Data-Driven Three-Phase Fundamental Diagram for Traffic Modeling

Macroscopic traffic flow models are widely used to estimate traffic status on a freeway, and the fundamental diagram (FD), that establishes a relationship between density and flux, is essential for these models to be effective. By visualizing the 2005 traffic trajectory data from Next Generation SIMulation (NGSIM) project on US Highway 101 and Interstate 80 in California, we observed three states of traffic condition: free flow, mildly congested flow, and highly congested flow; and the resulting shockwaves. The FD is critical in understanding the shockwave phenomenon of congested flow. Therefore, there is a need to develop a more accurate FD that captures the complexity of the density-flux relation observed in the empirical data. For this we develop a three phase FD of traffic flow. In our previous work, a log piecewise linear FD was shown to fit better than some other forms of FD on 2009 traffic data from Interstate 95 in Virginia. However, the previous FD considered two phases, free and congested flow. The three phase modification we propose here is able to distinguish between the highly and the mildly congested flow and explains the resulting shockwaves. The phase transition from mildly to highly congested state changes the nature of the flux-density function from a concave to a convex function of density. In the concave phase a forward moving and in the convex phase a backward moving shock results. This FD can also explain the rarefaction waves that arise in traffic flow. NGSIM data covers every vehicle within its range and we focus our study to the innermost lane. The visualized data is used to fit the three phases. This involved solving an optimization problem to determine the values of the parameters. A close relationship between the backward shockwaves during highly congested phase and the convex part of the FD is observed. A single parameter value (slope of the log-linear function) is shown to predict the various conditions of the traffic: free, mildly and highly congested flow. The proposed FD can be used in conjunction with any macroscopic traffic flow model, such as LighthillWhithamRichards (LWR), for traffic flow estimation with greatly improved accuracy. A three-phase FD and a stochastic macroscopic traffic flow model can reliably predict future traffic status, and provide advanced information to drivers and transportation authorities for travel planning, traffic management, and other real-time applications.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149454/1/TFTC2016.pd

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

Empirical exploration of air traffic and human dynamics in terminal airspaces

Air traffic is widely known as a complex, task-critical techno-social system, with numerous interactions between airspace, procedures, aircraft and air traffic controllers. In order to develop and deploy high-level operational concepts and automation systems scientifically and effectively, it is essential to conduct an in-depth investigation on the intrinsic traffic-human dynamics and characteristics, which is not widely seen in the literature. To fill this gap, we propose a multi-layer network to model and analyze air traffic systems. A Route-based Airspace Network (RAN) and Flight Trajectory Network (FTN) encapsulate critical physical and operational characteristics; an Integrated Flow-Driven Network (IFDN) and Interrelated Conflict-Communication Network (ICCN) are formulated to represent air traffic flow transmissions and intervention from air traffic controllers, respectively. Furthermore, a set of analytical metrics including network variables, complex network attributes, controllers' cognitive complexity, and chaotic metrics are introduced and applied in a case study of Guangzhou terminal airspace. Empirical results show the existence of fundamental diagram and macroscopic fundamental diagram at the route, sector and terminal levels. Moreover, the dynamics and underlying mechanisms of "ATCOs-flow" interactions are revealed and interpreted by adaptive meta-cognition strategies based on network analysis of the ICCN. Finally, at the system level, chaos is identified in conflict system and human behavioral system when traffic switch to the semi-stable or congested phase. This study offers analytical tools for understanding the complex human-flow interactions at potentially a broad range of air traffic systems, and underpins future developments and automation of intelligent air traffic management systems.Comment: 30 pages, 28 figures, currently under revie

Uncertainty damping in kinetic traffic models by driver-assist controls

In this paper, we propose a kinetic model of traffic flow with uncertain binary interactions, which explains the scattering of the fundamental diagram in terms of the macroscopic variability of aggregate quantities, such as the mean speed and the flux of the vehicles, produced by the microscopic uncertainty. Moreover, we design control strategies at the level of the microscopic interactions among the vehicles, by which we prove that it is possible to dampen the propagation of such an uncertainty across the scales. Our analytical and numerical results suggest that the aggregate traffic flow may be made more ordered, hence predictable, by implementing such control protocols in driver-assist vehicles. Remarkably, they also provide a precise relationship between a measure of the macroscopic damping of the uncertainty and the penetration rate of the driver-assist technology in the traffic stream

Fundamental diagrams for kinetic equations of traffic flow

In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the so-called "spatially homogeneous problem" and, in the representative case of an exploratory model, we study the qualitative properties of its solutions for a generic number of discrete microstates. This includes, in particular, asymptotic trends and equilibria, whence fundamental diagrams originate.Comment: 14 page