Uncertain queueing model with group arrivals

The main goal of mathematical modeling and analysis of queueing systems is to understand the dynamic behavior of the underlying processes, enabling informed and intelligent management decisions. While the queueing systems with random factors have received extensive scrutiny, this paper introduces an uncertain queueing model that considers the belief degree of customer behavior. In this model, customers arrive in groups and the interarrival times and service times are treated as uncertain variables. To evaluate the performance of this proposed uncertain queueing model, the busy index and busy period are also discussed, and the analytical formulas and uncertainty distribution are derived respectively. Additionally, two numerical examples are also given to illustrate the obtained results.