A Fuzzy Queuing Model with Unreliable Server, Fuzzy Arrival and Service Rates, and Fuzzy Service Time.

AbstractThis paper presents a fuzzy queuing model that incorporates uncertainty in arrival and service rates, service time, and service reliability. The model is formulated as a fuzzy M/M/1 queuing system with an unreliable server, where the arrival rate, service rate, and service time are represented by fuzzy numbers. The server is assumed to be unreliable, with a fuzzy failure rate and fuzzy repair rate. Using fuzzy arithmetic and fuzzy calculus, We derive the fuzzy steady - state probabilities and performance metrices, such as the fuzzy expected number of customers in the system, fuzzy expected waiting time, and server utilization.Numerical examples are provided to illustrate the application of the model and the effects at fuzzy parameters on the performance metrices. The results show that the fuzzy queuing model can effectively capture the uncertainty and imprecision in the real world queuing system, providing a more realistic and robust analysis.