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

The precise estimation of time-varying demand matrices using traffic data is an essential step for planning, scheduling, and evaluating advanced traffic management systems. This paper presents an innovative method, based on the least squares approach, to handle the inherent complexities of estimating the dynamic characteristics of changing demand flow over time while considering congestion conditions. The time-dependent origin–destination (OD) demand matrices of the network are estimated by exploiting the received partial paths data from an automated vehicle identification 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 are performed on three different approaches: utilizing only link counts data, utilizing only partial path flows data, and utilizing both of them. The results demonstrate that using variance–covariance matrices provides more precise estimates for time-dependent OD matrices. The effectiveness of the solution algorithm and the main ideas of the model are examined using the Sioux-Falls and Sodermalm networks. This paper reports the features of the discussed model based on different data as a proof of concept that incorporating partial path flows significantly improves the results for solving time-dependent OD matrix estimation problems.