Calibration of the Fundamental Diagram Based on Loop and Probe Data

The fundamental diagram is a key component of traffic flow. This diagram describes equilibrium traffic states and their propagation on a traffic network. Knowledge of traffic parameters is of paramount importance to understand traffic properties and characteristics. It is also critical to calibrate the elements of dynamic traffic flow simulation models and reproduce traffic states on road networks. This paper describes the development of a method for estimating fundamental diagram parameters that combines loop data and probe data. Loop data are considered boundary conditions of the problem. The travel times between any points located in the loop can be estimated on the basis of the fundamentals of the kinematic wave theory. The optimal fundamental diagram parameters are computed so that the discrepancy between estimated travel times and the actual travel times determined with probe vehicles is minimal. The method is validated by the use of simulated error-free data. The results demonstrate the accuracy of the method when it is applied to an error-free data set. The method is then implemented with realistic data, that is, data that were aggregated and noised beforehand. The robustness of the method is demonstrated, and the results are encouraging for the development of an algorithm that calibrates fundamental diagram parameters online and automatically.