Related papers: Side-Constrained Dynamic Traffic Equilibria
Fluid dynamics corresponds to the dynamics of a substance in the long wavelength limit. Writing down all terms in a gradient (long wavelength) expansion up to second order for a relativistic system at vanishing charge density, one obtains…
We study the nonlinear realization of supersymmetry in a dynamical/cosmological background in which derivative terms like kinetic terms are finite. Starting from linearly realized theories, we integrate out heavy modes without neglecting…
This work studies a macroscopic traffic flow model driven by a system of nonlinear hyperbolic partial differential equations. Using Lie symmetry analysis, we determine the infinitesimal generators and construct an optimal system of…
Macroscopic traffic models have recently been severely criticized to base on lax analogies only and to have a number of deficiencies. Therefore, this paper shows how to construct a logically consistent fluid-dynamic traffic model from basic…
In this paper we study a dynamic vehicle routing problem in which there are multiple vehicles and multiple classes of demands. Demands of each class arrive in the environment randomly over time and require a random amount of on-site service…
In dynamical systems governed by differential equations, a guarantee that trajectories emanating from a given set of initial conditions do not enter another given set can be obtained by constructing a barrier function that satisfies certain…
A model equation has been proposed to describe bimodal features in vehicular traffic flows. The dynamics of the bimodal distribution reveals the existence of a fixed point that is connected to itself by a homoclinic trajectory. The…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
Theoretical advances in the study of non-equilibrium phenomena are briefly reviewed with emphasis on steady state properties of one-dimensional driven lattice gases. The presentation is focused on the totally asymmetric simple-exclusion…
This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
We examine the duality theory for a class of non-convex functions obtained by composing a convex function with a continuous one. Using Fenchel duality, we derive a dual problem that satisfies weak duality under general assumptions. To…
This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…
Recent studies on transportation networks have shown that real-time route guidance can inadvertently induce congestion or oscillatory traffic patterns. Nevertheless, such technologies also offer a promising opportunity to manage traffic…
Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms.…
We study non-terminating graph rewriting models, whose local rules are applied non-deterministically -- and yet enjoy a strong form of determinism, namely space-time determinism. Of course in the case of terminating computation it is…
This paper presents a rigorous analytical model of traffic dynamics on a circular track, demonstrating the emergence of standing oscillations resulting from microscopic driver behaviour, delay responses, and proximity pressure. Without…
A partially hinged, partially free rectangular plate is considered, with the aim to address the possible unstable end behaviors of a suspension bridge subject to wind. This leads to a nonlinear plate evolution equation with a nonlocal…
Motivated by microscopic traffic modeling, we analyze dynamical systems which have a piecewise linear concave dynamics not necessarily monotonic. We introduce a deterministic Petri net extension where edges may have negative weights. The…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…