In public transport, e.g., railways, crowding is of major influence on passenger satisfaction and also on system performance. We study the passenger-oriented traffic control problem by means of integrated optimization, particularly considering the crowding effects on passenger route choices and on train traffic. The goal is to find the system optimum solution by adapting train schedules and rerouting passengers. A mixed-integer nonlinear programming (MINLP) model is proposed, identifying the train orders and departure and arrival times, as well as finding the best route for passengers, with the objective of minimizing passenger disutility and train delay. In the model, we allow free splits of the passengers in a group onto different routes and reasonable passenger transfers between trains. We value train crowding by using time multiplier, which is defined as a piecewise constant function of the train crowding ratio (also called load factor), indicating that passengers perceive a longer travel time on a more crowded train. Moreover, we assume variations of the minimum train dwell time, caused by the alighting and boarding passengers. The nonlinear terms in the MINLP model are linearized by using an exact reformulation method and three transformation properties, resulting in an equivalent mixed-integer linear programming (MILP) model. In the experiences, we adopt a real-world railway network, i.e., the urban railway network in Zürich city, to examine the proposed approach. The results demonstrate the effectiveness of the model. The results show that, by considering the crowding effects, some passengers are forced to choose the routes that are less crowded but have larger travel/delay times, which leads to the improved passenger comfort and makes the planned train timetable less affected (in terms of delays). We also find that flexibility in train schedules brings more possibilities to serve better the passengers. Moreover, it is observed that if the train dwell time is highly sensitive to the alighting and boarding passengers, then the transport network will become vulnerable and less reliable, which should be avoided in real operations.


Traffic management,    Passenger rerouting,    Integrated optimization,    Crowding effects,   System optimum


• We study the passenger-oriented traffic control problem, considering crowding effects.
• An MINLP model is proposed and further reformulated into an equivalent MILP model.
• Passengers of a group can split on different routes, depending on crowding and capacity.
• In the model, we restrict train capacity by penalizing train crowding.
• With passenger rerouting onto alternatives, the overall system performance is improved.

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