A Novel Model for Train Operation Adjustment in High-Speed Railway based on Max-plus Algebra

Abstract

The running time of high-speed train is generally not late, and it can run normally in most cases. However, when severe weather conditions, train components and equipment, accidents or emergencies occur, it will lead to train operation delay and traffic congestion. Therefore, when an accident occurs, we need to adjust the train time or route timely and accurately. As an important algebraic system, max-plus algebra is widely used in the field of industrial production control. In industrial production, the most production mode is the discrete system , but the characteristics and the ability of discrete systems depends on the periodic of system and the number of workpiece produced by the system in unit time, and the characteristics of the system are closely related to the properties of the matrix, especially, the eigenvalues and eigenvectors of the matrix in the sense of max-plus algebra. Therefore, this paper studies the max-plus algebra theory and the solution of eigenvalues and eigenvectors of matrices in the sense of max-plus algebra, establish the operation time matrix to optimize the train operation adjustment model of high-speed railway, and analyze the failure propagation model.