The fundamental diagram serves as the foundation of traffic flow modeling for almost a century. With the increasing availability of road sensor data, deterministic parametric models have proved inadequate in describing the variability of real-world data, especially in congested area of the density-flow diagram. In this paper we estimate the stochastic density-flow relation introducing a nonparametric method called convex quantile regression. The proposed method does not depend on any prior functional form assumptions, but thanks to the concavity constraints, the estimated function satisfies the theoretical properties of the fundamental diagram. The second contribution is to develop the new convex quantile regression with bags (CQRb) approach to facilitate practical implementation of CQR to the real-world data. We illustrate the CQRb estimation process using the road sensor data from Finland in years 2016-2018. Our third contribution is to demonstrate the excellent out-of-sample predictive power of the proposed CQRb method in comparison to the standard parametric deterministic approach.

翻译：基本图作为交通流建模的基础已近一个世纪。随着道路传感器数据日益丰富，确定性参数模型在描述真实数据变异性方面显得不足，尤其在密度-流量图的拥堵区域。本文通过引入一种称为凸分位数回归的非参数方法，估计了随机密度-流量关系。该方法无需依赖任何先验函数形式假设，但借助凹性约束，使得估计函数满足基本图的理论特性。第二项贡献是开发了新的带包凸分位数回归方法，以促进凸分位数回归在实际数据中的应用。我们利用芬兰2016-2018年间的道路传感器数据展示了CQRb估计过程。第三项贡献是证明相较于标准参数化确定性方法，所提出的CQRb方法具有卓越的样本外预测能力。