On a Batch Arrival Queue with Setup and Uncertain Parameter Patterns

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.