Macroscopic freeway model calibration with partially observed data, a case study

In this paper, we present a case study on the macroscopic model calibration of the I-680 freeway in Northern California. This calibration effort posed two major challenges: 1) Only about half of the detectors on the mainline were functioning, and 2) no detection was available on the ramps. The only available ramp flow information were the Census counts on about 15 days back in 2009. The model calibrated based on sparsely available data from 2009 was subsequently used for projecting the state of the freeway in 2013. This is due to the fact that data quality significantly deteriorates after 2009 and almost no data is available after 2012. We demonstrate the algorithms developed to automatically calibrate a couple of macroscopic traffic flow models derived from the Cell Transmission Model. The algorithms estimate the unobserved input flows and replace faulty or missing mainline measurements. The unknown input estimation is achieved by an adaptive imputation scheme that uses the partial knowledge of the ramp flows as lower and upper bounds for the estimates. Whereas the fault diagnosis algorithm identifies bad measurements on the mainline and replaces them with profiles that agree with the model dynamics. Due to the inherent unobservability of the system in the absence of both mainline and ramp flow data, this heuristic substitution method is employed rather than a more rigorous state estimation scheme. The resulting calibrated model is able to reproduce the observed congestion patterns on the mainline for the 2009 data while keeping the estimated boundary flow inputs within the expected bounds to the extent where they don´t violate the model dynamics. The model also performs well under projected conditions for 2013.