Towards automatic model calibration of first-order traffic flow model

Conservation law of traffic and an explicit flow-density relationship in equilibrium, also known as the fundamental diagram, are essential in the first-order macroscopic traffic flow models. Regardless of Despite its importance in macroscopic traffic flow modeling, comprehensive method for the calibration of fundamental diagram is very limited. Conventional empirical methods adopt a steady state analysis of the aggregated traffic data collected from measurement devices installed on a particular site to calibrate its fundamental diagram. Such kind of calibration methods do not consider the traffic dynamics, which renders the simulation may not be adaptive to the variability of measured data. Nonetheless, determining the fundamental diagram for each detection site is often infeasible. To remedy these, this study presents an automatic calibration method to estimate the parameters of a fundamental diagram through a dynamic approach. The process is conducted in an iterative manner that the fundamental diagram calibrated from last step is incorporated into the cell transmission model (CTM) to simulate its effect on traffic flow modeling. The simulated flow is compared against the measured flow wherein an optimization merit is conducted. The objective of this optimization is to minimize the discrepancy between model generated data and real data in terms of mean squared error based cost functions. The proposed method is validated by several empirical studies under both recurrent and abnormal traffic conditions. The empirical results prove that the proposed automatic calibration algorithm can significantly improve the accuracy of traffic state estimation and adapts to the variability of traffic data compared with several existing methods. The automatic calibration algorithm provides a powerful tool for model calibration when freeways are equipped with sparse detectors, new traffic surveillance systems lack of comprehensive traffic data or the case that lots of detectors lose their effectiveness for ageing systems even under abnormal traffic conditions such as accidents, special events, etc.