A parametric programming solution to the F -policy queue with fuzzy parameters.

This paper investigates theF-policy queue using fuzzy parameters, in which the arrival rate, service rate, and start-up rate are all fuzzy numbers. TheF-policy deals with the control of arrivals in a queueing system, in which the server requires a start-up time before allowing customers to enter. A crispF-policy queueing system generalised to a fuzzy environment would be widely applicable; therefore, we apply the α-cuts approach and Zadeh's extension principle to transform fuzzyF-policy queues into a family of crispF-policy queues. This study presents a mathematical programming approach applicable to the construction of membership functions for the expected number of customers in the system. Furthermore, we propose an efficient solution procedure to compute the membership function of the expected number of customers in the system under different levels of α. Finally, we give an example of the proposed system as applied to a case in the automotive industry to demonstrate its practicality. [ABSTRACT FROM PUBLISHER]