752 research outputs found
Modelling supported driving as an optimal control cycle: Framework and model characteristics
Driver assistance systems support drivers in operating vehicles in a safe,
comfortable and efficient way, and thus may induce changes in traffic flow
characteristics. This paper puts forward a receding horizon control framework
to model driver assistance and cooperative systems. The accelerations of
automated vehicles are controlled to optimise a cost function, assuming other
vehicles driving at stationary conditions over a prediction horizon. The
flexibility of the framework is demonstrated with controller design of Adaptive
Cruise Control (ACC) and Cooperative ACC (C-ACC) systems. The proposed ACC and
C-ACC model characteristics are investigated analytically, with focus on
equilibrium solutions and stability properties. The proposed ACC model produces
plausible human car-following behaviour and is unconditionally locally stable.
By careful tuning of parameters, the ACC model generates similar stability
characteristics as human driver models. The proposed C-ACC model results in
convective downstream and absolute string instability, but not convective
upstream string instability observed in human-driven traffic and in the ACC
model. The control framework and analytical results provide insights into the
influences of ACC and C-ACC systems on traffic flow operations.Comment: Submitted to Transportation Research Part C: Emerging Technologie
Memory effects in microscopic traffic models and wide scattering in flow-density data
By means of microscopic simulations we show that non-instantaneous adaptation
of the driving behaviour to the traffic situation together with the
conventional measurement method of flow-density data can explain the observed
inverse- 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 a new dynamical variable describing the adaptation of drivers to
the surrounding traffic situation during the past few minutes (``subjective
level of service'') 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 underlying model, characterize the
level of service solely by the velocity and couple the internal variable to the
IDM parameter ``netto time gap'', modelling an increase of the time gap in
congested traffic (``frustration effect''), that is supported by single-vehicle
data. % We simulate open systems with a bottleneck and obtain flow-density data
by implementing ``virtual detectors''. Both 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.Comment: 8 pages, submitted to Physical Review
The statistical properties of the city transport in Cuernavaca (Mexico) and Random matrix ensembles
We analyze statistical properties of the city bus transport in Cuernavaca
(Mexico) and show that the bus arrivals display probability distributions
conforming those given by the Unitary Ensemble of random matrices.Comment: 4 pages, 3 figure
Calibrating Car-Following Models using Trajectory Data: Methodological Study
The car-following behavior of individual drivers in real city traffic is
studied on the basis of (publicly available) trajectory datasets recorded by a
vehicle equipped with an radar sensor. By means of a nonlinear optimization
procedure based on a genetic algorithm, we calibrate the Intelligent Driver
Model and the Velocity Difference Model by minimizing the deviations between
the observed driving dynamics and the simulated trajectory when following the
same leading vehicle. The reliability and robustness of the nonlinear fits are
assessed by applying different optimization criteria, i.e., different measures
for the deviations between two trajectories. The obtained errors are in the
range between~11% and~29% which is consistent with typical error ranges
obtained in previous studies. In addition, we found that the calibrated
parameter values of the Velocity Difference Model strongly depend on the
optimization criterion, while the Intelligent Driver Model is more robust in
this respect. By applying an explicit delay to the model input, we investigated
the influence of a reaction time. Remarkably, we found a negligible influence
of the reaction time indicating that drivers compensate for their reaction time
by anticipation. Furthermore, the parameter sets calibrated to a certain
trajectory are applied to the other trajectories allowing for model validation.
The results indicate that ``intra-driver variability'' rather than
``inter-driver variability'' accounts for a large part of the calibration
errors. The results are used to suggest some criteria towards a benchmarking of
car-following models
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.Comment: For related publications see http://www.helbing.or
Direct observation of twist mode in electroconvection in I52
I report on the direct observation of a uniform twist mode of the director
field in electroconvection in I52. Recent theoretical work suggests that such a
uniform twist mode of the director field is responsible for a number of
secondary bifurcations in both electroconvection and thermal convection in
nematics. I show here evidence that the proposed mechanisms are consistent with
being the source of the previously reported SO2 state of electroconvection in
I52. The same mechanisms also contribute to a tertiary Hopf bifurcation that I
observe in electroconvection in I52. There are quantitative differences between
the experiment and calculations that only include the twist mode. These
differences suggest that a complete description must include effects described
by the weak-electrolyte model of electroconvection
Towards a Macroscopic Modelling of the Complexity in Traffic Flow
We present a macroscopic traffic flow model that extends existing fluid-like
models by an additional term containing the second derivative of the safe
velocity. Two qualitatively different shapes of the safe velocity are explored:
a conventional Fermi-type function and a function exhibiting a plateau at
intermediate densities. The suggested model shows an extremely rich dynamical
behaviour and shows many features found in real-world traffic data.Comment: submitted to Phys. Rev.
Estimating Acceleration and Lane-Changing Dynamics Based on NGSIM Trajectory Data
The NGSIM trajectory data sets provide longitudinal and lateral positional
information for all vehicles in certain spatiotemporal regions. Velocity and
acceleration information cannot be extracted directly since the noise in the
NGSIM positional information is greatly increased by the necessary numerical
differentiations. We propose a smoothing algorithm for positions, velocities
and accelerations that can also be applied near the boundaries. The smoothing
time interval is estimated based on velocity time series and the variance of
the processed acceleration time series. The velocity information obtained in
this way is then applied to calculate the density function of the
two-dimensional distribution of velocity and inverse distance, and the density
of the distribution corresponding to the ``microscopic'' fundamental diagram.
Furthermore, it is used to calculate the distributions of time gaps and
times-to-collision, conditioned to several ranges of velocities and velocity
differences. By simulating virtual stationary detectors we show that the
probability for critical values of the times-to-collision is greatly
underestimated when estimated from single-vehicle data of stationary detectors.
Finally, we investigate the lane-changing process and formulate a quantitative
criterion for the duration of lane changes that is based on the trajectory
density in normalized coordinates. Remarkably, there is a very noisy but
significant velocity advantage in favor of the targeted lane that decreases
immediately before the change due to anticipatory accelerations
Autonomous detection and anticipation of jam fronts from messages propagated by inter-vehicle communication
In this paper, a minimalist, completely distributed freeway traffic
information system is introduced. It involves an autonomous, vehicle-based jam
front detection, the information transmission via inter-vehicle communication,
and the forecast of the spatial position of jam fronts by reconstructing the
spatiotemporal traffic situation based on the transmitted information. The
whole system is simulated with an integrated traffic simulator, that is based
on a realistic microscopic traffic model for longitudinal movements and lane
changes. The function of its communication module has been explicitly validated
by comparing the simulation results with analytical calculations. By means of
simulations, we show that the algorithms for a congestion-front recognition,
message transmission, and processing predict reliably the existence and
position of jam fronts for vehicle equipment rates as low as 3%. A reliable
mode of operation already for small market penetrations is crucial for the
successful introduction of inter-vehicle communication. The short-term
prediction of jam fronts is not only useful for the driver, but is essential
for enhancing road safety and road capacity by intelligent adaptive cruise
control systems.Comment: Published in the Proceedings of the Annual Meeting of the
Transportation Research Board 200
Long-lived states in synchronized traffic flow. Empirical prompt and dynamical trap model
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 single vehicle data collected at the German highway A1, temporal velocity
patterns have been analyzed to show a collection of certain fragments with
approximately constant velocities and sharp jumps between them. The particular
velocity values in these fragments vary in a wide range. In contrast, the flow
rate is more or less constant because its fluctuations are mainly due to the
discreteness of traffic flow.
Subsequently, we develop a model for synchronized traffic that can explain
these characteristics. Following previous work (I.A.Lubashevsky, R.Mahnke,
Phys. Rev. E v. 62, p. 6082, 2000) the vehicle flow is specified by car
density, mean velocity, and additional order parameters and that are
due to the many-particle effects of the vehicle interaction. The parameter
describes the multilane correlations in the vehicle motion. Together with the
car density it determines directly the mean velocity. The parameter , in
contrast, controls the evolution of only. The model assumes that
fluctuates randomly around the value corresponding to the car configuration
optimal for lane changing. When it deviates from this value the lane change is
depressed for all cars forming a local cluster. Since exactly the overtaking
manoeuvres of these cars cause the order parameter to vary, the evolution
of the car arrangement becomes frozen for a certain time. In other words, the
evolution equations form certain dynamical traps responsible for the long-time
correlations in the synchronized mode.Comment: 16 pages, 10 figures, RevTeX
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