This paper aims to quantify uncertainty in traffic state estimation (TSE) using the generative adversarial network based physics-informed deep learning (PIDL). The uncertainty of the focus arises from fundamental diagrams, in other words, the mapping from traffic density to velocity. To quantify uncertainty for the TSE problem is to characterize the robustness of predicted traffic states. Since its inception, generative adversarial networks (GAN) has become a popular probabilistic machine learning framework. In this paper, we will inform the GAN based predictions using stochastic traffic flow models and develop a GAN based PIDL framework for TSE, named "PhysGAN-TSE". By conducting experiments on a real-world dataset, the Next Generation SIMulation (NGSIM) dataset, this method is shown to be more robust for uncertainty quantification than the pure GAN model or pure traffic flow models. Two physics models, the Lighthill-Whitham-Richards (LWR) and the Aw-Rascle-Zhang (ARZ) models, are compared as the physics components for the PhysGAN, and results show that the ARZ-based PhysGAN achieves a better performance than the LWR-based one.

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This paper proposes the TrafficFlowGAN, a physics-informed flow based generative adversarial network (GAN), for uncertainty quantification (UQ) of dynamical systems. TrafficFlowGAN adopts a normalizing flow model as the generator to explicitly estimate the data likelihood. This flow model is trained to maximize the data likelihood and to generate synthetic data that can fool a convolutional discriminator. We further regularize this training process using prior physics information, so-called physics informed deep learning (PIDL). To the best of our knowledge, we are the first to propose an integration of flow, GAN and PIDL for the UQ problems. We take the traffic state estimation (TSE), which aims to estimate the traffic variables (e.g. traffic density and velocity) using partially observed data, as an example to demonstrate the performance of our proposed model. We conduct numerical experiments where the proposed model is applied to learn the solutions of stochastic differential equations. The results demonstrate the robustness and accuracy of the proposed model, together with the ability to learn a machine learning surrogate model. We also test it on a real-world dataset, the Next Generation SIMulation (NGSIM), to show that the proposed TrafficFlowGAN can outperform the baselines, including the pure flow model, the physics-informed flow model, and the flow based GAN model.

This paper develops a reinforcement learning (RL) scheme for adaptive traffic signal control (ATSC), called "CVLight", that leverages data collected only from connected vehicles (CV). Seven types of RL models are proposed within this scheme that contain various state and reward representations, including incorporation of CV delay and green light duration into state and the usage of CV delay as reward. To further incorporate information of both CV and non-CV into CVLight, an algorithm based on actorcritic, A2C-Full, is proposed where both CV and non-CV information is used to train the critic network, while only CV information is used to update the policy network and execute optimal signal timing. These models are compared at an isolated intersection under various CV market penetration rates. A full model with the best performance (i.e., minimum average travel delay per vehicle) is then selected and applied to compare with state-of-the-art benchmarks under different levels of traffic demands, turning proportions, and dynamic traffic demands, respectively. Two case studies are performed on an isolated intersection and a corridor with three consecutive intersections located in Manhattan, New York, to further demonstrate the effectiveness of the proposed algorithm under real-world scenarios. Compared to other baseline models that use all vehicle information, the trained CVLight agent can efficiently control multiple intersections solely based on CV data and can achieve a similar or even greater performance when the CV penetration rate is no less than 20%.