Long-lived states in synchronized traffic flow: empirical prompt and dynamical trap model

Experimental study of short-range interactions in vehicular traffic

Single vehicle data obtained from magnetic loops on an expressway allowed us to measure velocity correlations and velocity differences between non-neighbor vehicles on the same lane, showing some strong correlations even for platoons of 7 or 8 vehicles. The corresponding time headway distribution for non-neighbor vehicles is also presented. We were also able to get some informations about interlane structures, through crossed time headway distributions. It should be noticed that these last results on crossed time headways are meaningful only because the subset of data we used corresponds to a unique stationary traffic state and still contains a large amount of data, with a large fraction of short time headways. The link with passing maneuvers is discussed.

Characteristics of vehicular traffic flow at a roundabout

We construct a stochastic cellular automata model for the description of vehicular traffic at a roundabout designed at the intersection of two perpendicular streets. The vehicular traffic is controlled by a self-organized scheme in which traffic lights are absent. This controlling method incorporates a yield-at-entry strategy for the approaching vehicles to the circulating traffic flow in the roundabout. Vehicular dynamics is simulated and the delay experienced by the traffic at each individual street is evaluated. We discuss the impact of the geometrical properties of the roundabout on the total delay. We compare our results with traffic-light signalization schemes, and obtain the critical traffic volume over which the intersection is optimally controlled through traffic-light signalization schemes.

Empirical test for cellular automaton models of traffic flow

Based on a detailed microscopic test scenario motivated by recent empirical studies of single-vehicle data, several cellular automaton models for traffic flow are compared. We find three levels of agreement with the empirical data: (1) models that do not reproduce even qualitatively the most important empirical observations, (2) models that are on a macroscopic level in reasonable agreement with the empirics, and (3) models that reproduce the empirical data on a microscopic level as well. Our results are not only relevant for applications, but also shed light on the relevant interactions in traffic flow.

Steady-state solutions of hydrodynamic traffic models

We investigate steady-state solutions of hydrodynamic traffic models in the absence of any intrinsic inhomogeneity on roads such as on-ramps. It is shown that typical hydrodynamic models possess seven different types of inhomogeneous steady-state solutions. The seven solutions include those that have been reported previously only for microscopic models. The characteristic properties of wide jam such as moving velocity of its spatiotemporal pattern and/or out-flux from wide jam are shown to be uniquely determined and thus independent of initial conditions of dynamic evolution. Topological considerations suggest that all of the solutions should be common to a wide class of traffic models. The results are discussed in connection with the universality conjecture for traffic models. Also the prevalence of the limit-cycle solution in a recent study of a microscopic model is explained in this approach.

Interpreting the wide scattering of synchronized traffic data by time gap statistics

Based on the statistical evaluation of experimental single-vehicle data, we propose a quantitative interpretation of the erratic scattering of flow-density data in synchronized traffic flows. A correlation analysis suggests that the dynamical flow-density data are well compatible with the so-called jam line characterizing fully developed traffic jams, if one takes into account the variation of their propagation speed due to the large variation of the netto time gaps (the inhomogeneity of traffic flow). The form of the time gap distribution depends not only on the density, but also on the measurement cross section: The most probable netto time gap in congested traffic flow upstream of a bottleneck is significantly increased compared to uncongested freeway sections. Moreover, we identify different power-law scaling laws for the relative variance of netto time gaps as a function of the sampling size. While the exponent is -1 in free traffic corresponding to statistically independent time gaps, the exponent is about -2/3 in congested traffic flow because of correlations between queued vehicles.

Memory effects in microscopic traffic models and wide scattering in flow-density data

By means of microscopic simulations we show that noninstantaneous adaptation of the driving behavior to the traffic situation together with the conventional method to measure flow-density data provides a possible explanation for the observed inverse-lambda shape and the wide scattering of flow-density data in "synchronized" congested traffic. We model a memory effect in the response of drivers to the traffic situation for a wide class of car-following models by introducing an additional dynamical variable (the "subjective level of service") describing the adaptation of drivers to the surrounding traffic situation during the past few minutes and couple this internal state to parameters of the underlying model that are related to the driving style. For illustration, we use the intelligent-driver model (IDM) as the underlying model, characterize the level of service solely by the velocity, and couple the internal variable to the IDM parameter "time gap" to model an increase of the time gap in congested traffic ("frustration effect"), which is supported by single-vehicle data. We simulate open systems with a bottleneck and obtain flow-density data by implementing "virtual detectors." The shape, relative size, and apparent "stochasticity" of the region of the scattered data points agree nearly quantitatively with empirical data. Wide scattering is even observed for identical vehicles, although the proposed model is a time-continuous, deterministic, single-lane car-following model with a unique fundamental diagram.

Fluctuation of riding passengers induced by chaotic motions of shuttle buses

We study the fluctuation of the number of riding passengers in a few shuttle buses that pass each other freely. We present a dynamical model of the shuttle buses that takes into account the maximum capacity of a bus. The dynamics of the buses is expressed in terms of a coupled nonlinear map with noise. The number of passengers carried by a bus and the time headway between buses exhibit complex behavior with varying trips. It is found that the behavior of the buses exhibits deterministic chaos even if there is no noise. The chaotic motion depends on the loading parameter, the maximum capacity of a bus, the bus's speed, and the number of buses. When the loading parameter is larger than a threshold value, each bus carries a full load of passengers throughout its trip. The dependence of the threshold (transition point) on both capacity and speed is clarified.