68 research outputs found
Probabilistic Description of Traffic Breakdowns
We analyze the characteristic features of traffic breakdown. To describe this
phenomenon we apply to the probabilistic model regarding the jam emergence as
the formation of a large car cluster on highway. In these terms the breakdown
occurs through the formation of a certain critical nucleus in the metastable
vehicle flow, which enables us to confine ourselves to one cluster model. We
assume that, first, the growth of the car cluster is governed by attachment of
cars to the cluster whose rate is mainly determined by the mean headway
distance between the car in the vehicle flow and, may be, also by the headway
distance in the cluster. Second, the cluster dissolution is determined by the
car escape from the cluster whose rate depends on the cluster size directly.
The latter is justified using the available experimental data for the
correlation properties of the synchronized mode. We write the appropriate
master equation converted then into the Fokker-Plank equation for the cluster
distribution function and analyze the formation of the critical car cluster due
to the climb over a certain potential barrier. The further cluster growth
irreversibly gives rise to the jam formation. Numerical estimates of the
obtained characteristics and the experimental data of the traffic breakdown are
compared. In particular, we draw a conclusion that the characteristic intrinsic
time scale of the breakdown phenomenon should be about one minute and explain
the case why the traffic volume interval inside which traffic breakdown is
observed is sufficiently wide.Comment: RevTeX 4, 14 pages, 10 figure
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
Phase diagram of congested traffic flow: an empirical study
We analyze traffic data from a highway section containing one effective
on-ramp. Based on two criteria, local velocity variation patterns and expansion
(or nonexpansion) of congested regions, three distinct congested traffic states
are identified. These states appear at different levels of the upstream flux
and the on-ramp flux, thereby generating a phase diagram of the congested
traffic flow. Compared to our earliear reports (including cond-mat/9905292)
based on 14 day traffic data, the present paper uses a much larger data set
(107 days) and the analysis is carried in a more systematic way, which leads to
the modification of a part of interpretation in the earlier reports. Observed
traffic states are compared with recent theoretical analyses and both agreeing
and disagreeing features are found.Comment: More extensive and systematic version of earlier reports (including
cond-mat/9905292). A part of interpretation in earlier reports is modified. 6
two-column pages. To appear in Phys. Rev. E (tentatively scheduled for Oct. 1
issue
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
Human behavior as origin of traffic phases
It is shown that the desire for smooth and comfortable driving is directly
responsible for the occurrence of complex spatio-temporal structures
(``synchronized traffic'') in highway traffic. This desire goes beyond the
avoidance of accidents which so far has been the main focus of microscopic
modeling and which is mainly responsible for the other two phases observed
empirically, free flow and wide moving jams. These features have been
incorporated into a microscopic model based on stochastic cellular automata and
the results of computer simulations are compared with empirical data. The
simple structure of the model allows for very fast implementations of realistic
networks. The level of agreement with the empirical findings opens new
perspectives for reliable traffic forecasts.Comment: 4 pages, 4 figures, colour figures with reduced resolutio
Single-vehicle data of highway traffic - a statistical analysis
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 relevant information about the microscopic states. Several fundamental
diagrams are also presented, which are based on time-averaged quantities and
compared with earlier empirical investigations. In the remaining part
time-series analyses of the averaged as well as the single-vehicle data are
carried out. The results will be used in order to propose objective criteria
for an identification of the different traffic states, e.g. synchronized
traffic.Comment: 12 pages, 19 figures, RevTe
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.Comment: 9 pages, 6 figure
Control of Spatial-Temporal Congested Traffic Patterns at Highway Bottlenecks
A microscopic theory of control of spatial-temporal congested traffic pattern
at freeway bottlenecks is presented. Based on empirical spatial-temporal
features of congested patterns at freeway bottlenecks which have recently been
found, different control strategies for prevention or reducing of the patterns
are simulated and compared. The studied control strategies include the on-ramp
metering with feedback and automatic cruise control (ACC) vehicles. A recent
microscopic traffic flow model within the author's three-phase traffic theory
is used for validation of spatial-temporal congested pattern control.Comment: 19 pages, 7 figure
Cellular Automata Simulating Experimental Properties of Traffic Flows
A model for 1D traffic flow is developed, which is discrete in space and
time. Like the cellular automaton model by Nagel and Schreckenberg [J. Phys. I
France 2, 2221 (1992)], it is simple, fast, and can describe stop-and-go
traffic. Due to its relation to the optimal velocity model by Bando et al.
[Phys. Rev. E 51, 1035 (1995)], its instability mechanism is of deterministic
nature. The model can be easily calibrated to empirical data and displays the
experimental features of traffic data recently reported by Kerner and Rehborn
[Phys. Rev. E 53, R1297 (1996)].Comment: For related work see
http://www.theo2.physik.uni-stuttgart.de/helbing.html and
http://traffic.comphys.uni-duisburg.de/member/home_schreck.htm
Congested Traffic States in Empirical Observations and Microscopic Simulations
We present data from several German freeways showing different kinds of
congested traffic forming near road inhomogeneities, specifically lane
closings, intersections, or uphill gradients. The states are localized or
extended, homogeneous or oscillating. Combined states are observed as well,
like the coexistence of moving localized clusters and clusters pinned at road
inhomogeneities, or regions of oscillating congested traffic upstream of nearly
homogeneous congested traffic. The experimental findings are consistent with a
recently proposed theoretical phase diagram for traffic near on-ramps [D.
Helbing, A. Hennecke, and M. Treiber, Phys. Rev. Lett. {\bf 82}, 4360 (1999)].
We simulate these situations with a novel continuous microscopic single-lane
model, the ``intelligent driver model'' (IDM), using the empirical boundary
conditions. All observations, including the coexistence of states, are
qualitatively reproduced by describing inhomogeneities with local variations of
one model parameter.
We show that the results of the microscopic model can be understood by
formulating the theoretical phase diagram for bottlenecks in a more general
way. In particular, a local drop of the road capacity induced by parameter
variations has practically the same effect as an on-ramp.Comment: Now published in Phys. Rev. E. Minor changes suggested by a referee
are incorporated; full bibliographic info added. For related work see
http://www.mtreiber.de/ and http://www.helbing.org
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