677 research outputs found
Upper Bounds for the Critical Car Densities in Traffic Flow Problems
In most models of traffic flow, the car density is the only free
parameter in determining the average car velocity . The
critical car density , which is defined to be the car density separating
the jamming phase (with ) and the moving phase (with
), is an important physical quantity to investigate. By
means of simple statistical argument, we show that for the
Biham-Middleton-Levine model of traffic flow in two or higher spatial
dimensions. In particular, we show that in 2 dimension and
in () dimensions.Comment: REVTEX 3.0, 5 pages with 1 figure appended at the back, Minor
revision, to be published in the Sept issue of J.Phys.Soc.Japa
Towards a variational principle for motivated vehicle motion
We deal with the problem of deriving the microscopic equations governing the
individual car motion based on the assumptions about the strategy of driver
behavior. We suppose the driver behavior to be a result of a certain compromise
between the will to move at a speed that is comfortable for him under the
surrounding external conditions, comprising the physical state of the road, the
weather conditions, etc., and the necessity to keep a safe headway distance
between the cars in front of him. Such a strategy implies that a driver can
compare the possible ways of his further motion and so choose the best one. To
describe the driver preferences we introduce the priority functional whose
extremals specify the driver choice. For simplicity we consider a single-lane
road. In this case solving the corresponding equations for the extremals we
find the relationship between the current acceleration, velocity and position
of the car. As a special case we get a certain generalization of the optimal
velocity model similar to the "intelligent driver model" proposed by Treiber
and Helbing.Comment: 6 pages, RevTeX
Anisotropic effect on two-dimensional cellular automaton traffic flow with periodic and open boundaries
By the use of computer simulations we investigate, in the cellular automaton
of two-dimensional traffic flow, the anisotropic effect of the probabilities of
the change of the move directions of cars, from up to right () and from
right to up (), on the dynamical jamming transition and velocities
under the periodic boundary conditions in one hand and the phase diagram under
the open boundary conditions in the other hand. However, in the former case,
the first order jamming transition disappears when the cars alter their
directions of move ( and/or ). In the open boundary
conditions, it is found that the first order line transition between jamming
and moving phases is curved. Hence, by increasing the anisotropy, the moving
phase region expand as well as the contraction of the jamming phase one.
Moreover, in the isotropic case, and when each car changes its direction of
move every time steps (), the transition from the jamming
phase (or moving phase) to the maximal current one is of first order.
Furthermore, the density profile decays, in the maximal current phase, with an
exponent .}Comment: 13 pages, 22 figure
Analytical Results For The Steady State Of Traffic Flow Models With Stochastic Delay
Exact mean field equations are derived analytically to give the fundamental
diagrams, i.e., the average speed - car density relations, for the
Fukui-Ishibashi one-dimensional traffic flow cellular automaton model of high
speed vehicles with stochastic delay. Starting with the basic
equation describing the time evolution of the number of empty sites in front of
each car, the concepts of inter-car spacings longer and shorter than are
introduced. The probabilities of having long and short spacings on the road are
calculated. For high car densities , it is shown that
inter-car spacings longer than will be shortened as the traffic flow
evolves in time, and any initial configurations approach a steady state in
which all the inter-car spacings are of the short type. Similarly for low car
densities , it can be shown that traffic flow approaches an
asymptotic steady state in which all the inter-car spacings are longer than
. The average traffic speed is then obtained analytically as a function of
car density in the asymptotic steady state. The fundamental diagram so obtained
is in excellent agreement with simulation data.Comment: 12 pages, latex, 2 figure
The Effect Of Delay Times On The Optimal Velocity Traffic Flow Behavior
We have numerically investigated the effect of the delay times and
of a mixture of fast and slow vehicles on the fundamental diagram of
the optimal velocity model. The optimal velocity function of the fast cars
depends not only on the headway of each car but also on the headway of the
immediately preceding one. It is found that the small delay times have almost
no effects, while, for sufficiently large delay time the current
profile displays qualitatively five different forms depending on ,
and the fractions and of the fast and slow cars
respectively. The velocity (current) exhibits first order transitions at low
and/or high densities, from freely moving phase to the congested state, and
from congested state to the jamming one respectively accompanied by the
existence of a local minimal current. Furthermore, there exist a critical value
of above which the metastability and hysteresis appear. The
spatial-temporal traffic patterns present more complex structur
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
A Cellular Automaton Model for Bi-Directionnal Traffic
We investigate a cellular automaton (CA) model of traffic on a bi-directional
two-lane road. Our model is an extension of the one-lane CA model of {Nagel and
Schreckenberg 1992}, modified to account for interactions mediated by passing,
and for a distribution of vehicle speeds. We chose values for the various
parameters to approximate the behavior of real traffic. The density-flow
diagram for the bi-directional model is compared to that of a one-lane model,
showing the interaction of the two lanes. Results were also compared to
experimental data, showing close agreement. This model helps bridge the gap
between simplified cellular automata models and the complexity of real-world
traffic.Comment: 4 pages 6 figures. Accepted Phys Rev
A realistic two-lane traffic model for highway traffic
A two-lane extension of a recently proposed cellular automaton model for
traffic flow is discussed. The analysis focuses on the reproduction of the lane
usage inversion and the density dependence of the number of lane changes. It is
shown that the single-lane dynamics can be extended to the two-lane case
without changing the basic properties of the model which are known to be in
good agreement with empirical single-vehicle data. Therefore it is possible to
reproduce various empirically observed two-lane phenomena, like the
synchronization of the lanes, without fine-tuning of the model parameters
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
Diffusion limited aggregation as a Markovian process. Part I: bond-sticking conditions
Cylindrical lattice Diffusion Limited Aggregation (DLA), with a narrow width
N, is solved using a Markovian matrix method. This matrix contains the
probabilities that the front moves from one configuration to another at each
growth step, calculated exactly by solving the Laplace equation and using the
proper normalization. The method is applied for a series of approximations,
which include only a finite number of rows near the front. The matrix is then
used to find the weights of the steady state growing configurations and the
rate of approaching this steady state stage. The former are then used to find
the average upward growth probability, the average steady-state density and the
fractal dimensionality of the aggregate, which is extrapolated to a value near
1.64.Comment: 24 pages, 20 figure
- …