Related papers: Evolution models for mass transportation problems
Schedule-based transit assignment describes congestion in public transport services by modeling the interactions of passenger behavior in a time-space network built directly on a transit schedule. This study investigates the theoretical…
In order to keep a green planet, in particular its important to limiting the pollution with gas emissions. In a specific capacitated fixed-charge transportation problem with fixed capacities for distribution centers and customers with…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
We consider the minimization of the $h$-mass over normal $1$-currents in $\mathbb{R}^n$ with coefficients in $\mathbb{R}^m$ and prescribed boundary. This optimization is known as multi-material transport problem and used in the context of…
The effects of the propagation of particles which have a finite life-time and an according width in their mass spectrum are discussed in the context of transport descriptions. In the first part the coupling of soft photon modes to a source…
We present a new method to derive transport equations for quantum many-particle systems. This method uses an equation-of-motion technique and is applicable to systems with bosons and fermions, arbitrary interactions and time-dependent…
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…
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…
We introduce a new approach to model and analyze \emph{Mobility}. It is fully based on discrete mathematics and yields a class of mobility models, called the \emph{Markov Trace} Model. This model can be seen as the discrete version of the…
The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various…
We introduce and investigate properties of a variant of the semi-discrete optimal transport problem. In this problem, one is given an absolutely continuous source measure and cost function, along with a finite set which will be the support…
This article considers execution and analysis of laboratory experiments of pedestrians moving in a quasi-one-dimensional system with periodic boundary conditions. To analyze characteristics of jams in the system we aim to use the whole…
The paper presents a systematic derivation of macroscopic equations for freeway traffic flow from an Enskog-like kinetic approach. The resulting fluid-dynamic traffic equations for the spatial density, average velocity, and velocity…
The capacity of a street segment quantifies the maximal density of vehicles before congestion arises. Here we show in a simple mathematical model that fluctuations in the instantaneous number of vehicles entering a street segment are…
Recently we proposed an extension to the traffic model of Aw, Rascle and Greenberg. The extended traffic model can be written as a hyperbolic system of balance laws and numerically reproduces the reverse $\lambda$ shape of the fundamental…
We include alignment interactions in a well-studied first-order attractive-repulsive macroscopic model for aggregation. The distinctive feature of the extended model is that the equation that specifies the velocity in terms of the…
In the present paper a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Macroscopic traffic equations with multi-valued fundamental…
Modeling of urban traffic flows is required due to the complexity of their successful forecasting, as well as due to the impact of various random factors on them, and the complexity of transport systems in modern cities. Forecasting of…
Modal shift in public transport as a consequence of a disruption on a line has in some cases unforeseen consequences such as an increase in congestion in the rest of the network. How information is provided to users and their behavior plays…
This is the first part of a general description in terms of mass transport for time-evolving interacting particles systems, at a mesoscopic level. Beyond kinetic theory, our framework naturally applies in biology, computer vision, and…