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A Data-driven Approach for Estimating the Fundamental Diagram
Neila Bhouri, Maurice Aron, Habib Hajsalem
Keywords:non-analytical, calibration, empirical data, shortest-path algorithm, convex quadratic program, safety constraint, critical density function


The fundamental diagram links average speed to density or traffic flow. An analytic form of this diagram, with its comprehensive and predictive power, is required in a number of problems. This paper argues, however, that, in some assessment studies, such a form is an unnecessary constraint resulting in a loss of accuracy. A non-analytical fundamental diagram which best fits the empirical data and respects the relationships between traffic variables is developed in this paper. In order to obtain an unbiased fundamental diagram, separating congested and non-congested observations is necessary. When defining congestion in parallel with a safety constraint, the density separating congestion and non-congestion appears as a decreasing function of the flow and not as a single critical density value. This function is here identified and used. Two calibration techniques – a shortest path algorithm and a quadratic optimization with linear constraints – are presented, tested, compared and validated.


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