I want to use a simple formula to represent the railway section running time based on a known track alignment, where the train adopts a speed-optimal control strategy. However, most current methods use relatively rough equalization speed methods, simulation methods and so on. Currently, much research on energy-efficient control uses running time as a constraint to solve the train control scheme. Is there research that studies the time-minimization-oriented train control strategy? Can a closed-form formula express the relation between track alignment and the section running time (speed-optimal train control strategy)?

I am quite new to this field, so feel free to recommend a fundamental textbook that might help.

Thanks.