Modeling the alighting and boarding process through train doors using a Markov process with flow-dependent transition probabilities

Understanding and modeling the alighting and boarding process in suburban train services is crucial to optimizing train dwellings. The alighting and boarding process is a bi-directional pedestrian flow through a bottleneck, being the door opening. Pedestrian flows, including alighting and boarding processes, are generally modeled by two-dimensional pedestrian models, such as cellular automata or social force models. These two-dimensional models are calibrated from two-dimensional data sources that are often complicated to access for privacy reasons. The availability of disaggregated passenger counting data led us to propose a different modeling approach based on cumulative flows. The model is a Markov process with variable transition probabilities. Transition probabilities are computed from the remaining number of alighting and boarding via a differential equation based on the pedestrian fundamental diagram and density estimations. The parameters of the differential equation were fitted using disaggregated passenger counting data. The model shows better predictive power than a linear benchmark model calibrated on the same data. The physical parameters of the model are consistent with the existing literature. The proposed approach offers an alternative to commonly used two-dimensional models, providing easier calibration. Such a model will enable the forecasting of alighting and boarding time distributions, facilitating better dwell time planning and train and platform design.