Estimating Transit Route OD Flow Matrices from APC Data on Multiple Bus Trips Using the IPF Method with an Iteratively Improved Base: Method and Empirical Evaluation

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, technology - passenger information, operations - service span


Transit route origin-destination (OD) flow estimation, Iterative proportional fitting (IPF) method, Automatic passenger count (APC) data, Empirical evaluation


An iterative method is proposed to estimate bus route origin-destination (OD) passenger flow matrices from boarding and alighting data for time-of-day periods in the absence of good a priori estimates of the flows. The algorithm is based on the widely used iterative proportional fitting (IPF) method and takes advantage of the large quantities of boarding and alighting data that are routinely collected by transit agencies using automatic passenger count (APC) technologies. An arbitrarily chosen OD matrix can be used as the base matrix required to initialize the algorithm, and the IPF method is applied with bus trip-level boarding and alighting data and the base matrix to produce an estimate of the OD flow matrix for each bus trip. The trip-level OD flow matrices are then aggregated to produce an estimate of the period-level OD flow matrix, which in turn is used as the base matrix for the following iteration. The process is repeated until convergence. Empirical results are conducted on operational bus routes using APC data collected during multiple season-years, where directly observed OD passenger flows are available to represent the ground truth. In all cases in which APC data are available for even a reasonably small number of bus trips, the iteratively improved base method produces better estimates than the application of the traditional IPF method when using a null base matrix, which is commonly adopted in the absence of a priori information without updating. Moreover, the algorithm converges in minimal computational time to the same estimates regardless of the initializing matrices used.
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