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The car-following model is an important micro-traffic model for simulating car-following behaviour in traffic engineering and research studies. Conventional car-following models are always presented using mathematical equations reflecting ideal traffic conditions. In the big data era, data-driven models become a popular trend. In this study, a data-driven car-following model based on the rough set theory is proposed to consider information hidden in a field data set. On the basis of field data obtained from measurement devices such as the next generation simulation (NGSIM) trajectory data set, and using the methods of the rough set theory, an optimal decision rule set is established. Redundant attributes and redundant attribute values are removed for simplifying the car-following behaviour decision problem. Attribute significance and weights are computed for selecting matching rules. A car-following behaviour decision algorithm is designed to choose appropriate rules to determine the follower's velocity according to current observations. Simulations illustrate that the proposed data-driven car-following model can simulate the micro-traffic behaviour of followers well. [ABSTRACT FROM AUTHOR]

This article proposes a numerical scheme for computing the evolution of vehicular traffic on a road network over a finite time horizon. The traffic dynamics on each link is modeled by the Hamilton{Jacobi (HJ) partial differential equation (PDE), which is an equivalent form of the Lighthill{Whitham{Richards PDE. The main contribution of this article is the construction of a single convex optimization program which computes the traffic ow at a junction over a finite time horizon and decouples the PDEs on connecting links. Compared to discretization schemes which require the computation of all traffic states on a time-space grid, the proposed convex optimization approach computes the boundary ows at the junction using only the initial condition on links and the boundary conditions of the network. The computed boundary ows at the junction specify the boundary condition for the HJ PDE on connecting links, which then can be separately solved using an existing semi-explicit scheme for single link HJ PDE. As demonstrated in a numerical example of ramp metering control, the proposed convex optimization approach also provides a natural framework for optimal traffic control applications. [ABSTRACT FROM AUTHOR]

This paper investigates the cell-transmission model (CTM)-based single destination system optimum dynamic traffic assignment (SO-DTA) problem, focusing attention on a case where the cell properties are time-invariant. We show the backward propagation of congestion in CTM does not affect the optimal arrival flow pattern of SO-DTA, if the fundamental diagram is of triangular/trapezoidal shape as in the CTM. We mathematically prove that the set of earliest arrival flows (EAFs) not constrained by the traffic wave propagation equations obtained on the node-arc network without cell division is a subset of the SO-DTA. This finding leads to a new approach to the SO-DTA that solves the EAF. Such an EAF can be obtained by merely applying static flow techniques and turning the static flows into dynamic flows over time. Therefore, SO-DTA can theoretically be solved with a run time at the link level depending polynomially on log T . We use numerical examples to verify the results and report the computational benefits of the proposed method by solving SO-DTA on a real-world network. [ABSTRACT FROM AUTHOR]

Abstract: We study the relation between the average traffic flow and the vehicle density on road networks that we call 2D-traffic fundamental diagram. We show that this diagram presents mainly four phases. We analyze different cases. First, the case of a junction managed with a priority rule is presented, four traffic phases are identified and described, and a good analytic approximation of the fundamental diagram is obtained by computing a generalized eigenvalue of the dynamics of the system. Then, the model is extended to the case of two junctions, and finally to a regular city. The system still presents mainly four phases. The role of a critical circuit of non-priority roads appears clearly in the two junctions case. In “Traffic control”, we use traffic light controls to improve the traffic diagram. We present the improvements obtained by open-loop, local feedback, and global feedback strategies. A comparison based on the response times to reach the stationary regime is also given. Finally, we show the importance of the design of the junction. It appears that if the junction is enough large, the traffic is almost not slowed down by the junction. [ABSTRACT FROM AUTHOR]

Recently, the modelling of heterogeneous traffic flow has gained significant attention from traffic theorists. The influence of slow vehicles (e.g. trucks) on traffic operations has been studied both from a micro and macroscopic level. Though multiclass traffic models have been successfully developed in literature, few of them are adequately used to describe traffic network operations. To this end, this article aims to propose a model to study the (heterogeneous) traffic network operations based on the macroscopic modelling approach. More specifically, on the one hand, we introduce an extension of the classic Lighthill-Whitham-Richards model to describe multiclass traffic operations in the network. The proposed model is based on solving a system of hyperbolic partial differential equations describing multiclass traffic dynamics with discontinuous fluxes. On the other hand, a dynamic routing algorithm is applied to determine the turning flow at nodes based on the information provision of the current network situation. Numerical results have shown that the proposed model can capture some real traffic phenomena in multiclass traffic networks. [ABSTRACT FROM AUTHOR]

Driven many-particle systems with nonlinear interactions are known to often display multi-stability, i.e. depending on the respective initial condition, there may be different outcomes. Here, we study this phenomenon for traffic models, some of which show stable and linearly unstable density regimes, but areas of metastability in between. In these areas, perturbations larger than a certain critical amplitude will cause a lasting breakdown of traffic, while smaller ones will fade away. While there are common methods to study linear instability, non-linear instability had to be studied numerically in the past. Here, we present an analytical study for the optimal velocity model with a stepwise specification of the optimal velocity function and a simple kind of perturbation. Despite various approximations, the analytical results are shown to reproduce numerical results very well. [ABSTRACT FROM AUTHOR]

This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use an approach reminding of smoothed particle hydrodynamics to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the “traffic pressure”, which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others. [ABSTRACT FROM AUTHOR]

There has been a debate in the transportation research community over the validity of a class of traffic flow models. These models have the peculiar property that one of its characteristic speeds is faster than that of vehicular traffic. This note attempts to provide an overview of the diverging views on how to interpret this property, and specific comments on the interpretation of Helbing and Johansson [ On the controversy around Daganzo’s requiem for and Aw-Rascle’s resurrection of second-order traffic flow models, Eur. Phys. J. B (2009), DOI: 10.1140/epjb/e2009-00182-7]. We showed that having faster-than-traffic characteristics does produce counterintuitive predictions, and they cannot be explained away by a linear stability analysis. As such, the existence of such characteristics must be justified by the physics of traffic, and verified through empirical observations. [ABSTRACT FROM AUTHOR]

A number of distinct mathematical models of how traffic flows along a one way stretch of road are considered. Two of the models are shown to have the same mathematical structure, despite corresponding to completely different aspect of traffic flow. A further set of two models provides an example of how to introduce students to the process of making physically meaningful comparisons between models which are based on differing key variables. [ABSTRACT FROM PUBLISHER]