T.J.J. van den Boom, B. Kersbergen, and B. De Schutter, "Structured modeling, analysis, and control of complex railway operations," Proceedings of the 51st IEEE Conference on Decision and Control, Maui, Hawaii, pp. 7366-7371, Dec. 2012.
In this paper we discuss the rescheduling of trains on a large-scale railway network in the case of perturbations using a max-plus-linear system description. We study the structure of the system matrices and derive how this structure can be manipulated by the control variables. In addition, we show that this leads to a system matrix that is affine in the control variables and the timing parameters. We also consider additional constraints for scheduling trains on multiple tracks and constraints for joining and splitting trains.