Related papers: Ergodic properties of a simple deterministic traff…
We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical…
This work addresses the problem of learning the dynamics of high-dimensional probability densities over time using unlabeled samples, without assuming access to trajectory information. We introduce two-parameter flows that learn only…
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…
This paper offers an integrative data-driven physics-inspired approach to model and control traffic congestion in a resilient and efficient manner. While existing physics-based approaches commonly assign density and flow traffic states by…
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…
Symbolic dynamics, which partitions an infinite number of finite-length trajectories into a finite number of trajectory sets, describes the dynamics of a system in a simplified and coarse-grained way with a limited number of symbols. The…
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…
Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of…
Density fluctuations in traffic current are studied by computer simulations using the deterministic coupled map lattice model on a closed single-lane circuit. By calculating a power spectral density of temporal density fluctuations at a…
The present paper proposes a novel interpretation of the widely scattered states (called synchronized traffic) stimulated by Kerner's hypotheses about the existence of a multitude of metastable states in the fundamental diagram. Using…
A successful method to describe the asymptotic behavior of various deterministic and stochastic processes such as asymptotically autonomous differential equations or stochastic approximation processes is to relate it to an appropriately…
We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars…
Recent literature has proved that stable dynamic routing algorithms have solid theoretical foundation that makes them suitable to be implemented in a real protocol, and used in practice in many different operational network contexts. Such…
Intermittent maps of the interval are simple and widely-studied models for chaos with slow mixing rates, but have been notoriously resistant to numerical study. In this paper we present an effective framework to compute many ergodic…
A new vehicular traffic flow model based on a stochastic jump process in vehicle acceleration and braking is introduced. It is based on a master equation for the single car probability density in space, velocity and acceleration with an…
This paper studies a stochastic model that describes the evolution of vehicle densities in a road network. It is consistent with the class of (deterministic) kinematic wave models, which describe traffic flows on the basis of conservation…
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…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…
We study the microscopic time fluctuations of traffic-load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates $R$ the traffic is stationary and the load…
We study the dynamics of a transformation that acts on infinite paths in the graph associated with Pascal's triangle. For each ergodic invariant measure the asymptotic law of the return time to cylinders is given by a step function. We…