Mathematical Study of Queue System with Impatient Customers Under Fuzzy Environment

Queuing models with impatient customers have wide variant of applications in modeling such as business and industries. Impatient customers affect the progress and sustainability of any business. Therefore, it is necessary to study the behavior of such customers. In the present study, authors analyze a queue system having two queues in series with reneging customers. In real-world scenario it has been observed that the arrival pattern, service rates and reneging rates of customers are uncertain, i.e., in linguistic form may be slow, moderate, fast, etc. The amount of uncertainty in a system can be reduced by using fuzzy logic because it offers better capabilities to handle linguistic uncertainties by modeling vagueness and unreliability of information. Hence, fuzzy concept has been introduced which results the queue characteristics as a fuzzy expression. It has also been assumed that the service rates as well as the reneging rates depend upon their respective numbers. A numerical illustration is given at the end to clarify the model.