Matrix estimation for static traffic assignment models with queuing

Abstract

A matrix estimation method using the semi dynamic assignment model STAQ is developed exploiting its methodological advantages over full DTA models. The matrix estimation problem is formulated as a bi-level problem and is solved on the node level taking flow metering into account. In the lower level the method uses marginal simulation of the node model within the assignment model to approximate the response function. The implicit relations between turn demand and link flows as defined by the directional capacity proportional node model are analyzed and made explicit. In the upper level an objective function minimizing differences between estimated and observed link flows and differences between prior and posterior ODmatrices is used, both components using a MSE distance function. The two components in the objective function are weighted and normalized. A method to prevent overshooting due to approximation errors is proposed as well as a method to correct the prior ODmatrix in case of insensitivity of the link flow due to supply constraints inconsistent with observed link flows. Test runs are conducted showing that the method finds (non-unique) solutions to the matrix estimation problem when only differences in link flows are taken into account, but may fail to converge when also differences between prior and estimated ODmatrix are taken into account. Further investigation suggests that secondary interaction effects should be included in the response function to solve the problem in these cases.