Recent advances in operations research and machine learning have revived interest in solving complex real-world, large-size traffic control problems. 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 density-flow curve. 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：运筹学与机器学习的最新进展重新激发了解决复杂现实、大规模交通控制问题的兴趣。随着道路传感器数据日益普及，确定性参数模型已被证明不足以描述真实世界数据的变异性，尤其是在密度-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，估计随机密度-流量关系。所提方法不依赖于任何先验的函数形式假设，但借助凹性约束，估计函数满足密度-流量曲线的理论性质。第二个贡献是开发了新的带袋的凸分位数回归方法，以促进凸分位数回归在实际数据中的实现。我们使用芬兰2016-2018年道路传感器数据展示了CQRb的估计过程。第三个贡献是证明所提CQRb方法在样本外预测能力上优于标准参数确定性方法。