorithm, International Journal of Advance Research, ideas and innovations in technology, Vol. 3, Issue 5, 2017, Impact factor 4.295

Published
2018-04-30
How to Cite
Ritha, W., & Vinnarasi, S. J. (2018). ANALYSIS OF PRIORITY QUEUES WITH PENTAGON FUZZY NUMBER . International Journal of Engineering Technologies and Management Research, 5(4), 90-100. https://doi.org/10.29121/ijetmr.v5.i4.2018.213
Section
Articles