81 research outputs found
Metastable States in Cellular Automata for Traffic Flow
Measurements on real traffic have revealed the existence of metastable states
with very high flow. Such states have not been observed in the
Nagel-Schreckenberg (NaSch) model which is the basic cellular automaton for the
description of traffic. Here we propose a simple generalization of the NaSch
model by introducing a velocity-dependent randomization. We investigate a
special case which belongs to the so-called slow-to-start rules. It is shown
that this model exhibits metastable states, thus sheding some light on the
prerequisites for the occurance of hysteresis effects in the flow-density
relation.Comment: 15 pages, 8 ps-figures included; accepted for publication in EPJ
Localized defects in a cellular automaton model for traffic flow with phase separation
We study the impact of a localized defect in a cellular automaton model for
traffic flow which exhibits metastable states and phase separation. The defect
is implemented by locally limiting the maximal possible flow through an
increase of the deceleration probability. Depending on the magnitude of the
defect three phases can be identified in the system. One of these phases shows
the characteristics of stop-and-go traffic which can not be found in the model
without lattice defect. Thus our results provide evidence that even in a model
with strong phase separation stop-and-go traffic can occur if local defects
exist. From a physical point of view the model describes the competition
between two mechanisms of phase separation.Comment: 14 pages, 7 figure
On- and Off-ramps Generating 1/f Noise in Traffic Flow
A simple model of a motorway junction consisting of two connected periodic roads is presented; each of them is connected to the other by on- and off-ramps. This constitutes a detailed structure for the region of on- and off-ramps, which is a new aspect of this paper and a useful step towards a more realistic modelling of the vehicular dynamics near the ramps. The traffic flow through the ramps has an effect on the capacity of the main roads. This effect is identified by the formation of the so-called āplateauā in the fundamental diagram. The value increase of one of the probabilities pin and pout decreases the value of the indicated plateau. Here pin is the probability to enter the main road through the on-ramp and pout denotes the probability to exit the main road through the off-ramp. The first important feature in the simulated system is the symmetry between the connected main roads. This symmetry does not depend on the variation of the difference between the probabilities pin and pout. The other most outstanding feature is the existence of correlations between the connected main roads, which can be traced back to the lane change of vehicles in the ramp regions. These correlations are characterized by the occurrence of 1/fĪ± fluctuations in the global traffic flow of a chosen main road of the simulated system.A simple model of a motorway junction consisting of two connected periodic roads is presented; each of them is connected to the other by on- and off-ramps. This constitutes a detailed structure for the region of on- and off-ramps, which is a new aspect of this paper and a useful step towards a more realistic modelling of the vehicular dynamics near the ramps. The traffic flow through the ramps has an effect on the capacity of the main roads. This effect is identified by the formation of the so-called āplateauā in the fundamental diagram. The value increase of one of the probabilities pin and pout decreases the value of the indicated plateau. Here pin is the probability to enter the main road through the on-ramp and pout denotes the probability to exit the main road through the off-ramp. The first important feature in the simulated system is the symmetry between the connected main roads. This symmetry does not depend on the variation of the difference between the probabilities pin and pout. The other most outstanding feature is the existence of correlations between the connected main roads, which can be traced back to the lane change of vehicles in the ramp regions. These correlations are characterized by the occurrence of 1/fĪ± fluctuations in the global traffic flow of a chosen main road of the simulated system
Optimizing Traffic Lights in a Cellular Automaton Model for City Traffic
We study the impact of global traffic light control strategies in a recently
proposed cellular automaton model for vehicular traffic in city networks. The
model combines basic ideas of the Biham-Middleton-Levine model for city traffic
and the Nagel-Schreckenberg model for highway traffic. The city network has a
simple square lattice geometry. All streets and intersections are treated
equally, i.e., there are no dominant streets. Starting from a simple
synchronized strategy we show that the capacity of the network strongly depends
on the cycle times of the traffic lights. Moreover we point out that the
optimal time periods are determined by the geometric characteristics of the
network, i.e., the distance between the intersections. In the case of
synchronized traffic lights the derivation of the optimal cycle times in the
network can be reduced to a simpler problem, the flow optimization of a single
street with one traffic light operating as a bottleneck. In order to obtain an
enhanced throughput in the model improved global strategies are tested, e.g.,
green wave and random switching strategies, which lead to surprising results.Comment: 13 pages, 10 figure
Condensation Transitions in a One-Dimensional Zero-Range Process with a Single Defect Site
Condensation occurs in nonequilibrium steady states when a finite fraction of
particles in the system occupies a single lattice site. We study condensation
transitions in a one-dimensional zero-range process with a single defect site.
The system is analysed in the grand canonical and canonical ensembles and the
two are contrasted. Two distinct condensation mechanisms are found in the grand
canonical ensemble. Discrepancies between the infinite and large but finite
systems' particle current versus particle density diagrams are investigated and
an explanation for how the finite current goes above a maximum value predicted
for infinite systems is found in the canonical ensemble.Comment: 18 pages, 4 figures, revtex
Breakdown and recovery in traffic flow models
Most car-following models show a transition from laminar to ``congested''
flow and vice versa. Deterministic models often have a density range where a
disturbance needs a sufficiently large critical amplitude to move the flow from
the laminar into the congested phase. In stochastic models, it may be assumed
that the size of this amplitude gets translated into a waiting time, i.e.\
until fluctuations sufficiently add up to trigger the transition. A recently
introduced model of traffic flow however does not show this behavior: in the
density regime where the jam solution co-exists with the high-flow state, the
intrinsic stochasticity of the model is not sufficient to cause a transition
into the jammed regime, at least not within relevant time scales. In addition,
models can be differentiated by the stability of the outflow interface. We
demonstrate that this additional criterion is not related to the stability of
the flow. The combination of these criteria makes it possible to characterize
commonalities and differences between many existing models for traffic in a new
way
Fuzzy cellular model for on-line traffic simulation
This paper introduces a fuzzy cellular model of road traffic that was
intended for on-line applications in traffic control. The presented model uses
fuzzy sets theory to deal with uncertainty of both input data and simulation
results. Vehicles are modelled individually, thus various classes of them can
be taken into consideration. In the proposed approach, all parameters of
vehicles are described by means of fuzzy numbers. The model was implemented in
a simulation of vehicles queue discharge process. Changes of the queue length
were analysed in this experiment and compared to the results of NaSch cellular
automata model.Comment: The original publication is available at http://www.springerlink.co
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
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