Fuzzy analysis of queueing systems with an unreliable server: A nonlinear programming approach
Abstract This work constructs the membership functions of the system characteristics of a queuing model with an unreliable server, in which the arrival rate and the service rate of customers, as well as the breakdown rate and repair rate of server are all fuzzy numbers. The α -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 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 an unreliable server. An efficient algorithm is provided to find the optimal solutions at a different possibility level α . Three numerical examples are solved successfully to illustrate the validity of the proposed approach. Due to the system characteristics being expressed and governed by the membership functions, more information is provided for use by management. By extending the fuzzy environment, the fuzzy queues with an unreliable server can be represented more accurately by using the proposed approach, and the analysis results for such queuing model will be useful and significant for system designers and practitioners.