Related papers: Stability Analysis of Optimal Velocity Model for T…
The spatio-temporal structure of traffic flow pattern is investigated under the open boundary condition using the optimal velocity (OV) model. The parameter region where the uniform solution is convectively unstable is determined. It is…
A generalized optimal velocity model is analyzed, where the optimal velocity function depends not only on the headway of each car but also the headway of the immediately preceding one. The stability condition of the model is derived by…
We consider the stability of a system of equations which are a singular perturbation of the incompressible rigid-plastic flow equations used to model granular flow. A linear stability analysis shows that solutions of these equations are…
In the optimal velocity model with a time lag, we show that there appear multiple exact solutions in some ranges of car density, describing a uniform flow, a stable and an unstable congested flows. This establishes the presence of…
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,…
We study numerically the stability of granular flow on a rough slope in collisional flow regime in the two-dimension. We examine the density dependence of the flowing behavior in low density region, and demonstrate that the particle…
Oscillatory zoning, i.e. self-formation of spatial quasi-periodic oscillations in the composition of solid growing from aqueous solution, is analyzed theoretically. Keeping in mind systems like (Ba,Sr)SO4 we propose a 1D model that takes…
In this letter we propose an optimization-based boundary controller for traffic flow dynamics capable of achieving both stability and invariance conditions. The approach is based on the definition of Boundary Control Barrier Functionals,…
We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larger space of perturbation than previous results. Furthermore,…
In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this…
In the Optimal Velocity Model proposed as a new version of Car Following Model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established…
The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena.…
An accurate system to study the stability of pipe flow that ensures regularity is presented. The system produces a spectrum that is as accurate as Meseguer \& Trefethen (2000), while providing flexibility to amend the boundary conditions…
This paper studies steady-state traffic flow on a ring road with up- and down- slopes using a semi-discrete model. By exploiting the relations between the semi-discrete and the continuum models, a steady-state solution is uniquely…
The emerging connected and automated vehicle technologies allow vehicles to perceive and process traffic information in a wide spatial range. Modeling nonlocal interactions between connected vehicles and analyzing their impact on traffic…
Traffic flow oscillations, including traffic waves, are a common yet incompletely understood feature of congested traffic. Possible mechanisms include traffic flow instabilities, indifference regions or finite human perception thresholds…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
This paper investigates the mathematical modeling and the stability of multi-lane traffic in the microscopic scale, studying a model based on two interaction terms. To do this we propose simple lane changing conditions and we study the…
The initial boundary value problem for a class of scalar non autonomous conservation laws in one space dimension is proved to be well posed and stable with respect to variations in the flux. Targeting applications to traffic, the regularity…
The paper provides results for a non-standard, hyperbolic, 1-D, nonlinear traffic flow model on a bounded domain. The model consists of two first-order PDEs with a dynamic boundary condition that involves the time derivative of the…