Spread-based Stochastic High Frequency Railway Optimization

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Abstract

This paper outlines a mathematical model for the creation of a robust timetable for the optimization of the lightrail network in Rotterdam and The Hague. A novel spread-based goal function focuses on minimizing wait time as opposed to delay. The situation is modeled as a Quadratic Stochastic Programming problem, and solved by employing Monte Carlo techniques to make the Quadratic Program deterministic. The solution informs what the optimal rate of train departures per hour is and provides a timetable that has over 120% more train capacity than the status quo, which has a higher delay resistance than the current timetable. For the inevitable unpredicted delay, a real-time implementation of this algorithm is used dynamically to create a new optimal timetable on the fly.