11 research outputs found
Stochastic boundary conditions in the deterministic Nagel-Schreckenberg traffic model
We consider open systems where cars move according to the deterministic
Nagel-Schreckenberg rules and with maximum velocity , what is an
extension of the Asymmetric Exclusion Process (ASEP). It turns out that the
behaviour of the system is dominated by two features: a) the competition
between the left and the right boundary b) the development of so-called
"buffers" due to the hindrance an injected car feels from the front car at the
beginning of the system. As a consequence, there is a first-order phase
transition between the free flow and the congested phase accompanied by the
collapse of the buffers and the phase diagram essentially differs from that of
(ASEP).Comment: 29 pages, 26 figure
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
Traffic and Related Self-Driven Many-Particle Systems
Since the subject of traffic dynamics has captured the interest of
physicists, many astonishing effects have been revealed and explained. Some of
the questions now understood are the following: Why are vehicles sometimes
stopped by so-called ``phantom traffic jams'', although they all like to drive
fast? What are the mechanisms behind stop-and-go traffic? Why are there several
different kinds of congestion, and how are they related? Why do most traffic
jams occur considerably before the road capacity is reached? Can a temporary
reduction of the traffic volume cause a lasting traffic jam? Under which
conditions can speed limits speed up traffic? Why do pedestrians moving in
opposite directions normally organize in lanes, while similar systems are
``freezing by heating''? Why do self-organizing systems tend to reach an
optimal state? Why do panicking pedestrians produce dangerous deadlocks? All
these questions have been answered by applying and extending methods from
statistical physics and non-linear dynamics to self-driven many-particle
systems. This review article on traffic introduces (i) empirically data, facts,
and observations, (ii) the main approaches to pedestrian, highway, and city
traffic, (iii) microscopic (particle-based), mesoscopic (gas-kinetic), and
macroscopic (fluid-dynamic) models. Attention is also paid to the formulation
of a micro-macro link, to aspects of universality, and to other unifying
concepts like a general modelling framework for self-driven many-particle
systems, including spin systems. Subjects such as the optimization of traffic
flows and relations to biological or socio-economic systems such as bacterial
colonies, flocks of birds, panics, and stock market dynamics are discussed as
well.Comment: A shortened version of this article will appear in Reviews of Modern
Physics, an extended one as a book. The 63 figures were omitted because of
storage capacity. For related work see http://www.helbing.org