Analytical Study of Fuzzified Queue System with Impatient Customers

Queue model plays a significant role in design and analysis of the system. These models with customer's impatience find its applications in modeling various situations in business and industries. The customers’ impatience has worse effect on the progress and sustainability of any business. Recently T.P. Singh and Arti in 2014 explored the transient solution of serial queue model and studied the impact of probability of retaining the reneged customers on mean queue length of system. However, in real world situations, it has been observed that arrival rate, service rate and reneging rates all are uncertain. In the study of behavioral analysis of a queue system having two queues in series with reneging customers, we have introduced fuzzy logic concept as fuzzy arrival, fuzzy service rates, fuzzy reneging rates which result in deriving the queue characteristics as a fuzzy expression. It has been assumed that the service rates as well as the reneging rates depend upon their respective numbers. A numerical problem with design implication rounds up the paper.