International Journal of Applied Science and Engineering
Published by Chaoyang University of Technology

Chuen-Horng Lina1, Hsin-I Huangb and Jau-Chuan Kec

a Graduate School of Computer Science and Information Technology.
b Department of Computer Science and Information Engineering. National Taichung Institute of Technology, Taiwan 404, R.O.C.
c Department of Applied Statistics, National Taichung Institute of Technology, Taiwan 404, R.O.C.


 

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ABSTRACT


This work constructs the membership functions of the system characteristics of a batch queuing system with server setup, in which the batch arrival rate, customer service rate, and server setup 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 queues with server setup. Two numerical examples are solved successfully to illustrate the validity of the proposed approach. Because the system characteristics are expressed and governed by the membership functions, the fuzzy queues with server setup are represented more accurately and the analytic results are more useful for system designers and practitioners.


Keywords: Fuzzy sets; Membership function; Nonlinear programming; Setup


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ARTICLE INFORMATION




Accepted: 2008-12-12
Available Online: 2008-11-01


Cite this article:

Lin, C.-H., Huang, H.-I., Ke, J.-C. 2008. On a batch arrival queue with setup and uncertain parameter patterns. International Journal of Applied Science and Engineering, 6, 163–180.https://doi.org/10.6703/IJASE.2008.6(2).163