319 research outputs found
A Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process
A new vehicular traffic flow model based on a stochastic jump process in
vehicle acceleration and braking is introduced. It is based on a master
equation for the single car probability density in space, velocity and
acceleration with an additional vehicular chaos assumption and is derived via a
Markovian ansatz for car pairs. This equation is analyzed using simple driver
interaction models in the spatial homogeneous case. Velocity distributions in
stochastic equilibrium, together with the car density dependence of their
moments, i.e. mean velocity and scattering and the fundamental diagram are
presented.Comment: 27 pages, 6 figure
Order parameter model for unstable multilane traffic flow
We discuss a phenomenological approach to the description of unstable vehicle
motion on multilane highways that explains in a simple way the observed
sequence of the phase transitions "free flow -> synchronized motion -> jam" as
well as the hysteresis in the transition "free flow synchronized motion".
We introduce a new variable called order parameter that accounts for possible
correlations in the vehicle motion at different lanes. So, it is principally
due to the "many-body" effects in the car interaction, which enables us to
regard it as an additional independent state variable of traffic flow. Basing
on the latest experimental data (cond-mat/9905216) we assume that these
correlations are due to a small group of "fast" drivers. Taking into account
the general properties of the driver behavior we write the governing equation
for the order parameter. In this context we analyze the instability of
homogeneous traffic flow manifesting itself in both of the mentioned above
phase transitions where, in addition, the transition "synchronized motion ->
jam" also exhibits a similar hysteresis. Besides, the jam is characterized by
the vehicle flows at different lanes being independent of one another. We
specify a certain simplified model in order to study the general features of
the car cluster self-formation under the phase transition "free flow
synchronized motion". In particular, we show that the main local parameters of
the developed cluster are determined by the state characteristics of vehicle
motion only.Comment: REVTeX 3.1, 10 pages with 10 PostScript figure
Kinetic derivation of a Hamilton-Jacobi traffic flow model
Kinetic models for vehicular traffic are reviewed and considered from the
point of view of deriving macroscopic equations. A derivation of the associated
macroscopic traffic flow equations leads to different types of equations: in
certain situations modified Aw-Rascle equations are obtained. On the other
hand, for several choices of kinetic parameters new Hamilton-Jacobi type
traffic equations are found. Associated microscopic models are discussed and
numerical experiments are presented discussing several situations for highway
traffic and comparing the different models
A class of multi-phase traffic theories for microscopic, kinetic and continuum traffic models
In the present paper a review and numerical comparison of a special class of
multi-phase traffic theories based on microscopic, kinetic and macroscopic
traffic models is given. Macroscopic traffic equations with multi-valued
fundamental diagrams are derived from different microscopic and kinetic models.
Numerical experiments show similarities and differences of the models, in
particular, for the appearance and structure of stop and go waves for highway
traffic in dense situations. For all models, but one, phase transitions can
appear near bottlenecks depending on the local density and velocity of the
flow
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
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
The BGK approximation of kinetic models for traffic
We study spatially non-homogeneous kinetic models for vehicular traffic flow.
Classical formulations, as for instance the BGK equation, lead to
unconditionally unstable solutions in the congested regime of traffic. We
address this issue by deriving a modified formulation of the BGK-type equation.
The new kinetic model allows to reproduce conditionally stable non-equilibrium
phenomena in traffic flow. In particular, stop and go waves appear as bounded
backward propagating signals occurring in bounded regimes of the density where
the model is unstable. The BGK-type model introduced here also offers the
mesoscopic description between the microscopic follow-the-leader model and the
macroscopic Aw-Rascle and Zhang model
Analysis of a heterogeneous kinetic model for traffic flow
In this work we extend a recent kinetic traffic model to the case of more
than one class of vehicles, each of which is characterized by few different
microscopic features. We consider a Boltzmann-like framework with only binary
interactions, which take place among vehicles belonging to the various classes.
Our approach differs from the multi-population kinetic model based on a lattice
of speeds because here we assume continuous velocity spaces and we introduce a
parameter describing the physical velocity jump performed by a vehicle that
increases its speed after an interaction. The model is discretized in order to
investigate numerically the structure of the resulting fundamental diagrams and
the system of equations is analyzed by studying well posedness. Moreover, we
compute the equilibria of the discretized model and we show that the exact
asymptotic kinetic distributions can be obtained with a small number of
velocities in the grid. Finally, we introduce a new probability law in order to
attenuate the sharp capacity drop occurring in the diagrams of traffic.Comment: 31 page
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