Model and algorithm of coordinated flow controlling with station-based constraints in a metro system

Document Type

Journal Article

Publication Date


Subject Area

mode - subway/metro, place - asia, place - urban, ridership - modelling, planning - methods


Metro system oversaturation, Passenger flow control, Nonconvex nonlinear programming, Dynamic programming


With the growing urban population and its rapid growth of mobility needs, metro systems often suffer from congestion in peak hours in many mega-cities over the world. This incurs severe travel delays for commuters and safety risks for metro operators. Hence, passenger flow management and control becomes an essential way to reduce station congestion during high-peak hours. This paper investigates the passenger flow control problem with the objective of increasing the number of boarding passengers. Considering the scenario that the destination of each passenger entering the station is unknown, a flow control problem with dynamic and station-based constraints is proposed to dynamically determine the number of passengers boarding each train at each station. Compared with existing flow control strategies, this model can improve the equity for boarding passengers of different OD pairs. The station-based flow control problem is formulated as a complicated nonlinear nonconvex quadratic programming model. To solve the intractable nonlinear programming model, we reformulate it into the dynamic programming formation and develop two efficient heuristic algorithms to solve it. We carry out two sets of numerical experiments, including the small-scale case with synthetic data and the real-world case with the operation data of Beijing metro system, to evaluate the performance of our model and algorithms. Several performance indicators, e.g. average waiting time and Gini coefficient, are presented to verify the efficiency and fairness of proposed model. The numerical results applied to Beijing urban subway network indicate that our approach can reduce the passengers’ waiting time and the line-level Gini coefficient by 5.21% and 23.52% compared with the benchmark flow control strategy with maximum loading and station-based constraints.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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