A Nonlinear Programming Approach for a Fuzzy Queue with an Unreliable Server

Kumar, V. Ashok

doi:10.18052/www.scipress.com/BSMaSS.2.44

BSMaSS > BSMaSS Volume 2 > A Nonlinear Programming Approach for a Fuzzy Queue...

< Back to Volume

A Nonlinear Programming Approach for a Fuzzy Queue with an Unreliable Server

Full Text PDF

Abstract:

The aim of this paper is to develop the membership functions of the system characteristic of a queuing g model with an unreliable server, in which the arrival rate, service rate, breakdown rate and repair rate are all fuzzy numbers. The α-cut approach is used to transform a fuzzy queue with an unreliable server into a family of conventional crisp queues with an unreliable server. By using membership functions, a set of parametric nonlinear programmes are developed to describe the family of crisp queues with an unreliable server. An efficient algorithm is developed to find the optimal solutions at or different possibility level α. Numerical examples are solved successfully. Since the system characteristics being expressed and governed by membership functions, more information is provided for the management.

Info:

Periodical:

The Bulletin of Society for Mathematical Services and Standards (Volume 2)

Pages:

44-56

DOI:

https://doi.org/10.18052/www.scipress.com/BSMaSS.2.44

Citation:

V. A. Kumar, "A Nonlinear Programming Approach for a Fuzzy Queue with an Unreliable Server", The Bulletin of Society for Mathematical Services and Standards, Vol. 2, pp. 44-56, 2012

Online since:

June 2012

Authors:

V. Ashok Kumar

Keywords:

Fuzzy Sets, Nonlinear Programming, Queue, Solution Algorithm, Unreliable Server

Export:

RIS, BibTeX, Text

Distribution:

Open Access

This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

J. Bozacatt, J. Shanthikumar, Stochostic models of manufacturing systems, Prentice-Hall, Englewood cliffs, NJ, (1993).

J. Gal, Postoplimal Analysis, Parametric Programming and Related Topics, McGraw-Hill, New York, (1979).

D.P. Gaver, A waiting time with interrupted service, including priorities, Royal statistical society series B 24 (1962) 73-96.

D. Gross, C.M. Harris, Fundamentals of Queuing theory, third ed., John Wiley, New York, (1998).

A. Kaufmann, Introduction to the Theory of Fuzzy subsets, Vol. 1, Academic Press, New York, 1075.

W. Li, D. Shi, X. Chao, Reliability analysis of M/G/I queuing systems with server breakdowns and vacations, Journal of Applied probability 34 (1997) 546-555.

H.M. Prade, An outline of fuzzy or possibilistic models for queuing systems, in P.P. wong, S.K. Chang (Eds. ), Fuzzy Sets, Plenum Press, New York (1980).

B. Sengupta, A queue with service interruptions in an alternating random environment, operations Research 38 (1990) 308-318.

K.S. Trivedi, probability and Statistics with Reliability, Queuing and Computer Science Applications, John Wiley & Sons Inc., New York (2002).

K.H. Wang, H.J. Kao, G. Chen, Optimal management of a remarkable and non-reliable server in an infinite and a finite M/Hk/I queuing systems Quality Technology and quantitative Management 1(2) (2004) 325-339.

L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, fuzzy sets and systems 1 (1978) 328.

H.J. Zimmermann, Fuzzy set Theory and its Applications, 4th ed., Kluor Academic, Bostan, (2001).

Show More Hide

Cited By:

This article has no citations.