Two-dimensional LWR model for lane-free traffic

While macroscopic models for single or multi-lane traffic flow are well established, these models are not applicable to the dynamics and characteristics of disordered traffic which is characterized by widely different types of vehicles and no lane discipline. We propose a first-order two-dimensional Lighthill-Whitham-Richards (LWR) model for the continuous macroscopic longitudinal and lateral dynamics of this type of traffic flow. The continuity equation is extended into two dimensions and the equation is closed by assuming a longitudinal flow-density relationship as in traditional one-dimensional models while the lateral dynamics is based on boundary repulsion and a desire of a majority of the drivers to go to less dense regions. This is equivalent to Fick's law giving rise to a lateral diffusion term. Using the proposed model, several numerical tests were conducted under different traffic scenarios representing a wide range of traffic conditions. Even for extreme initial conditions, the model's outcome turned out to be plausible and consistent with observed traffic flow dynamics. Moreover, the numerical convergence test is performed using an analytical solution for lateral steady-state conditions. The model was applied for bicycle simulation and reproduced the evolution of lateral density profile with asymmetric behavior

A two-dimensional data-driven model for traffic flow on highways

Based on experimental traffic data obtained from German and US highways, we propose a novel two-dimensional first-order macroscopic traffic flow model. The goal is to reproduce a detailed description of traffic dynamics for the real road geometry. In our approach both the dynamic along the road and across the lanes is continuous. The closure relations, being necessary to complete the hydrodynamic equation, are obtained by regression on fundamental diagram data. Comparison with prediction of one-dimensional models shows the improvement in performance of the novel model.Comment: 27 page

The BGK approximation of kinetic models for traffic

We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by deriving a modified formulation of the BGK-type equation. The new kinetic model allows to reproduce conditionally stable non-equilibrium phenomena in traffic flow. In particular, stop and go waves appear as bounded backward propagating signals occurring in bounded regimes of the density where the model is unstable. The BGK-type model introduced here also offers the mesoscopic description between the microscopic follow-the-leader model and the macroscopic Aw-Rascle and Zhang model

Two Lane Traffic Simulations using Cellular Automata

We examine a simple two lane cellular automaton based upon the single lane CA introduced by Nagel and Schreckenberg. We point out important parameters defining the shape of the fundamental diagram. Moreover we investigate the importance of stochastic elements with respect to real life traffic.Comment: to be published in Physica A, 19 pages, 9 out of 13 postscript figures, 24kB in format .tar.gz., 33kB in format .tar.gz.uu, for a full version including all figures see http://studguppy.tsasa.lanl.gov/research_team/papers

Derivation and stability analysis of macroscopic multi-lane models for vehicular traffic flow

The mathematical modeling and the stability analysis of multi-lane traffic in the macroscopic scale is considered. We propose a new first order model derived from microscopic dynamics with lane changing, leading to a coupled system of hyperbolic balance laws. The macroscopic limit is derived without assuming ad hoc space and time scalings. The analysis of the stability of the equilibria of the model is discussed. The proposed numerical tests confirm the theoretical findings between the macroscopic and microscopic modeling, and the results of the stability analysis

Coordination and Analysis of Connected and Autonomous Vehicles in Freeway On-Ramp Merging Areas

Freeway on-ramps are typical bottlenecks in the freeway network, where the merging maneuvers of ramp vehicles impose frequent disturbances on the traffic flow and cause negative impacts on traffic safety and efficiency. The emerging Connected and Autonomous Vehicles (CAVs) hold the potential for regulating the behaviors of each individual vehicle and are expected to substantially improve the traffic operation at freeway on-ramps. The aim of this research is to explore the possibilities of optimally facilitating freeway on-ramp merging operation through the coordination of CAVs, and to discuss the impacts of CAVs on the traffic performance at on-ramp merging.In view of the existing research efforts and gaps in the field of CAV on-ramp merging operation, a novel CAV merging coordination strategy is proposed by creating large gaps on the main road and directing the ramp vehicles into the created gaps in the form of platoon. The combination of gap creation and platoon merging jointly facilitates the mainline and ramp traffic and targets at the optimal performance at the traffic flow level. The coordination consists of three components: (1) mainline vehicles proactively decelerate to create large merging gaps; (2) ramp vehicles form platoons before entering the main road; (3) the gaps created on the main road and the platoons formed on the ramp are coordinated with each other in terms of size, speed, and arrival time. The coordination is analytically formulated as an optimization problem, incorporating the macroscopic and microscopic traffic flow models. The model uses traffic state parameters as inputs and determines the optimal coordination plan adaptive to real-time traffic conditions.The impacts of CAV coordination strategies on traffic efficiency are investigated through illustrative case studies conducted on microscopic traffic simulation platforms. The results show substantial improvements in merging efficiency, throughput, and traffic flow stability. In addition, the safety benefits of CAVs in the absence of specially designed cooperation strategies are investigated to reveal the CAV’s ability to eliminate critical human factors in the ramp merging process