27,818 research outputs found
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
Mean-Field-Type Games in Engineering
A mean-field-type game is a game in which the instantaneous payoffs and/or
the state dynamics functions involve not only the state and the action profile
but also the joint distributions of state-action pairs. This article presents
some engineering applications of mean-field-type games including road traffic
networks, multi-level building evacuation, millimeter wave wireless
communications, distributed power networks, virus spread over networks, virtual
machine resource management in cloud networks, synchronization of oscillators,
energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201
Continuum Equilibria and Global Optimization for Routing in Dense Static Ad Hoc Networks
We consider massively dense ad hoc networks and study their continuum limits
as the node density increases and as the graph providing the available routes
becomes a continuous area with location and congestion dependent costs. We
study both the global optimal solution as well as the non-cooperative routing
problem among a large population of users where each user seeks a path from its
origin to its destination so as to minimize its individual cost. Finally, we
seek for a (continuum version of the) Wardrop equilibrium. We first show how to
derive meaningful cost models as a function of the scaling properties of the
capacity of the network and of the density of nodes. We present various
solution methodologies for the problem: (1) the viscosity solution of the
Hamilton-Jacobi-Bellman equation, for the global optimization problem, (2) a
method based on Green's Theorem for the least cost problem of an individual,
and (3) a solution of the Wardrop equilibrium problem using a transformation
into an equivalent global optimization problem
A Study of Truck Platooning Incentives Using a Congestion Game
We introduce an atomic congestion game with two types of agents, cars and
trucks, to model the traffic flow on a road over various time intervals of the
day. Cars maximize their utility by finding a trade-off between the time they
choose to use the road, the average velocity of the flow at that time, and the
dynamic congestion tax that they pay for using the road. In addition to these
terms, the trucks have an incentive for using the road at the same time as
their peers because they have platooning capabilities, which allow them to save
fuel. The dynamics and equilibria of this game-theoretic model for the
interaction between car traffic and truck platooning incentives are
investigated. We use traffic data from Stockholm to validate parts of the
modeling assumptions and extract reasonable parameters for the simulations. We
use joint strategy fictitious play and average strategy fictitious play to
learn a pure strategy Nash equilibrium of this game. We perform a comprehensive
simulation study to understand the influence of various factors, such as the
drivers' value of time and the percentage of the trucks that are equipped with
platooning devices, on the properties of the Nash equilibrium.Comment: Updated Introduction; Improved Literature Revie
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