Estimation of Passengers Left Behind by Trains in High-Frequency Transit Service Operating Near Capacity

Document Type

Journal Article

Publication Date


Subject Area

place - north america, place - urban, mode - rail, ridership - demand, operations - capacity, operations - crowding, operations - performance, planning - safety/accidents, planning - service level, technology - intelligent transport systems, technology - automatic vehicle monitoring, technology - passenger information


high-frequency trains, crowding, capacity


Measuring rail system crowding is important to transit agencies. Crowding data has implications for safety, operations control, service planning, performance measurement, and customer information. This paper proposes a bi-level regression model that transit agencies can use to estimate the number of passengers left behind on a platform by high-frequency trains operating at capacity. Inputs to the model include the number of passenger arrivals between trains and train departure times, which are derived from automatic fare collection and vehicle location data. The data are used to calculate the proposed measure of cumulative capacity shortage, which is shown to have high correlation with the number of passengers left behind. A bi-level regression approach is introduced and applied to calibrate the model parameters based on manual counts of passengers left behind. A case study using data from the Chicago Transit Authority’s Blue Line demonstrates promising results, with an adjusted coefficient of determination of 0.81. The model could be used for post-hoc analysis of crowding performance or, in the context of real-time operations monitoring, for near-term predictions of passengers left behind.


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