Abstract
In this communication, the queuing system has two different types of queues namely primary and secondary queue. The existence of secondary queue is possible only when server has limited services to provide, and the system has a characteristic of service surrender facility. The paper deals with the analytical study of such system in which the parameter of the primary queue is probabilistic while parameter of the secondary queue is considered totally uncertain. We are the first to apply fuzzy logic to deal with the secondary queue. The average waiting time in the system by a customer and service wastage rate has been explored in our study through fuzzy arithmetic using α-cut. The service wastage rate is helpful in finding the level of amount of instability in the system when the secondary queue is in existence and is fuzzified.
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