  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.
