Parametric programming approach for batch arrival queues with vacation policies and fuzzy parameters

This work constructs the membership functions of the system characteristics of a batch arrival queuing model with vacation policies and fuzzy batch arrival, customer service and server vacation rates. 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 a vacationing server. 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, more information is provided for use by management. By extending this model to the fuzzy environment, fuzzy queues with a vacationing server are represented more accurately and the analytic results are more useful for system designers and practitioners.