Related papers: Comparing comparisons between vehicular traffic st…

This paper leverages macroscopic models and multi-source spatiotemporal data collected from automatic traffic counters and probe vehicles to accurately estimate traffic flow and travel time in links where these measurements are unavailable.…

We introduce a formalism to deal with the microscopic modeling of vehicular traffic on a road network. Traffic on each road is uni-directional, and the dynamics of each vehicle is described by a Follow-the-Leader model. From a mathematical…

The relation between flow and density is an essential quantitative characteristic to describe the efficiency of traffic systems. We have performed experiments with single-file motion of bicycles and compare the results with previous studies…

Traffic flow at low densities (free traffic) is characterized by a quasi-one-dimensional relation between traffic flow and vehicle density, while no such fundamental diagram exists for `synchronized' congested traffic flow. Instead, a…

Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the fundamental and speed diagrams) show some peculiarities not yet…

Traffic waves can rise even from single lane car-following behaviour. To better understand and mitigate traffic waves, it is necessary to use analytical tools like mathematical models, data analysis, and micro-simulations that can capture…

Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…

The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…

In this paper we propose two models describing the dynamics of heavy and light vehicles on a road network, taking into account the interactions between the two classes. The models are tailored for two-lane highways where heavy vehicles…

In this paper a comparison between first order microscopic and macroscopic differential models of crowd dynamics is established for an increasing number $N$ of pedestrians. The novelty is the fact of considering massive agents, namely…

We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having…

We consider traffic flow models at different scales of observation. Starting from the well known hierarchy between microscopic, kinetic and macroscopic scales, we will investigate the propagation of uncertainties through the models using…

The goal of this paper is to derive rigorously macroscopic traffic flow models from microscopic models. More precisely, for the microscopic models, we consider follow-the-leader type models with different types of drivers and vehicles which…

Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this…

The simulation of traffic flow on networks requires knowledge on the behavior across traffic intersections. For macroscopic models based on hyperbolic conservation laws there exist nowadays many ad-hoc models describing this behavior. Based…

We introduce microscopic and macroscopic stochastic traffic models including traffic accidents. The microscopic model is based on a Follow-the-Leader approach whereas the macroscopic model is described by a scalar conservation law with…

A driving algorithm that aligns with good human driving practices, or at the very least collaborates effectively with human drivers, is crucial for developing safe and efficient autonomous vehicles. In practice, two main approaches are…

Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing…

Traffic is constrained by the information involved in locating the receiver and the physical distance between sender and receiver. We here focus on the former, and investigate traffic in the perspective of information handling. We re-plot…

We investigate a stochastic model hierarchy for pedestrian flow. Starting from a microscopic social force model, where the pedestrians switch randomly between the two states stop-or-go, we derive an associated macroscopic model of…