Estimation of Time-Dependent Origin-Destination Matrices Using the Path Flow Proportion Method

This research formulates the time-dependent origin-destination (O-D) matrix estimation problem as a system of linear equations and solves this problem by using the conditional inverse matrix theory. One of the unique aspects of the adopted matrix inverse method is that it provides a generalized matrix inverse procedure even if the target matrix is either singular or non-squared. Due to the multiple solutions problem when solving the O-D matrix estimation problem, the path flow proportion method is developed in the present study and the unique solution of the O-D matrix estimation problem can be obtained. In the numerical analysis, the developed model framework and solution algorithm are evaluated based on a simplified network. The numerical analysis result reveals that the time-dependent O-D demand estimates given by the proposed models and adopted solution algorithm can be estimated exactly.