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A Batch-Arrival Queue with Multiple Servers and Fuzzy Parameters: Parametric Programming Approach

This work constructs the membership functions of the system characteristics of a batch-arrival queuing system with multiple servers, in which the batch-arrival rate and customer service rate are all fuzzy numbers. The  -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 batch-arrival queues with multiple servers. A numerical example is solved successfully to illustrate the validity of the proposed approach. Because the system characteristics are expressed and governed by the membership functions, the fuzzy batch-arrival queues with multiple servers are represented more accurately and the analytic results are more useful for system designers and practitioners.