Time-Expanded Network Model of Train-Level Subway Ridership Flows Using Actual Train Movement Data

Document Type

Journal Article

Publication Date


Subject Area

place - north america, place - urban, mode - subway/metro, technology - ticketing systems, technology - passenger information, ridership - modelling


Subway ridership estimates, electronic systems, schedules, New York City Transit (NYCT), model


Subway ridership estimates are important to transit operators for both internal applications (e.g., setting service frequencies, prioritizing station upgrades) and external reporting (e.g., to the National Transit Database). New York City Transit (NYCT) is developing a new model that will accomplish three primary objectives: (a) estimating subway ridership at a train level for the first time, (b) basing path choice on actual train movements rather than on schedules so that uneven loadings can be accurately captured, and (c) running fast enough to be used daily and being sufficiently automated to run with minimal human intervention. The model integrates entry data from fare cards with actual train movement data from a wide range of electronic systems and schedules. The model assigns riders to trains by using a Frank–Wolfe approach, including Dijkstra’s algorithm for shortest paths, with customizations designed for transit. These customizations improve speed, enable the algorithm to model delays better, and allow for multiple types of riders with different preferences for transfers and crowding. The size and the complexity of the NYCT system make for a challenging test case computationally. Approximately 6 million trips are made on a busy weekday, and these are assigned to a time-expanded network containing more than 3 million nodes and 7 million arcs. The model is automated and runs fast enough that it can be used daily. Validation against manual counts indicates strong results, with the R2 for max load point volumes for the morning peak hour equal to .91.


Permission to publish the abstract has been given by Transportation Research Board, Washington, copyright remains with them.