Optimal congestion control strategies for near-capacity urban metros: informing intervention via fundamental diagrams

Congestion; operational delays due to a vicious circle of passenger-congestion and train-queuing; is an escalating problem for metro systems because it has negative consequences from passenger discomfort to eventual mode-shifts. Congestion arises due to large volumes of passenger boardings and alightings at bottleneck stations, which may lead to increased stopping times at stations and consequent queuing of trains upstream, further reducing line throughput and implying an even greater accumulation of passengers at stations. Alleviating congestion requires control strategies such as regulating the inflow of passengers entering bottleneck stations. The availability of large-scale smartcard and train movement data from day-to-day operations facilitates the development of models that can inform such strategies in a data-driven way. In this paper, we propose to model station-level passenger-congestion via empirical passenger boarding-alightings and train flow relationships, henceforth, fundamental diagrams (FDs). We emphasise that estimating FDs using station-level data is empirically challenging due to confounding biases arising from the interdependence of operations at different stations, which obscures the true sources of congestion in the network. We thus adopt a causal statistical modelling approach to produce FDs that are robust to confounding and as such suitable to properly inform control strategies. The closest antecedent to the proposed model is the FD for road traffic networks, which informs traffic management strategies, for instance, via locating the optimum operation point. Our analysis of data from the Mass Transit Railway, Hong Kong indicates the existence of concave FDs at identified bottleneck stations, and an associated critical level of boarding-alightings above which congestion sets-in unless there is an intervention.