A Nonlinear Programming Approach for a Fuzzy Queue with an Unreliable Server

Abstract

ABSTRACT. The aim of this paper is to develop the membership functions of the system characteristic of a queuing g model with an unreliable server, in which the arrival rate, service rate, breakdown rate and repair rate are all fuzzy numbers. The -cut approach is used to transform a fuzzy queue with an unreliable server into a family of conventional crisp queues with an unreliable server. By using membership functions, a set of parametric nonlinear programmes are developed to describe the family of crisp queues with an unreliable server. An efficient algorithm is developed to find the optimal solutions at or different possibility level . Numerical examples are solved successfully. Since the system characteristics being expressed and governed by membership functions, more information is provided for the management.

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“…Consider an automated process in which the service is divided into two phases, with an arrival rate 𝜆 ̃= (2,3,4) and service rate 𝜇 ̃= (12,13,14) with 𝑘 = 2. Determine the TFN in the form of (𝑚 ̃, 𝛼 ̃, 𝛽 ̃) as 𝜆 ̃= (3,1,1) and 𝜇 ̃= (13,1,1). To determine the values of a no.…”

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