133 research outputs found
A stochastic cellular automaton model for traffic flow with multiple metastable states
A new stochastic cellular automaton (CA) model of traffic flow, which
includes slow-to-start effects and a driver's perspective, is proposed by
extending the Burgers CA and the Nagel-Schreckenberg CA model. The flow-density
relation of this model shows multiple metastable branches near the transition
density from free to congested traffic, which form a wide scattering area in
the fundamental diagram. The stability of these branches and their velocity
distributions are explicitly studied by numerical simulations.Comment: 11 pages, 20 figures, submitted for publicatio
Max-plus analysis on some binary particle systems
We concern with a special class of binary cellular automata, i.e., the
so-called particle cellular automata (PCA) in the present paper. We first
propose max-plus expressions to PCA of 4 neighbors. Then, by utilizing basic
operations of the max-plus algebra and appropriate transformations, PCA4-1, 4-2
and 4-3 are solved exactly and their general solutions are found in terms of
max-plus expressions. Finally, we analyze the asymptotic behaviors of general
solutions and prove the fundamental diagrams exactly.Comment: 24 pages, 5 figures, submitted to J. Phys.
Probabilistic cellular automata with conserved quantities
We demonstrate that the concept of a conservation law can be naturally
extended from deterministic to probabilistic cellular automata (PCA) rules. The
local function for conservative PCA must satisfy conditions analogous to
conservation conditions for deterministic cellular automata. Conservation
condition for PCA can also be written in the form of a current conservation
law. For deterministic nearest-neighbour CA the current can be computed
exactly. Local structure approximation can partially predict the equilibrium
current for non-deterministic cases. For linear segments of the fundamental
diagram it actually produces exact results.Comment: 17 pages, 2 figure
Characterizing correlations of flow oscillations at bottlenecks
"Oscillations" occur in quite different kinds of many-particle-systems when
two groups of particles with different directions of motion meet or intersect
at a certain spot. We present a model of pedestrian motion that is able to
reproduce oscillations with different characteristics. The Wald-Wolfowitz test
and Gillis' correlated random walk are shown to hold observables that can be
used to characterize different kinds of oscillations
Discrete symmetry's chains and links between integrable equations
The discrete symmetry's dressing chains of the nonlinear Schrodinger equation
(NLS) and Davey-Stewartson equations (DS) are consider. The modified NLS (mNLS)
equation and the modified DS (mDS) equations are obtained. The explicitly
reversible Backlund auto-transformations for the mNLS and mDS equations are
constructed. We demonstrate discrete symmetry's conjugate chains of the KP and
DS models. The two-dimensional generalization of the P4 equation are obtained.Comment: 20 page
Collective traffic-like movement of ants on a trail: dynamical phases and phase transitions
The traffic-like collective movement of ants on a trail can be described by a
stochastic cellular automaton model. We have earlier investigated its unusual
flow-density relation by using various mean field approximations and computer
simulations. In this paper, we study the model following an alternative
approach based on the analogy with the zero range process, which is one of the
few known exactly solvable stochastic dynamical models. We show that our theory
can quantitatively account for the unusual non-monotonic dependence of the
average speed of the ants on their density for finite lattices with periodic
boundary conditions. Moreover, we argue that the model exhibits a continuous
phase transition at the critial density only in a limiting case. Furthermore,
we investigate the phase diagram of the model by replacing the periodic
boundary conditions by open boundary conditions.Comment: 8 pages, 6 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
Experimental study of pedestrian flow through a bottleneck
In this work the results of a bottleneck experiment with pedestrians are
presented in the form of total times, fluxes, specific fluxes, and time gaps. A
main aim was to find the dependence of these values from the bottleneck width.
The results show a linear decline of the specific flux with increasing width as
long as only one person at a time can pass, and a constant value for larger
bottleneck widths. Differences between small (one person at a time) and wide
bottlenecks (two persons at a time) were also found in the distribution of time
gaps.Comment: accepted for publication in J. Stat. Mec
Two-way multi-lane traffic model for pedestrians in corridors
We extend the Aw-Rascle macroscopic model of car traffic into a two-way
multi-lane model of pedestrian traffic. Within this model, we propose a
technique for the handling of the congestion constraint, i.e. the fact that the
pedestrian density cannot exceed a maximal density corresponding to contact
between pedestrians. In a first step, we propose a singularly perturbed
pressure relation which models the fact that the pedestrian velocity is
considerably reduced, if not blocked, at congestion. In a second step, we carry
over the singular limit into the model and show that abrupt transitions between
compressible flow (in the uncongested regions) to incompressible flow (in
congested regions) occur. We also investigate the hyperbolicity of the two-way
models and show that they can lose their hyperbolicity in some cases. We study
a diffusive correction of these models and discuss the characteristic time and
length scales of the instability
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