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Math. Comput. Appl. 2006, 11(3), 181-191; doi:10.3390/mca11020181

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

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.
Published: 1 December 2006
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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
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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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.

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Math. Comput. Appl. EISSN 2297-8747 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
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