Decomposition algorithm for statistical estimation of OD matrix with random link choice proportions from traffic counts

Statistical models for the estimation of Origin-Destination (OD) matrix from traffic counts that consider explicitly the presence of randomness in the link choice proportions have been developed recently. These models are more receptive to the fluctuations in the observations due to measurement errors and temporal variations and they can make better use of traffic information. However, the estimation based on the new models involves the optimization of functions that may not be convex and for large networks in real situations, conventional numerical algorithms such as Newton types may have difficulty in attaining the global optimum. In this paper, a decomposition algorithm that makes combined use of the Coordinate Descent method and the Partial Linearization Algorithm is proposed and its convergence proved. The proposed algorithm is shown to perform better with regard to finding the global optimum than the conventional quasi-Newton algorithm. Its implementation is demonstrated by a numerical example and a Hong Kong case study.