A membership function solution to multiple-server fuzzy queues

Problems of multiple-server fuzzy queues are often encountered in service industry, such as in hospital clinics. Herein, a membership function of the performance measure of multiple-server fuzzy queues with the arrival rate and service rate are fuzzy numbers is derived, in which α-cut and Zadeh's extension principle are applied to transform multiple-server fuzzy queues to a family of conversional multiple-server queues, and a pair of parametric programs is formulated to calculate the upper and lower bounds of the performance measure. As α varies, the membership function of the expected sojourn time per patient in the clinic with 2-server fuzzy queues is solved in the presented numerical example. Since the performance measures are expressed by membership functions rather than by crisp values, more information is provided for managerial decision-making in hospitals.