Iterative Proportional Fitting Procedure to Determine Bus Route Passenger Origin–Destination Flows

Abstract

The advent of automatic passenger counter (APC) technologies is resulting in the collection of comprehensive boarding and alighting data on an ongoing basis across transit networks. The availability of APC data offers a new opportunity to determine origin–destination (O-D) flows on a frequent and comprehensive basis. In this paper, the performance of a simple procedure for route-level O-D flow determination requiring only boarding and alighting data is investigated. Specifically, the performance of the iterative proportional fitting (IPF) procedure used with a null base matrix is examined on the basis of a field experiment in which true O-D flows are observed. Because of the noninformative nature of the null matrix, using the IPF procedure with the null matrix as its input base may not be expected to produce good results. In a comparison of empirical results with those produced by other benchmark procedures, the IPF–null procedure is found to perform surprisingly well. The quality of the resulting matrices appears to be roughly similar to that of matrices derived from an onboard survey, the benchmark for what has been achieved in practice, but at much higher cost. The results indicate that much can be gained from using readily available APC data, even when the simple IPF–null procedure is applied. Moreover, using the better base obtained from an onboard survey with the IPF procedure improved performance, but less markedly compared with use of the null base; this difference indicates that combining onboard survey information with APC data provides a better O-D matrix than what can be derived from an onboard survey alone, even when the simple IPF procedure is used.

Statistical inference on transit route‐level origin–destination flows using automatic passenger counter data

“…When a priori information is not available, a null base matrix, which assigns the same value (e.g., one) to all feasible OD pairs and zeroes to all infeasible OD pairs, can be used. Empirical studies have shown that the IPF method produces reasonably good OD flow estimates ] and that the IPF estimates are similar to those produced by some other methods .…”

“…By doing so, the origin and destination stops of this passenger are identified. Eventually, OD flow information was collected from 2,244 passengers .…”

Termination of the iterative proportional fitting procedure

“…To this end, the IPF procedure generates a sequence of matrices (A(t)), called the IPF sequence, by alternately fitting rows and columns to match their respective marginals. The procedure is in use in many disciplines for problems such as calculating maximum likelihood estimators in graphical log-affine models (Lauritzen, 1996, Chapter 4.3.1), ranking webpages (Knight, 2008), determining passenger flows (McCord et al, 2010) or calculating seats in parliaments (Pukelsheim, 2014b, Chapter 14).…”

Continuity of f-projections and applications to the iterative proportional fitting procedure

“…To this end, the IPF procedure generates a sequence of matrices, called the IPF sequence, by alternately fitting rows and columns to match their respective marginals. The procedure is in use in many disciplines for problems such as calculating maximum likelihood estimators in graphical log-affine models (Lauritzen [13,Chapter 4.3.1]), ranking webpages (Knight [11]) or determining passenger flows (McCord et al [15]). …”