Model on empirically calibrating stochastic traffic flow fundamental diagram

Abstract

This paper addresses two shortcomings of the data-driven stochastic fundamental diagram for freeway traffic. The first shortcoming is related to the least-squares methods which have been widely used in establishing traffic flow fundamental diagrams. We argue that these methods are not suitable to generate the percentile-based stochastic fundamental diagrams, because the results generated by least-squares methods represent weighted sample mean, rather than percentile. The second shortcoming is widespread use of independent modeling methodology for a family of percentile-based fundamental diagrams. Existing methods are inadequate to coordinate the fundamental diagrams in the same family, and consequently, are not in alignment with the basic rules in probability theory and statistics. To address these issues, this paper proposes a holistic modeling framework based on the concept of mean absolute error minimization. The established model is convex, but non-differentiable. To efficiently implement the proposed methodology, we further reformulate this model as a linear programming problem which could be solved by the state-of-the-art solvers. Experimental results using real-world traffic flow data validate the proposed method.