Related papers: Deterministic Models for Traffic Jams
Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and…
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…
A new single lane car following model of traffic flow is presented. The model is inertial and free of collisions. It demonstrates experimentally observed features of traffic flow such as the existence of three regimes: free, fluctuative…
We propose a stochastic model for the intersection of two urban streets. The vehicular traffic at the intersection is controlled by a set of traffic lights which can be operated subject to fix-time as well as traffic adaptive schemes.…
As a dynamical complex system, traffic is characterized by a transition from free flow to congestions, which is mostly studied in highways. However, despite its importance in developing congestion mitigation strategies, the understanding of…
We study a family of deterministic models for highway traffic flow which generalize cellular automaton rule 184. This family is parametrized by the speed limit $m$ and another parameter $k$ that represents a ``degree of aggressiveness'' in…
The Biham, Middleton and Levine (BML) model is extended to describe dynamic route choices between the residence and workplace in cities. The traffic dynamic in the city with a single workplace is studied from the velocity diagram, arrival…
We present a model of traffic flow, with rules that describe the behaviour of automated vehicles in an open system. We show first of all that the fundamental diagram of this system collapses to a point, where states of free and jammed…
This paper presents a mathematical model for the train dynamics in a mass-transit metro line system with one symmetrically operated junction. We distinguish three parts: a central part and two branches. The tracks are spatially discretized…
This article deals with the modeling for an individual car path through a road network, where the dynamics is driven by a coupled system of ordinary and partial differential equations. The network is characterized by bounded buffers at…
Traffic congestion represents a complex urban phenomenon that has been the subject of extensive research employing various modeling techniques grounded in the principles of physics and molecular theory. Although factors such as road design,…
We propose a macroscopic traffic network flow model suitable for analysis as a dynamical system, and we qualitatively analyze equilibrium flows as well as convergence. Flows at a junction are determined by downstream supply of capacity as…
We propose a new model of one-dimensional traffic flow using a coupled map lattice. In the model, each vehicle is assigned a map and changes its velocity according to it. A single map is designed so as to represent the motion of a vehicle…
We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…
The cellular automaton model for traffic flow exhibits a jamming transition from a free-flow phase to a congested phase. In the deterministic case this transition corresponds to a critical point with diverging correlation length. We present…
The dynamical properties of road traffic time series from North-Rhine Westphalian motorways are investigated. The article shows that road traffic dynamics is well described as a persistent stochastic process with two fixed points…
We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential…
We present data from several German freeways showing different kinds of congested traffic forming near road inhomogeneities, specifically lane closings, intersections, or uphill gradients. The states are localized or extended, homogeneous…
We study the microscopic time fluctuations of traffic-load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates $R$ the traffic is stationary and the load…
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…