Related papers: Fundamentals of Traffic Flow
Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and…
From single vehicle data a number of new empirical results about the temporal evolution, correlation, and density-dependence of macroscopic traffic quantities have been determined. These have relevant implications for traffic modeling and…
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…
To gain essential understandings of traffic flow, four theorems are derived to establish the kinematics of the basic unit of traffic flow, namely two consecutive vehicles. The first is to determine the two critical distances of the vehicle…
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…
In this paper we study dependencies of fundamental diagrams, time gap distributions, and velocity-distance relations on vehicle types, lanes and/or measurement sites. We also propose measurement and aggregation methods that have more…
Due to the complexity of the traffic flow dynamics in urban road networks, most quantitative descriptions of city traffic so far are based on computer simulations. This contribution pursues a macroscopic (fluid-dynamic) simulation approach,…
By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear…
We present large scale and detailed analysis of the microscopic empirical data of the traffic flow, focusing on the non-linear interactions between the vehicles when the traffic is congested. By implementing a "renormalisation" procedure…
In the present paper single-vehicle data of highway traffic are analyzed in great detail. By using the single-vehicle data directly empirical time-headway distributions and speed-distance relations can be established. Both quantities yield…
A discrete model of traffic on a multilane road is considered. The traffic is presented as particles movement with a deterministic component and a stochastic one. Formulas for the traffic characteristics have been found. The model can…
The paper analyzes traffic data of the Dutch freeway A9 with respect to certain aspects which are relevant for traffic flow modeling as well as the calibration of model parameters and functions. Apart from the dynamic velocity distribution,…
The scientific field of traffic engineering encompasses a rich set of mathematical techniques, as well as researchers with entirely different backgrounds. This paper provides an overview of what is currently the state-of-the-art with…
Statistical mechanics of a small system of cars on a single-lane road is developed. The system is not characterized by a Hamiltonian but by a conditional probability of a velocity of a car for the given velocity and distance of the car…
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…
Recent advances in time series, where deterministic and stochastic modelings as well as the storage and analysis of big data are useless, permit a new approach to short-term traffic flow forecasting and to its reliability, i.e., to the…
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…
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…
We present a detailed analysis of single-vehicle data which sheds some light on the microscopic interaction of the vehicles. Besides the analysis of free flow and synchronized traffic the data sets especially provide information about wide…
We study traffic flow on roads with a localized periodic inhomogeneity such as traffic signals, using a stochastic car-following model. We find that in cases of congestion, traffic flow can be optimized by controlling the inhomogeneity's…