Continuous SBC Method: A Queuing Theory Model for Handling Non-Stationary Finite Queues

Queuing theory is a mathematical theory that studies the operation laws and optimization methods of queuing systems. Classical queuing theory has limitations in handling non-stationary arrival processes, and while the SBC method can address this issue, it still has other shortcomings that can be improved. To address these problems, this paper proposes the Continuous SBC method. Based on the basic principles of the SBC method, this method continuously extends it and introduces restrictions such as maximum queue length, thus enabling more accurate and versatile handling of queuing problems. This paper first introduces the basic principles and advantages and disadvantages of the SBC method, and then elaborates on the basic principles, parameters, and model formulas of the Continuous SBC method. Python simulation experiments are used to verify the accuracy of the method. The results show that the Continuous SBC method can effectively estimate the queue length and other mathematical characteristics under non-stationary finite queuing conditions, providing new ideas and methods for optimizing queuing systems and improving service efficiency.