19,433 research outputs found
Influence of the number of predecessors in interaction within acceleration-based flow models
In this paper, the stability of the uniform solutions is analysed for
microscopic flow models in interaction with predecessors. We calculate
general conditions for the linear stability on the ring geometry and explore
the results with particular pedestrian and car-following models based on
relaxation processes. The uniform solutions are stable if the relaxation times
are sufficiently small. The analysis is focused on the relevance of the number
of predecessors in the dynamics. Unexpected non-monotonic relations between
and the stability are presented.Comment: 18 pages, 14 figure
Towards the fast and robust optimal design of Wireless Body Area Networks
Wireless body area networks are wireless sensor networks whose adoption has
recently emerged and spread in important healthcare applications, such as the
remote monitoring of health conditions of patients. A major issue associated
with the deployment of such networks is represented by energy consumption: in
general, the batteries of the sensors cannot be easily replaced and recharged,
so containing the usage of energy by a rational design of the network and of
the routing is crucial. Another issue is represented by traffic uncertainty:
body sensors may produce data at a variable rate that is not exactly known in
advance, for example because the generation of data is event-driven. Neglecting
traffic uncertainty may lead to wrong design and routing decisions, which may
compromise the functionality of the network and have very bad effects on the
health of the patients. In order to address these issues, in this work we
propose the first robust optimization model for jointly optimizing the topology
and the routing in body area networks under traffic uncertainty. Since the
problem may result challenging even for a state-of-the-art optimization solver,
we propose an original optimization algorithm that exploits suitable linear
relaxations to guide a randomized fixing of the variables, supported by an
exact large variable neighborhood search. Experiments on realistic instances
indicate that our algorithm performs better than a state-of-the-art solver,
fast producing solutions associated with improved optimality gaps.Comment: Authors' manuscript version of the paper that was published in
Applied Soft Computin
Convexity and Robustness of Dynamic Traffic Assignment and Freeway Network Control
We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA)
problem to design optimal traffic flow controls for freeway networks as modeled
by the Cell Transmission Model, using variable speed limit, ramp metering, and
routing. We consider two optimal control problems: the DTA problem, where
turning ratios are part of the control inputs, and the Freeway Network Control
(FNC), where turning ratios are instead assigned exogenous parameters. It is
known that relaxation of the supply and demand constraints in the cell-based
formulations of the DTA problem results in a linear program. However, solutions
to the relaxed problem can be infeasible with respect to traffic dynamics.
Previous work has shown that such solutions can be made feasible by proper
choice of ramp metering and variable speed limit control for specific traffic
networks. We extend this procedure to arbitrary networks and provide insight
into the structure and robustness of the proposed optimal controllers. For a
network consisting only of ordinary, merge, and diverge junctions, where the
cells have linear demand functions and affine supply functions with identical
slopes, and the cost is the total traffic volume, we show, using the maximum
principle, that variable speed limits are not needed in order to achieve
optimality in the FNC problem, and ramp metering is sufficient. We also prove
bounds on perturbation of the controlled system trajectory in terms of
perturbations in initial traffic volume and exogenous inflows. These bounds,
which leverage monotonicity properties of the controlled trajectory, are shown
to be in close agreement with numerical simulation results
Statistical Physics of Vehicular Traffic and Some Related Systems
In the so-called "microscopic" models of vehicular traffic, attention is paid
explicitly to each individual vehicle each of which is represented by a
"particle"; the nature of the "interactions" among these particles is
determined by the way the vehicles influence each others' movement. Therefore,
vehicular traffic, modeled as a system of interacting "particles" driven far
from equilibrium, offers the possibility to study various fundamental aspects
of truly nonequilibrium systems which are of current interest in statistical
physics. Analytical as well as numerical techniques of statistical physics are
being used to study these models to understand rich variety of physical
phenomena exhibited by vehicular traffic. Some of these phenomena, observed in
vehicular traffic under different circumstances, include transitions from one
dynamical phase to another, criticality and self-organized criticality,
metastability and hysteresis, phase-segregation, etc. In this critical review,
written from the perspective of statistical physics, we explain the guiding
principles behind all the main theoretical approaches. But we present detailed
discussions on the results obtained mainly from the so-called
"particle-hopping" models, particularly emphasizing those which have been
formulated in recent years using the language of cellular automata.Comment: 170 pages, Latex, figures include
The BGK approximation of kinetic models for traffic
We study spatially non-homogeneous kinetic models for vehicular traffic flow.
Classical formulations, as for instance the BGK equation, lead to
unconditionally unstable solutions in the congested regime of traffic. We
address this issue by deriving a modified formulation of the BGK-type equation.
The new kinetic model allows to reproduce conditionally stable non-equilibrium
phenomena in traffic flow. In particular, stop and go waves appear as bounded
backward propagating signals occurring in bounded regimes of the density where
the model is unstable. The BGK-type model introduced here also offers the
mesoscopic description between the microscopic follow-the-leader model and the
macroscopic Aw-Rascle and Zhang model
Corrugation of Roads
We present a one dimensional model for the development of corrugations in
roads subjected to compressive forces from a flux of cars. The cars are modeled
as damped harmonic oscillators translating with constant horizontal velocity
across the surface, and the road surface is subject to diffusive relaxation. We
derive dimensionless coupled equations of motion for the positions of the cars
and the road surface H(x,t), which contain two phenomenological variables: an
effective diffusion constant Delta(H) that characterizes the relaxation of the
road surface, and a function alpha(H) that characterizes the plasticity or
erodibility of the road bed. Linear stability analysis shows that corrugations
grow if the speed of the cars exceeds a critical value, which decreases if the
flux of cars is increased. Modifying the model to enforce the simple fact that
the normal force exerted by the road can never be negative seems to lead to
restabilized, quasi-steady road shapes, in which the corrugation amplitude and
phase velocity remain fixed.Comment: 20 pages, 8 figures, typos correcte
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