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Mobil.TUM 2018, International Scientific Conference on Mobility and Transport: Urban Mobility - Shaping the Future Together, MUNICH, ALLEMAGNE, 13-/06/2018 - 14/06/2018; Urban population and mobility needs are rapidly growing while transportation infrastructures are constrained by both limited space and budget allocation. Demand is greater than supply which produces saturation phenomena. Congestion is a major issue impacting the performance of urban transit systems in many ways: operating costs, efficiency and quality of service to name just a few. Regarding rail transit, congestion phenomena are observed in both train and pedestrian traffic. At metro stations, train and pedestrian flows meet and interact with each other. Pedestrian arrivals are pulsed by train arrivals and, inversely, train departures may be delayed because of an excessive number of passengers boarding or/and alighting.The interaction mainly occurs at the platform level where the exchange between passengers is observed.

We present here a real-time control model for the train dynamics in a linear metro line system. The model describes the train dynamics taking into account average passenger arrival rates on platforms, including control laws for train dwell and run times, based on the feedback of the train dynamics. The model extends a recently developed Max-plus linear traffic model with demand-dependent dwell times and a run time control. The extension permits the elimination of eventual irregularities on the train time-headway. The resulting train dynamics are interpreted as a dynamic programming system of a stochastic optimal control problem of a Markov chain. The train dynamics still admit a stable stationary regime with a unique average growth rate interpreted as the asymptotic average train time-headway. Moreover, beyond the transient regime of the train dynamics, our extension guarantees uniformity in time of the train time-headways at every platform., Version updated on 29/10/2018, index error corrected. arXiv preprint, to appear in Proceedings of the 2018 IEEE Intelligent Transportation Systems Conference, Maui/Hawaii