2,008 research outputs found
A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks
In this paper we propose a LWR-like model for traffic flow on networks which
allows one to track several groups of drivers, each of them being characterized
only by their destination in the network. The path actually followed to reach
the destination is not assigned a priori, and can be chosen by the drivers
during the journey, taking decisions at junctions.
The model is then used to describe three possible behaviors of drivers,
associated to three different ways to solve the route choice problem: 1.
Drivers ignore the presence of the other vehicles; 2. Drivers react to the
current distribution of traffic, but they do not forecast what will happen at
later times; 3. Drivers take into account the current and future distribution
of vehicles. Notice that, in the latter case, we enter the field of
differential games, and, if a solution exists, it likely represents a global
equilibrium among drivers.
Numerical simulations highlight the differences between the three behaviors
and suggest the existence of multiple Wardrop equilibria
A Switching Fluid Limit of a Stochastic Network Under a State-Space-Collapse Inducing Control with Chattering
Routing mechanisms for stochastic networks are often designed to produce
state space collapse (SSC) in a heavy-traffic limit, i.e., to confine the
limiting process to a lower-dimensional subset of its full state space. In a
fluid limit, a control producing asymptotic SSC corresponds to an ideal sliding
mode control that forces the fluid trajectories to a lower-dimensional sliding
manifold. Within deterministic dynamical systems theory, it is well known that
sliding-mode controls can cause the system to chatter back and forth along the
sliding manifold due to delays in activation of the control. For the prelimit
stochastic system, chattering implies fluid-scaled fluctuations that are larger
than typical stochastic fluctuations. In this paper we show that chattering can
occur in the fluid limit of a controlled stochastic network when inappropriate
control parameters are used. The model has two large service pools operating
under the fixed-queue-ratio with activation and release thresholds (FQR-ART)
overload control which we proposed in a recent paper. We now show that, if the
control parameters are not chosen properly, then delays in activating and
releasing the control can cause chattering with large oscillations in the fluid
limit. In turn, these fluid-scaled fluctuations lead to severe congestion, even
when the arrival rates are smaller than the potential total service rate in the
system, a phenomenon referred to as congestion collapse. We show that the fluid
limit can be a bi-stable switching system possessing a unique nontrivial
periodic equilibrium, in addition to a unique stationary point
Wardrop Equilibrium in Discrete-Time Selfish Routing with Time-Varying Bounded Delays
This paper presents a multi-commodity, discrete-
time, distributed and non-cooperative routing algorithm, which is
proved to converge to an equilibrium in the presence of
heterogeneous, unknown, time-varying but bounded delays.
Under mild assumptions on the latency functions which describe
the cost associated to the network paths, two algorithms are
proposed: the former assumes that each commodity relies only on
measurements of the latencies associated to its own paths; the
latter assumes that each commodity has (at least indirectly) access
to the measures of the latencies of all the network paths. Both
algorithms are proven to drive the system state to an invariant set
which approximates and contains the Wardrop equilibrium,
defined as a network state in which no traffic flow over the
network paths can improve its routing unilaterally, with the latter
achieving a better reconstruction of the Wardrop equilibrium.
Numerical simulations show the effectiveness of the proposed
approach
Data-Driven Estimation in Equilibrium Using Inverse Optimization
Equilibrium modeling is common in a variety of fields such as game theory and
transportation science. The inputs for these models, however, are often
difficult to estimate, while their outputs, i.e., the equilibria they are meant
to describe, are often directly observable. By combining ideas from inverse
optimization with the theory of variational inequalities, we develop an
efficient, data-driven technique for estimating the parameters of these models
from observed equilibria. We use this technique to estimate the utility
functions of players in a game from their observed actions and to estimate the
congestion function on a road network from traffic count data. A distinguishing
feature of our approach is that it supports both parametric and
\emph{nonparametric} estimation by leveraging ideas from statistical learning
(kernel methods and regularization operators). In computational experiments
involving Nash and Wardrop equilibria in a nonparametric setting, we find that
a) we effectively estimate the unknown demand or congestion function,
respectively, and b) our proposed regularization technique substantially
improves the out-of-sample performance of our estimators.Comment: 36 pages, 5 figures Additional theorems for generalization guarantees
and statistical analysis adde
Modeling rationality to control self-organization of crowds: An environmental approach
In this paper we propose a classification of crowd models in built
environments based on the assumed pedestrian ability to foresee the movements
of other walkers. At the same time, we introduce a new family of macroscopic
models, which make it possible to tune the degree of predictiveness (i.e.,
rationality) of the individuals. By means of these models we describe both the
natural behavior of pedestrians, i.e., their expected behavior according to
their real limited predictive ability, and a target behavior, i.e., a
particularly efficient behavior one would like them to assume (for, e.g.,
logistic or safety reasons). Then we tackle a challenging shape optimization
problem, which consists in controlling the environment in such a way that the
natural behavior is as close as possible to the target one, thereby inducing
pedestrians to behave more rationally than what they would naturally do. We
present numerical tests which elucidate the role of rational/predictive
abilities and show some promising results about the shape optimization problem
Proposal of a risk model for vehicular traffic: A Boltzmann-type kinetic approach
This paper deals with a Boltzmann-type kinetic model describing the interplay
between vehicle dynamics and safety aspects in vehicular traffic. Sticking to
the idea that the macroscopic characteristics of traffic flow, including the
distribution of the driving risk along a road, are ultimately generated by
one-to-one interactions among drivers, the model links the personal (i.e.,
individual) risk to the changes of speeds of single vehicles and implements a
probabilistic description of such microscopic interactions in a Boltzmann-type
collisional operator. By means of suitable statistical moments of the kinetic
distribution function, it is finally possible to recover macroscopic
relationships between the average risk and the road congestion, which show an
interesting and reasonable correlation with the well-known free and congested
phases of the flow of vehicles.Comment: 23 pages, 3 figures, Commun. Math. Sci., 201
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