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Article

A Batch-Arrival Queue with Multiple Servers and Fuzzy Parameters: Parametric Programming Approach

by
Jau-Chuan Ke
1,*,
Hsin-I Huang
2,* and
Chuen-Horng Lin
2
1
Department of Statistics, National Taichung Institute of Technology, Taichung 404, Taiwan, R.O.C.
2
Department of Information Management, National Taichung Institute of Technology, Taichung 404, Taiwan, R.O.C.
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2006, 11(3), 181-191; https://doi.org/10.3390/mca11020181
Published: 1 December 2006
Versions Notes

Abstract

This work constructs the membership functions of the system characteristics of a batch-arrival queuing system with multiple servers, in which the batch-arrival rate and customer service rate are all fuzzy numbers. The α-cut approach is used to transform a fuzzy queue into a family of conventional crisp queues in this context. By means of the membership functions of the system characteristics, a set of parametric nonlinear programs is developed to describe the family of crisp batch-arrival queues with multiple servers. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the system characteristics are expressed and governed by the membership functions, the fuzzy batch-arrival queues with multiple servers are represented more accurately and the analytic results are more useful for system designers and practitioners.
Keywords: Fuzzy sets; Membership function; Multiple server; Nonlinear programming Fuzzy sets; Membership function; Multiple server; Nonlinear programming

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MDPI and ACS Style

Ke, J.-C.; Huang, H.-I.; Lin, C.-H. A Batch-Arrival Queue with Multiple Servers and Fuzzy Parameters: Parametric Programming Approach. Math. Comput. Appl. 2006, 11, 181-191. https://doi.org/10.3390/mca11020181

AMA Style

Ke J-C, Huang H-I, Lin C-H. A Batch-Arrival Queue with Multiple Servers and Fuzzy Parameters: Parametric Programming Approach. Mathematical and Computational Applications. 2006; 11(3):181-191. https://doi.org/10.3390/mca11020181

Chicago/Turabian Style

Ke, Jau-Chuan, Hsin-I Huang, and Chuen-Horng Lin. 2006. "A Batch-Arrival Queue with Multiple Servers and Fuzzy Parameters: Parametric Programming Approach" Mathematical and Computational Applications 11, no. 3: 181-191. https://doi.org/10.3390/mca11020181

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