Uncoupled Method for Equilibrium-Based Linear Path Flow Estimator for Origin-Destination Trip Matrices

Recently, models of the path flow estimator, in which origin–destination (O-D) matrices are determined according to the solutions of path flows, have been adopted for O-D matrix estimation with the equilibrium assignment assumption. This research suggests that the linear path flow estimator can be solved independently by employing the K-shortest-paths ranking algorithm. This intuitive and simple mechanism finds the user-equilibrium (UE) path columns and a simplex decomposition that specifies the most likely O-D trip matrix. A modified version of the K-shortest-paths ranking algorithm is presented to guarantee that all cyclic-free path columns satisfying the UE condition are recognized. The proposed method uncouples the conventional equilibrium-based O-D estimation model, in which the reproduction of the equilibrium flow pattern and the estimation of the O-D matrix are executed simultaneously and iteratively, into two simple individual problems. The uncoupled approach allocates flows directly onto the path that has been ensured as one of the optimal paths. The excess computational overhead, such as the repeated shortest-path search and redundant column operations brought by the column generation method, is thus avoided. According to the computational results, the presented approach is capable of reproducing the UE flow pattern perfectly while obtaining a substantially accurate O-D matrix with fewer iterations consumed.