Related papers: Side-Constrained Dynamic Traffic Equilibria
Stochastic effects significantly influence the dynamics of traffic flows. Many dynamic traffic assignment (DTA) models attempt to capture these effects by prescribing a specific ratio that determines how flow splits across different routes…
The residual queue during a given study period (e.g., peak hour) is an important feature that should be considered when solving a traffic assignment problem under equilibrium for strategic traffic planning. Although studies have focused…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
Recently we proposed an extension to the traffic model of Aw, Rascle and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse $\lambda$ shape of the fundamental…
In this paper, a new model for traffic on roads with multiple lanes is developed, where the vehicles do not adhere to a lane discipline. Assuming identical vehicles, the dynamics is split along two independent directions: the Y-axis…
The unreal high flows may appear on the actually congested links in the result when a monotonically increasing link travel time function of flow volume is adopted in traffic assignment. The fixed link flow results of a static traffic…
While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…
It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong…
Traffic flow is a very prominent example of a driven non-equilibrium system. A characteristic phenomenon of traffic dynamics is the spontaneous and abrupt drop of the average velocity on a stretch of road leading to congestion. Such a…
We have revealed physical features of autonomous driving in the framework of the three-phase traffic theory for which there is no fixed time headway to the preceding vehicle. A comparison with the classical model approach to autonomous…
We introduce a general formulation for an implicit equation-free method in the setting of slow-fast systems. First, we give a rigorous convergence result for equation-free analysis showing that the implicitly defined coarse-level time…
The Static User Equilibrium is a powerful framework for the theoretical study of traffic. Despite the restricting assumption of stationary flows that intuitively limit its application to real traffic systems, many operational models…
The balanced vehicular traffic model is a macroscopic model for vehicular traffic flow. We use this model to study the traffic dynamics at highway bottlenecks either caused by the restriction of the number of lanes or by on-ramps or…
In this Doctoral Dissertation we propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special (multilevel) type. We propose different…
Simple physical models based on fluid mechanics have long been used to understand the flow of vehicular traffic on freeways; analytically tractable models of flow on an urban grid, however, have not been as extensively explored. In an ideal…
Statistical mechanics of a disordered system of cars on a single-lane road is developed. Behaviour of cars is defined by conditional probability of car velocity depending on the distance and velocity of the car ahead. A system consisting of…
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…
We present a new fluid-dynamical model of traffic flow. This model generalizes the model of Aw and Rascle [SIAM J. Appl. Math. 60 916-938] and Greenberg [SIAM J. Appl. Math 62 729-745] by prescribing a more general source term to the…
We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian…
As a typical self-driven many-particle system far from equilibrium, traffic flow exhibits diverse fascinating non-equilibrium phenomena, most of which are closely related to traffic flow stability and specifically the growth/dissipation…