Related papers: A kinetic traffic network model and its macroscopi…
While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…
The evolution of particulate and multiphase systems can transition from dynamic regimes, governed by classical transport equations with well-defined damping coefficients, to anomalously slow relaxation described by rate equations when the…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
In this paper, we present a class of systems of non-local conservation laws in one space-dimension incorporating time delay, which can be used to investigate the interaction between autonomous and human-driven vehicles, each characterized…
We propose a novel scheme to numerically solve scalar conservation laws on networks without the necessity to solve Riemann problems at the junction. The scheme is derived using the relaxation system introduced in [Jin and Xin, Comm. Pure…
The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly…
This paper presents an online smooth-path lane-change control framework. We focus on dense traffic where inter-vehicle space gaps are narrow, and cooperation with surrounding drivers is essential to achieve the lane-change maneuver. We…
In this thesis, Riemann problems and Godunov methods are developed for higher order traffic flow models. A rigorous analysis of the first order traffic flow model of inhomogeneous road is presented. A two-level simulation framework of…
We have developed a modified Nagel-Schreckenberg cellular automata model for describing a conflicting vehicular traffic flow at the intersection of two streets. No traffic lights control the traffic flow. The approaching cars to the…
In this paper we study hyperbolic and parabolic nonlinear partial differential equation models, which describe the evolution of two intersecting pedestrian flows. We assume that individuals avoid collisions by sidestepping, which is encoded…
Cellular traffic prediction is of great importance for operators to manage network resources and make decisions. Traffic is highly dynamic and influenced by many exogenous factors, which would lead to the degradation of traffic prediction…
We propose and analyse a new microscopic second order Follow-the-Leader type scheme to describe traffic flows. The main novelty of this model consists in multiplying the second order term by a nonlinear function of the global density, with…
Random intersection graphs containing an underlying community structure are a popular choice for modelling real-world networks. Given the group memberships, the classical random intersection graph is obtained by connecting individuals when…
We investigate a cellular automaton (CA) model of traffic on a bi-directional two-lane road. Our model is an extension of the one-lane CA model of {Nagel and Schreckenberg 1992}, modified to account for interactions mediated by passing, and…
Vehicular traffic is a classical example of a multi-agent system in which autonomous drivers operate in a shared environment. The article provides an overview of the state-of-the-art in microscopic traffic modeling and the implications for…
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…
Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics such as links, paths, cycles, and components are obtained analytically using the rate…
We rigorously derive the dense graph limit of a discrete model describing the formation of biological transportation networks. The discrete model, defined on undirected graphs with pressure-driven flows, incorporates a convex energy…
We introduce an individual-based model for fiber elements having the ability to cross-link or unlink each other and to align with each other at the cross links. We first formally derive a kinetic model for the fiber and cross-links…
A new coupling rule for the Lighthill-Whitham-Richards model at merging junctions is introduced that imposes the preservation of the ratio between inflow from a given road to the total inflow into the junction. This rule is considered both…