Related papers: The Aw-Rascle-Zhang model with constraints
We consider a system of two conservation laws and provide a detailed description of both classical and non-classical self-similar Riemann solutions. In particular, we demonstrate the existence of overcompressive delta shocks as singular…
We consider a class of convex optimization problems modelling temporal mass transport and mass change between two given mass distributions (the so-called dynamic formulation of unbalanced transport), where we focus on those models for which…
We study forward and inverse problems for a semilinear radiative transport model where the absorption coefficient depends on the angular average of the transport solution. Our first result is the well-posedness theory for the transport…
The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…
We describe traffic flows in one lane roadways using kinetic theory, with special emphasis on the role of quenched randomness in the velocity distributions. When passing is forbidden, growing clusters are formed behind slow cars and the…
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…
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…
We investigate optimal mass transport problem of affine-nonlinear dynamical systems with input and density constraints. Three algorithms are proposed to tackle this problem, including two Uzawa-type methods and a splitting algorithm based…
A uni-directional two-lane road is approximated by a set of two parallel closed one-dimensional chains. Two types of car i.e. slow and fast ones are considered in the system. Based on the Nagel-Schreckenberg (Na-Sch) model of traffic flow,…
We study the multi-dimensional Euler-alignment system with a matrix-valued communication kernel, motivated by models of anticipation dynamics in collective behaviour. A key feature of this system is its formal equivalence to a nonlocal…
Adaptive cruise control systems are fundamental components of the automation of the driving. At upper control level, ACC systems are based on car-following models determining the acceleration rate of a vehicle according to the distance gap…
Moving and fixed bottlenecks are moving or fixed capacity restrictions that affect the propagation of traffic flow. They are a very important modeling approach to describe the effects of slow vehicles and traffic signals in transportation…
This paper investigates the well-posedness of contact discontinuity solutions and the vanishing pressure limit for the Aw-Rascle traffic flow model with general pressure functions. The well-posedness problem is formulated as a free boundary…
With the prevailing of mobility as a service (MaaS), it becomes increasingly important to manage multi-traffic modes simultaneously and cooperatively. As an important component of MaaS, short-term passenger flow prediction for multi-traffic…
The problem of traffic congestion not only causes a large amount of economic losses, but also seriously endangers the urban environment. Predicting traffic congestion has important practical significance. So far, most studies have been…
We review our analytical and numerical results obtained on the microscopic Follow-The-Leader (FTL) many particle approximation of one-dimensional conservation laws. More precisely, we introduce deterministic particle schemes for the Hughes…
In this paper, a particle method is used to approximate the solutions of a "fluid-like" macroscopic traffic flow model for automated vehicles. It is shown that this method preserves certain differential inequalities that hold for the…
A field deterministic model of the vehicular dynamics in a generic urban street canyon with two neighboring canyons is considered. The assumed hydrodynamical model of vehicular movement is coupled to the gasdynamical model of the air and…
Traffic congestion and violations pose significant challenges for urban mobility and road safety. Traditional traffic monitoring systems, such as fixed cameras and sensor-based methods, are often constrained by limited coverage, low…
Driving in urban environments often presents difficult situations that require expert maneuvering of a vehicle. These situations become even more challenging when considering large vehicles, such as buses. We present a path planning…