Related papers: Reaction-Diffusion Models describing a Two-Lane Tr…
A detailed description and validation of a recently developed integration scheme is here reported for one- and two-dimensional reaction-diffusion models. As paradigmatic examples of this class of partial differential equations the complex…
The theory of urban traffic flow has been developed and new types of meta-automata have emerged and simulate realistic traffic conditions relatively well. Among these models, the brake light model can simulate the three-phase traffic flow…
A system of identical cars on a single-lane road is treated as a microcanonical and canonical ensemble. Behaviour of the cars is characterized by the probability of car velocity as a function of distance and velocity of the car ahead. The…
In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…
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…
We consider a system of ordered cars moving in $\R$ from right to left. Each car is represented by a point in $\R$; two or more cars can occupy the same point but cannot overpass. Cars have two possible velocities: either 0 or 1. An…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…
We treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
This work presents algebraic closure models associated with advective transport and nonlinear reactions in a Reynolds-averaged Navier-Stokes context for a system of species subject to binary reactions and transport by advection and…
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…
We introduced a probability of traffic light, PL, at an intersection when approaching cars in two roads are in same conditions. As a application, we proposed a modified Nagel-Schreckenberg cellular automata model for describing a…
In this paper, the influence of fan-shaped buffer zone on the performance of the toll plaza is researched. A two-dimensional traffic flow model and a comprehensive evaluation model based on mechanical model and psychological field are…
A one-dimensional reaction-diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and…
We have studied the front propagation in a one dimensional case of combustion by solving numerically an advection-reaction-diffusion equation. The physical model is simplified so that no coupling phenomena are considered and the reacting…
We extend the classical LWR traffic model allowing different maximal speeds to different vehicles. Then, we add a uniform bound on the traffic speed. The result, presented in this paper, is a new macro- scopic model displaying 2 phases,…
Authors describe a two-stage traffic assignment model. It contains of two blocks. The first block consists of model for calculating correspondence (demand) matrix, whereas the second block is a traffic assignment model. The first model…
Modeling how network-level traffic flow changes in the urban environment is useful for decision-making in transportation, public safety and urban planning. The traffic flow system can be viewed as a dynamic process that transits between…
In this paper, we introduce a traffic flow model based on a microscopic follow-the-leader model, while enforcing maximal constraints on the density and velocity of the flow. The related macroscopic model can be represented in conservative…
We study random velocity effects on a two-species reaction-diffusion system consisting of three reaction processes $A + A \rightarrow (\varnothing, A),A+B \rightarrow A$. Using the field-theoretic perturbative renormalization group we…