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Estimation of Origin-Destination Matrices: Relationship Between Practical and Theoretical Considerations

A comprehensive overview of the entire class of formulations and most recognized solutions for estimating origin–destination (O-D) demand tables is presented. Specifically, trip distribution formulations are compared with less-known synthetic O-D estimation solution techniques. It is demonstrated that the trip distribution gravity model is nothing but a subset of the maximum-likelihood solution to the synthetic O-D problem. Finally, a numerical solution to the maximum-likelihood synthetic O-D problem is proposed that overcomes the shortcomings of the state-of-practice formulations. The proposed solution, which has been implemented in QueensOD software, does not require flow continuity at the network nodes, as is the case for most formulations. The latest version of QueensOD can be shown to yield results consistent with standard equation solvers (Excel and MATLAB) and with exhaustive enumeration, for small networks, for which all three methods are feasible. However, QueensOD has also been applied to networks with more than 1,000 zones and 5,000 links on a personal computer, typically requiring no more than 1 h to solve problems of this size. The solutions obtained by QueensOD reflect multipath routings, consider correctly that the total number of trips in the network may not be constant, and properly reflect the role of the seed matrix. The model can also be applied to deal with problems in which the routes are not known a priori.