14 research outputs found
Vehicular traffic flow at an intersection with the possibility of turning
We have developed a Nagel-Schreckenberg cellular automata model for
describing of vehicular traffic flow at a single intersection. A set of traffic
lights operating in fixed-time scheme controls the traffic flow. Open boundary
condition is applied to the streets each of which conduct a uni-directional
flow. Streets are single-lane and cars can turn upon reaching to the
intersection with prescribed probabilities. Extensive Monte Carlo simulations
are carried out to find the model flow characteristics. In particular, we
investigate the flows dependence on the signalisation parameters, turning
probabilities and input rates. It is shown that for each set of parameters,
there exist a plateau region inside which the total outflow from the
intersection remains almost constant. We also compute total waiting time of
vehicles per cycle behind red lights for various control parameters.Comment: 8 pages, 17 eps figures, Late
Asymmetric simple exclusion process describing conflicting traffic flows
We use the asymmetric simple exclusion process for describing vehicular
traffic flow at the intersection of two streets. No traffic lights control the
traffic flow. The approaching cars to the intersection point yield to each
other to avoid collision. This yielding dynamics is model by implementing
exclusion process to the intersection point of the two streets. Closed boundary
condition is applied to the streets. We utilize both mean-field approach and
extensive simulations to find the model characteristics. In particular, we
obtain the fundamental diagrams and show that the effect of interaction between
chains can be regarded as a dynamic impurity at the intersection point.Comment: 7 pages, 10 eps figures, Revte
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
Stripe formation instability in crossing traffic flows
At the intersection of two unidirectional traffic flows a stripe formation
instability is known to occur. In this paper we consider coupled time evolution
equations for the densities of the two flows in their intersection area. We
show analytically how the instability arises from the randomness of the traffic
entering the area. The Green function of the linearized equations is shown to
form a Gaussian wave packet whose oscillations correspond to the stripes.
Explicit formulas are obtained for various characteristic quantities in terms
of the traffic density and comparison is made with the much simpler calculation
on a torus and with numerical solution of the evolution equations