ANALYSIS OF PERFORMANCE MEASURES OF FUZZY QUEUING MODEL WITH AN UNRELIABLE SERVER USING RANKING FUNCTION METHOD

In this paper we propose a procedure to find the various performance measures in terms of crisp values for fuzzy queuing model with an unreliable server where the arrival rate, service rate, breakdown rate and repair rate are all fuzzy numbers. Here the inter arrival time, service time, breakdown and repair rates are Triangular and also Trapezoidal fuzzy numbers. Our idea is to convert the fuzzy inter arrival rate, service rate breakdown rate and repair rate into crisp values by applying ranking function method. Then apply the crisp values in the classical queuing performance measure formulas. Ranking fuzzy numbers plays a huge role in decision making under fuzzy environment. This ranking method is most reliable method, simple to apply and can be used for all types of queuing problems. A numerical example is solved successfully for both triangular and trapezoidal fuzzy numbers.

[1]  Soheil Sadi-Nezhad,et al.  Ranking fuzzy numbers by preference ratio , 2001, Fuzzy Sets Syst..

[2]  Bala Srinivasan,et al.  A complex two-unit system with random breakdown of repair facility , 1995 .

[3]  Qi Liu,et al.  A TOPSIS-BASED CENTROID–INDEX RANKING METHOD OF FUZZY NUMBERS AND ITS APPLICATION IN DECISION-MAKING , 2005, Cybern. Syst..

[4]  Ching-Hsue Cheng,et al.  A new approach for ranking fuzzy numbers by distance method , 1998, Fuzzy Sets Syst..

[5]  Hsuan-Shih Lee,et al.  The revised method of ranking fuzzy numbers with an area between the centroid and original points , 2008, Comput. Math. Appl..

[6]  Changyong Liang,et al.  Ranking Indices and Rules for Fuzzy Numbers based on Gravity Center Point , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[7]  Madan M. Gupta,et al.  Fuzzy mathematical models in engineering and management science , 1988 .

[8]  F. Choobineh,et al.  An index for ordering fuzzy numbers , 1993 .

[9]  Mao-Jiun J. Wang,et al.  Ranking fuzzy numbers with integral value , 1992 .

[10]  T. Chu,et al.  Ranking fuzzy numbers with an area between the centroid point and original point , 2002 .

[11]  Saeid Abbasbandy,et al.  A new approach for ranking of trapezoidal fuzzy numbers , 2009, Comput. Math. Appl..

[12]  Jee-Hyong Lee,et al.  A method for ranking fuzzy numbers and its application to decision-making , 1999, IEEE Trans. Fuzzy Syst..

[13]  Shan-Huo Chen.  Ranking fuzzy numbers with maximizing set and minimizing set , 1985 .

[14]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers , 2007, Applied Intelligence.

[15]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[16]  R. Nagarajan,et al.  Computing Improved Fuzzy Optimal Hungarian Assignment Problems with Fuzzy Costs under Robust Ranking Techniques , 2010 .

[17]  Bhaskar Sengupta,et al.  A Queue with Service Interruptions in an Alternating Random Environment , 1990, Oper. Res..

[18]  L. M. D. C. Ibáñez,et al.  A subjective approach for ranking fuzzy numbers , 1989 .

[19]  Ramesh Jain,et al.  DECISION MAKING IN THE PRESENCE OF FUZZY VARIABLES , 1976 .

[20]  Ronald R. Yager,et al.  A procedure for ordering fuzzy subsets of the unit interval , 1981, Inf. Sci..