Time-dependent estimation of origin-destination matrices using partial path data and link counts

Abstract

Abstract The precise estimation of time-varying demand matrices using traffic data is an essential step for planning, scheduling, and evaluating advanced traffic management systems (ATMS). This paper presents an innovative method (based on the least squares approach) to deal with the inherent complexities in estimating the dynamic characteristics of changing demand flow over time and considering congestion conditions. The time-dependent Origin-Destination (OD) demand matrices of the network are estimated by exploitation of the received partial paths data from an automated vehicle identification (AVI) system, and vehicle counts data from loop detectors on a subset of the links. A traffic assignment approach based on partial paths is embedded into the measurement equations of the least squares model. For all time intervals, the relation between the variable aspects of congestion (the temporal and spatial distribution of the OD traffic flows) is established by their variance-covariance matrices. The LSQR algorithm, an iterative algorithm that is logically equivalent to the conjugate gradient method, is employed for solving the proposed least squares problem. Numerical examples performed on three different approaches (only link counts data, only partial path flows data, and both of them) show that using the variance-covariance matrices is more precise for estimating time-dependent OD matrices. The Sioux Falls network is presented to examine the solution algorithm’s effectiveness and the model’s main ideas. This paper reports the features of the discussed model based on synthetic data as proof of concept that using partial path flows significantly improves the results for solving time-dependent OD matrices estimation problems.