2,178 research outputs found
Cellular automata approach to three-phase traffic theory
The cellular automata (CA) approach to traffic modeling is extended to allow
for spatially homogeneous steady state solutions that cover a two dimensional
region in the flow-density plane. Hence these models fulfill a basic postulate
of a three-phase traffic theory proposed by Kerner. This is achieved by a
synchronization distance, within which a vehicle always tries to adjust its
speed to the one of the vehicle in front. In the CA models presented, the
modelling of the free and safe speeds, the slow-to-start rules as well as some
contributions to noise are based on the ideas of the Nagel-Schreckenberg type
modelling. It is shown that the proposed CA models can be very transparent and
still reproduce the two main types of congested patterns (the general pattern
and the synchronized flow pattern) as well as their dependence on the flows
near an on-ramp, in qualitative agreement with the recently developed continuum
version of the three-phase traffic theory [B. S. Kerner and S. L. Klenov. 2002.
J. Phys. A: Math. Gen. 35, L31]. These features are qualitatively different
than in previously considered CA traffic models. The probability of the
breakdown phenomenon (i.e., of the phase transition from free flow to
synchronized flow) as function of the flow rate to the on-ramp and of the flow
rate on the road upstream of the on-ramp is investigated. The capacity drops at
the on-ramp which occur due to the formation of different congested patterns
are calculated.Comment: 55 pages, 24 figure
Mechanical restriction versus human overreaction triggering congested traffic states
A new cellular automaton (CA) traffic model is presented. The focus is on
mechanical restrictions of vehicles realized by limited acceleration and
deceleration capabilities. These features are incorporated into the model in
order to construct the condition of collision-free movement. The strict
collision-free criterion imposed by the mechanical restrictions is softened in
certain traffic situations, reflecting human overreaction. It is shown that the
present model reliably reproduces most empirical findings including
synchronized flow, the so-called {\it pinch effect}, and the time-headway
distribution of free flow. The findings suggest that many free flow phenomena
can be attributed to the platoon formation of vehicles ({\it platoon effect})Comment: 5 pages, 3 figures, to appear in PR
Stability Analysis of Optimal Velocity Model for Traffic and Granular Flow under Open Boundary Condition
We analyzed the stability of the uniform flow solution in the optimal
velocity model for traffic and granular flow under the open boundary condition.
It was demonstrated that, even within the linearly unstable region, there is a
parameter region where the uniform solution is stable against a localized
perturbation. We also found an oscillatory solution in the linearly unstable
region and its period is not commensurate with the periodicity of the car index
space. The oscillatory solution has some features in common with the
synchronized flow observed in real traffic.Comment: 4 pages, 6 figures. Typos removed. To appear in J. Phys. Soc. Jp
Traffic Network Optimum Principle - Minimum Probability of Congestion Occurrence
We introduce an optimum principle for a vehicular traffic network with road
bottlenecks. This network breakdown minimization (BM) principle states that the
network optimum is reached, when link flow rates are assigned in the network in
such a way that the probability for spontaneous occurrence of traffic breakdown
at one of the network bottlenecks during a given observation time reaches the
minimum possible value. Based on numerical simulations with a stochastic
three-phase traffic flow model, we show that in comparison to the well-known
Wardrop's principles the application of the BM principle permits considerably
greater network inflow rates at which no traffic breakdown occurs and,
therefore, free flow remains in the whole network.Comment: 22 pages, 6 figure
General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems
An asymptotic method for finding instabilities of arbitrary -dimensional
large-amplitude patterns in a wide class of reaction-diffusion systems is
presented. The complete stability analysis of 2- and 3-dimensional localized
patterns is carried out. It is shown that in the considered class of systems
the criteria for different types of instabilities are universal. The specific
nonlinearities enter the criteria only via three numerical constants of order
one. The performed analysis explains the self-organization scenarios observed
in the recent experiments and numerical simulations of some concrete
reaction-diffusion systems.Comment: 21 pages (RevTeX), 8 figures (Postscript). To appear in Phys. Rev. E
(April 1st, 1996
The cubic chessboard
We present a survey of recent results, scattered in a series of papers that
appeared during past five years, whose common denominator is the use of cubic
relations in various algebraic structures. Cubic (or ternary) relations can
represent different symmetries with respect to the permutation group S_3, or
its cyclic subgroup Z_3. Also ordinary or ternary algebras can be divided in
different classes with respect to their symmetry properties. We pay special
attention to the non-associative ternary algebra of 3-forms (or ``cubic
matrices''), and Z_3-graded matrix algebras. We also discuss the Z_3-graded
generalization of Grassmann algebras and their realization in generalized
exterior differential forms. A new type of gauge theory based on this
differential calculus is presented. Finally, a ternary generalization of
Clifford algebras is introduced, and an analog of Dirac's equation is
discussed, which can be diagonalized only after taking the cube of the
Z_3-graded generalization of Dirac's operator. A possibility of using these
ideas for the description of quark fields is suggested and discussed in the
last Section.Comment: 23 pages, dedicated to A. Trautman on the occasion of his 64th
birthda
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