15 research outputs found
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
Optimizing evacuation flow in a two-channel exclusion process
We use a basic setup of two coupled exclusion processes to model a stylised
situation in evacuation dynamics, in which evacuees have to choose between two
escape routes. The coupling between the two processes occurs through one common
point at which particles are injected, the process can be controlled by
directing incoming individuals into either of the two escape routes. Based on a
mean-field approach we determine the phase behaviour of the model, and
analytically compute optimal control strategies, maximising the total current
through the system. Results are confirmed by numerical simulations. We also
show that dynamic intervention, exploiting fluctuations about the mean-field
stationary state, can lead to a further increase in total current.Comment: 16 pages, 6 figure
Calibration of the Particle Density in Cellular-Automaton Models for Traffic Flow
We introduce density dependence of the cell size in cellular-automaton models
for traffic flow, which allows a more precise correspondence between real-world
phenomena and what observed in simulation. Also, we give an explicit
calibration of the particle density particularly for the asymmetric simple
exclusion process with some update rules. We thus find that the present method
is valid in that it reproduces a realistic flow-density diagram.Comment: 2 pages, 2 figure
Frozen shuffle update for an asymmetric exclusion process on a ring
We introduce a new rule of motion for a totally asymmetric exclusion process
(TASEP) representing pedestrian traffic on a lattice. Its characteristic
feature is that the positions of the pedestrians, modeled as hard-core
particles, are updated in a fixed predefined order, determined by a phase
attached to each of them. We investigate this model analytically and by Monte
Carlo simulation on a one-dimensional lattice with periodic boundary
conditions. At a critical value of the particle density a transition occurs
from a phase with `free flow' to one with `jammed flow'. We are able to
analytically predict the current-density diagram for the infinite system and to
find the scaling function that describes the finite size rounding at the
transition point.Comment: 16 page
Intersection of two TASEP traffic lanes with frozen shuffle update
Motivated by interest in pedestrian traffic we study two lanes
(one-dimensional lattices) of length that intersect at a single site. Each
lane is modeled by a TASEP (Totally Asymmetric Exclusion Process). The
particles enter and leave lane (where ) with probabilities
and , respectively. We employ the `frozen
shuffle' update introduced in earlier work [C. Appert-Rolland et al, J. Stat.
Mech. (2011) P07009], in which the particle positions are updated in a fixed
random order. We find analytically that each lane may be in a `free flow' or in
a `jammed' state. Hence the phase diagram in the domain
consists of four regions with boundaries
depending on and . The regions meet in a single point on the
diagonal of the domain. Our analytical predictions for the phase boundaries as
well as for the currents and densities in each phase are confirmed by Monte
Carlo simulations.Comment: 7 figure
A multi-lane TASEP model for crossing pedestrian traffic flows
A one-way {\em street} of width M is modeled as a set of M parallel
one-dimensional TASEPs. The intersection of two perpendicular streets is a
square lattice of size M times M. We consider hard core particles entering each
street with an injection probability \alpha. On the intersection square the
hard core exclusion creates a many-body problem of strongly interacting TASEPs
and we study the collective dynamics that arises. We construct an efficient
algorithm that allows for the simulation of streets of infinite length, which
have sharply defined critical jamming points. The algorithm employs the `frozen
shuffle update', in which the randomly arriving particles have fully
deterministic bulk dynamics. High precision simulations for street widths up to
M=24 show that when \alpha increases, there occur jamming transitions at a
sequence of M critical values \alphaM,M < \alphaM,M-1 < ... < \alphaM,1. As M
grows, the principal transition point \alphaM,M decreases roughly as \sim
1/(log M) in the range of M values studied. We show that a suitable order
parameter is provided by a reflection coefficient associated with the particle
current in each TASEP.Comment: 30 pages, 9 figure