Analysis of kinematic waves arising in diverging traffic flow models

Diverging junctions are important network bottlenecks, and a better understanding of diverging traffic dynamics has both theoretical and practical implications. In this paper, we first introduce a continuous multi-commodity kinematic wave model of diverging traffic and then present a new framework for constructing kinematic wave solutions to its Riemann problem with jump initial conditions. In supply-demand space, the solutions on a link consist of an interior state and a stationary state, subject to admissible conditions such that there are no positive and negative kinematic waves on the upstream and downstream links respectively. In addition, the solutions have to satisfy entropy conditions consistent with various discrete diverge models. In the proposed analytical framework, kinematic waves on each link can be uniquely determined by the stationary and initial conditions, and we prove that the stationary states and boundary fluxes exist and are unique for the Riemann problem of diverge models when all or partial of vehicles have predefined routes. We show that the two diverge models by Lebacque and Daganzo are asymptotically equivalent. We also prove that the supply-proportional and priority-based diverge models are locally optimal evacuation strategies. With numerical examples, we demonstrate the validity of the analytical solutions of interior states, stationary states, and corresponding kinematic waves. This study presents a unified framework for analyzing traffic dynamics arising in diverging traffic and could be helpful for developing emergency evacuation strategies.Comment: 48 pages, 14 figure

Stability and bifurcation in network traffic flow: A Poincar\'e map approach

Previous studies have shown that, in a diverge-merge network with two intermediate links (the DM network), the kinematic wave model always admits stationary solutions under constant boundary conditions, but periodic oscillations can develop from empty initial conditions. Such contradictory observations suggest that the stationary states be unstable. In this study we develop a new approach to investigate the stability property of traffic flow in this and other networks. Based on the observation that kinematic waves propagate in a circular path when only one of the two intermediate links is congested, we derive a one-dimensional, discrete Poincar\'e map in the out-flux at a Poincar\'e section. We then prove that the fixed points of the Poincar\'e map correspond to stationary flow-rates on the two links. With Lyapunov's first method, we demonstrate that the Poincar\'e map can be finite-time stable, asymptotically stable, or unstable. When unstable, the map is found to have periodical points of period two, but no chaotic solutions. Comparing the results with those in existing studies, we conclude that the Poincar\'e map can be used to represent network-wide dynamics in the kinematic wave model. We further analyze the bifurcation in the stability of the Poincar\'e map caused by varying route choice proportions. We further apply the Poincar\'e map approach to analyzing traffic patterns in more general $(DM)^n$ and beltway networks, which are sufficient and necessary structures for network-induced unstable traffic and gridlock, respectively. This study demonstrates that the Poincar\'e map approach can be efficiently applied to analyze traffic dynamics in any road networks with circular information propagation and provides new insights into unstable traffic dynamics caused by interactions among network bottlenecks.Comment: 31 pages, 10 figures, 2 table

Kinematic Wave Models of Network Vehicular Traffic

The kinematic wave theory, originally proposed by (Lighthill and Whitham, 1955b; Richards, 1956), has been a good candidate for studying vehicular traffic. In this dissertation, we study kinematic wave models of network traffic, which are expected to be theoretically rigorous, numerically reliable, and computationally efficient. For traffic systems with inhomogeneous links, merges, diverges, or mixed-type vehicles, we study the kinematic waves in their Riemann solutions and develop numerical solution methods of the Godunov type and the supply-demand type. For a network traffic system, we propose a multi-commodity kinematic wave (MCKW) model and an implementation of it. The model observes First-In-First-Out principle in the order of a time interval and is numerically convergent. Further, we apply this simulation model to study equilibrium states and periodic waves in road networks. Finally, we summarize our work and discuss future research directions.Comment: Ph.D. Dissertation. UC Davis. 218 pages, 12 tables, 61 figure

The State-of-the-art of Coordinated Ramp Control with Mixed Traffic Conditions

Ramp metering, a traditional traffic control strategy for conventional vehicles, has been widely deployed around the world since the 1960s. On the other hand, the last decade has witnessed significant advances in connected and automated vehicle (CAV) technology and its great potential for improving safety, mobility and environmental sustainability. Therefore, a large amount of research has been conducted on cooperative ramp merging for CAVs only. However, it is expected that the phase of mixed traffic, namely the coexistence of both human-driven vehicles and CAVs, would last for a long time. Since there is little research on the system-wide ramp control with mixed traffic conditions, the paper aims to close this gap by proposing an innovative system architecture and reviewing the state-of-the-art studies on the key components of the proposed system. These components include traffic state estimation, ramp metering, driving behavior modeling, and coordination of CAVs. All reviewed literature plot an extensive landscape for the proposed system-wide coordinated ramp control with mixed traffic conditions.Comment: 8 pages, 1 figure, IEEE INTELLIGENT TRANSPORTATION SYSTEMS CONFERENCE - ITSC 201

Vision-Based Lane-Changing Behavior Detection Using Deep Residual Neural Network

Accurate lane localization and lane change detection are crucial in advanced driver assistance systems and autonomous driving systems for safer and more efficient trajectory planning. Conventional localization devices such as Global Positioning System only provide road-level resolution for car navigation, which is incompetent to assist in lane-level decision making. The state of art technique for lane localization is to use Light Detection and Ranging sensors to correct the global localization error and achieve centimeter-level accuracy, but the real-time implementation and popularization for LiDAR is still limited by its computational burden and current cost. As a cost-effective alternative, vision-based lane change detection has been highly regarded for affordable autonomous vehicles to support lane-level localization. A deep learning-based computer vision system is developed to detect the lane change behavior using the images captured by a front-view camera mounted on the vehicle and data from the inertial measurement unit for highway driving. Testing results on real-world driving data have shown that the proposed method is robust with real-time working ability and could achieve around 87% lane change detection accuracy. Compared to the average human reaction to visual stimuli, the proposed computer vision system works 9 times faster, which makes it capable of helping make life-saving decisions in time