5,146 research outputs found
A fully-discrete-state kinetic theory approach to traffic flow on road networks
This paper presents a new approach to the modeling of vehicular traffic flows
on road networks based on kinetic equations. While in the literature the
problem has been extensively studied by means of macroscopic hydrodynamic
models, to date there are still not, to the authors' knowledge, contributions
tackling it from a genuine statistical mechanics point of view. Probably one of
the reasons is the higher technical complexity of kinetic traffic models,
further increased in case of several interconnected roads. Here such
difficulties of the theory are overcome by taking advantage of a discrete
structure of the space of microscopic states of the vehicles, which is also
significant in view of including the intrinsic microscopic granularity of the
system in the mesoscopic representation.Comment: 36 pages, 10 figure
A numerical method for junctions in networks of shallow-water channels
There is growing interest in developing mathematical models and appropriate
numerical methods for problems involving networks formed by, essentially,
one-dimensional (1D) domains joined by junctions. Examples include hyperbolic
equations in networks of gas tubes, water channels and vessel networks for
blood and lymph in the human circulatory system. A key point in designing
numerical methods for such applications is the treatment of junctions, i.e.
points at which two or more 1D domains converge and where the flow exhibits
multidimensional behaviour. This paper focuses on the design of methods for
networks of water channels. Our methods adopt the finite volume approach to
make full use of the two-dimensional shallow water equations on the true
physical domain, locally at junctions, while solving the usual one-dimensional
shallow water equations away from the junctions. In addition to mass
conservation, our methods enforce conservation of momentum at junctions; the
latter seems to be the missing element in methods currently available. Apart
from simplicity and robustness, the salient feature of the proposed methods is
their ability to successfully deal with transcritical and supercritical flows
at junctions, a property not enjoyed by existing published methodologies.
Systematic assessment of the proposed methods for a variety of flow
configurations is carried out. The methods are directly applicable to other
systems, provided the multidimensional versions of the 1D equations are
available
A Review of Traffic Signal Control.
The aim of this paper is to provide a starting point for the future research within the SERC sponsored project "Gating and Traffic Control: The Application of State Space Control Theory". It will provide an introduction to State Space Control Theory, State Space applications in transportation in general, an in-depth review of congestion control (specifically traffic signal control in congested situations), a review of theoretical works, a review of existing systems and will conclude with recommendations for the research to be undertaken within this project
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