692 research outputs found
Complex Dynamics of Bus, Tram and Elevator Delays in Transportation System
It is necessary and important to operate buses and trams on time. The bus
schedule is closely related to the dynamic motion of buses. In this part, we
introduce the nonlinear maps for describing the dynamics of shuttle buses in
the transportation system. The complex motion of the buses is explained by the
nonlinear-map models. The transportation system of shuttle buses without
passing is similar to that of the trams. The transport of elevators is also
similar to that of shuttle buses with freely passing. The complex dynamics of a
single bus is described in terms of the piecewise map, the delayed map, the
extended circle map and the combined map. The dynamics of a few buses is
described by the model of freely passing buses, the model of no passing buses,
and the model of increase or decrease of buses. The nonlinear-map models are
useful to make an accurate estimate of the arrival time in the bus
transportation
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
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
Dynamical Phase Transition in One Dimensional Traffic Flow Model with Blockage
Effects of a bottleneck in a linear trafficway is investigated using a simple
cellular automaton model. Introducing a blockage site which transmit cars at
some transmission probability into the rule-184 cellular automaton, we observe
three different phases with increasing car concentration: Besides the free
phase and the jam phase, which exist already in the pure rule-184 model, the
mixed phase of these two appears at intermediate concentration with
well-defined phase boundaries. This mixed phase, where cars pile up behind the
blockage to form a jam region, is characterized by a constant flow. In the
thermodynamic limit, we obtain the exact expressions for several characteristic
quantities in terms of the car density and the transmission rate. These
quantities depend strongly on the system size at the phase boundaries; We
analyse these finite size effects based on the finite-size scaling.Comment: 14 pages, LaTeX 13 postscript figures available upon
request,OUCMT-94-
Jamming Transition of Point-to-Point Traffic Through Cooperative Mechanisms
We study the jamming transition of two-dimensional point-to-point traffic
through cooperative mechanisms using computer simulation. We propose two
decentralized cooperative mechanisms which are incorporated into the
point-to-point traffic models: stepping aside (CM-SA) and choosing alternative
routes (CM-CAR). Incorporating CM-SA is to prevent a type of ping-pong jumps
from happening when two objects standing face-to-face want to move in opposite
directions. Incorporating CM-CAR is to handle the conflict when more than one
object competes for the same point in parallel update. We investigate and
compare four models mainly from fundamental diagrams, jam patterns and the
distribution of cooperation probability. It is found that although it decreases
the average velocity a little, the CM-SA increases the critical density and the
average flow. Despite increasing the average velocity, the CM-CAR decreases the
average flow by creating substantially vacant areas inside jam clusters. We
investigate the jam patterns of four models carefully and explain this result
qualitatively. In addition, we discuss the advantage and applicability of
decentralized cooperation modeling.Comment: 17 pages, 14 figure
Experiences with a simplified microsimulation for the Dallas/Fort Worth area
We describe a simple framework for micro simulation of city traffic. A medium
sized excerpt of Dallas was used to examine different levels of simulation
fidelity of a cellular automaton method for the traffic flow simulation and a
simple intersection model. We point out problems arising with the granular
structure of the underlying rules of motion.Comment: accepted by Int.J.Mod.Phys.C, 20 pages, 14 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
Solvable Optimal Velocity Models and Asymptotic Trajectory
In the Optimal Velocity Model proposed as a new version of Car Following
Model, it has been found that a congested flow is generated spontaneously from
a homogeneous flow for a certain range of the traffic density. A
well-established congested flow obtained in a numerical simulation shows a
remarkable repetitive property such that the velocity of a vehicle evolves
exactly in the same way as that of its preceding one except a time delay .
This leads to a global pattern formation in time development of vehicles'
motion, and gives rise to a closed trajectory on -
(headway-velocity) plane connecting congested and free flow points. To obtain
the closed trajectory analytically, we propose a new approach to the pattern
formation, which makes it possible to reduce the coupled car following
equations to a single difference-differential equation (Rondo equation). To
demonstrate our approach, we employ a class of linear models which are exactly
solvable. We also introduce the concept of ``asymptotic trajectory'' to
determine and (the backward velocity of the pattern), the global
parameters associated with vehicles' collective motion in a congested flow, in
terms of parameters such as the sensitivity , which appeared in the original
coupled equations.Comment: 25 pages, 15 eps figures, LaTe
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