1,281 research outputs found
Cellular automata approach to three-phase traffic theory
The cellular automata (CA) approach to traffic modeling is extended to allow
for spatially homogeneous steady state solutions that cover a two dimensional
region in the flow-density plane. Hence these models fulfill a basic postulate
of a three-phase traffic theory proposed by Kerner. This is achieved by a
synchronization distance, within which a vehicle always tries to adjust its
speed to the one of the vehicle in front. In the CA models presented, the
modelling of the free and safe speeds, the slow-to-start rules as well as some
contributions to noise are based on the ideas of the Nagel-Schreckenberg type
modelling. It is shown that the proposed CA models can be very transparent and
still reproduce the two main types of congested patterns (the general pattern
and the synchronized flow pattern) as well as their dependence on the flows
near an on-ramp, in qualitative agreement with the recently developed continuum
version of the three-phase traffic theory [B. S. Kerner and S. L. Klenov. 2002.
J. Phys. A: Math. Gen. 35, L31]. These features are qualitatively different
than in previously considered CA traffic models. The probability of the
breakdown phenomenon (i.e., of the phase transition from free flow to
synchronized flow) as function of the flow rate to the on-ramp and of the flow
rate on the road upstream of the on-ramp is investigated. The capacity drops at
the on-ramp which occur due to the formation of different congested patterns
are calculated.Comment: 55 pages, 24 figure
Mechanical restriction versus human overreaction triggering congested traffic states
A new cellular automaton (CA) traffic model is presented. The focus is on
mechanical restrictions of vehicles realized by limited acceleration and
deceleration capabilities. These features are incorporated into the model in
order to construct the condition of collision-free movement. The strict
collision-free criterion imposed by the mechanical restrictions is softened in
certain traffic situations, reflecting human overreaction. It is shown that the
present model reliably reproduces most empirical findings including
synchronized flow, the so-called {\it pinch effect}, and the time-headway
distribution of free flow. The findings suggest that many free flow phenomena
can be attributed to the platoon formation of vehicles ({\it platoon effect})Comment: 5 pages, 3 figures, to appear in PR
Stability Analysis of Optimal Velocity Model for Traffic and Granular Flow under Open Boundary Condition
We analyzed the stability of the uniform flow solution in the optimal
velocity model for traffic and granular flow under the open boundary condition.
It was demonstrated that, even within the linearly unstable region, there is a
parameter region where the uniform solution is stable against a localized
perturbation. We also found an oscillatory solution in the linearly unstable
region and its period is not commensurate with the periodicity of the car index
space. The oscillatory solution has some features in common with the
synchronized flow observed in real traffic.Comment: 4 pages, 6 figures. Typos removed. To appear in J. Phys. Soc. Jp
General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems
An asymptotic method for finding instabilities of arbitrary -dimensional
large-amplitude patterns in a wide class of reaction-diffusion systems is
presented. The complete stability analysis of 2- and 3-dimensional localized
patterns is carried out. It is shown that in the considered class of systems
the criteria for different types of instabilities are universal. The specific
nonlinearities enter the criteria only via three numerical constants of order
one. The performed analysis explains the self-organization scenarios observed
in the recent experiments and numerical simulations of some concrete
reaction-diffusion systems.Comment: 21 pages (RevTeX), 8 figures (Postscript). To appear in Phys. Rev. E
(April 1st, 1996
Traffic Network Optimum Principle - Minimum Probability of Congestion Occurrence
We introduce an optimum principle for a vehicular traffic network with road
bottlenecks. This network breakdown minimization (BM) principle states that the
network optimum is reached, when link flow rates are assigned in the network in
such a way that the probability for spontaneous occurrence of traffic breakdown
at one of the network bottlenecks during a given observation time reaches the
minimum possible value. Based on numerical simulations with a stochastic
three-phase traffic flow model, we show that in comparison to the well-known
Wardrop's principles the application of the BM principle permits considerably
greater network inflow rates at which no traffic breakdown occurs and,
therefore, free flow remains in the whole network.Comment: 22 pages, 6 figure
Derivation, Properties, and Simulation of a Gas-Kinetic-Based, Non-Local Traffic Model
We derive macroscopic traffic equations from specific gas-kinetic equations,
dropping some of the assumptions and approximations made in previous papers.
The resulting partial differential equations for the vehicle density and
average velocity contain a non-local interaction term which is very favorable
for a fast and robust numerical integration, so that several thousand freeway
kilometers can be simulated in real-time. The model parameters can be easily
calibrated by means of empirical data. They are directly related to the
quantities characterizing individual driver-vehicle behavior, and their optimal
values have the expected order of magnitude. Therefore, they allow to
investigate the influences of varying street and weather conditions or freeway
control measures. Simulation results for realistic model parameters are in good
agreement with the diverse non-linear dynamical phenomena observed in freeway
traffic.Comment: For related work see
http://www.theo2.physik.uni-stuttgart.de/helbing.html and
http://www.theo2.physik.uni-stuttgart.de/treiber.htm
Microscopic features of moving traffic jams
Empirical and numerical microscopic features of moving traffic jams are
presented. Based on a single vehicle data analysis, it is found that within
wide moving jams, i.e., between the upstream and downstream jam fronts there is
a complex microscopic spatiotemporal structure. This jam structure consists of
alternations of regions in which traffic flow is interrupted and flow states of
low speeds associated with "moving blanks" within the jam. Empirical features
of the moving blanks are found. Based on microscopic models in the context of
three-phase traffic theory, physical reasons for moving blanks emergence within
wide moving jams are disclosed. Structure of moving jam fronts is studied based
in microscopic traffic simulations. Non-linear effects associated with moving
jam propagation are numerically investigated and compared with empirical
results.Comment: 19 pages, 12 figure
Physics of traffic gridlock in a city
Based of simulations of a stochastic three-phase traffic flow model, we
reveal that at a signalized city intersection under small link inflow rates at
which a vehicle queue developed during the red phase of light signal dissolves
fully during the green phase, i.e., no traffic gridlock should be expected,
nevertheless, traffic breakdown with the subsequent city gridlock occurs with
some probability after a random time delay. This traffic breakdown is initiated
by a first-order phase transition from free flow to synchronized flow occurring
upstream of the vehicle queue at light signal. The probability of traffic
breakdown at light signal is an increasing function of the link inflow rate and
duration of the red phase of light signal
Solitons and kinks in a general car-following model
We study a car-following model of traffic flow which assumes only that a
car's acceleration depends on its own speed, the headway ahead of it, and the
rate of change of headway, with only minimal assumptions about the functional
form of that dependence. The velocity of uniform steady flow is found
implicitly from the acceleration function, and its linear stability criterion
can be expressed simply in terms of it. Crucially, unlike in previously
analyzed car-following models, the threshold of absolute stability does not
generally coincide with an inflection point in the steady velocity function.
The Burgers and KdV equations can be derived under the usual assumptions, but
the mKdV equation arises only when absolute stability does coincide with an
inflection point. Otherwise, the KdV equation applies near absolute stability,
while near the inflection point one obtains the mKdV equation plus an extra,
quadratic term. Corrections to the KdV equation "select" a single member of the
one-parameter set of soliton solutions. In previous models this has always
marked the threshold of a finite- amplitude instability of steady flow, but
here it can alternatively be a stable, small-amplitude jam. That is, there can
be a forward bifurcation from steady flow. The new, augmented mKdV equation
which holds near an inflection point admits a continuous family of kink
solutions, like the mKdV equation, and we derive the selection criterion
arising from the corrections to this equation.Comment: 25 page
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