Analysis on a queue system with heterogeneous servers and uncertain patterns

Jau-Chuan Ke; Hsin-I Huang; Chuen-Horng Lin

doi:10.3934/jimo.2010.6.57

Article Contents

2010, Volume 6, Issue 1: 57-71. Doi: 10.3934/jimo.2010.6.57

This issue Previous Article Necessary optimality conditions for switching control problems Next Article Optimal service capacity in a multiple-server queueing system: A game theory approach

Analysis on a queue system with heterogeneous servers and uncertain patterns

1.
Department of Applied Statistics, National Taichung Institute of Technology
2.
Department of Computer Science and Information Engineering, National Taichung Institute of Technology
3.
Graduate School of Computer and Information Technology, National Taichung Institute of Technology

Received: July 31, 2008

Revised: July 31, 2009

Published: December 2009

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Abstract

This work constructs the membership functions of the system characteristics of a heterogeneous-server queueing model with fuzzy customer arrival and service rates. The $\alpha$-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 heterogeneous-server queues. A numerical example is solved successfully to illustrate the validity of the proposed approach. By extending this model to the fuzzy environment, the system characteristics are expressed and governed by the membership functions, and more information is provided for use by designers and practitioners.

Keywords:

Gaussian fuzzy numbers; Heterogeneous servers; Membership functions; Nonlinear programming; Trapezoidal fuzzy numbers.

Mathematics Subject Classification: Primary 94D05; Secondary: 60K25.

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