221 research outputs found
Dynamic Congestion and Tolls with Mobile Source Emission
This paper proposes a dynamic congestion pricing model that takes into
account mobile source emissions. We consider a tollable vehicular network where
the users selfishly minimize their own travel costs, including travel time,
early/late arrival penalties and tolls. On top of that, we assume that part of
the network can be tolled by a central authority, whose objective is to
minimize both total travel costs of road users and total emission on a
network-wide level. The model is formulated as a mathematical program with
equilibrium constraints (MPEC) problem and then reformulated as a mathematical
program with complementarity constraints (MPCC). The MPCC is solved using a
quadratic penalty-based gradient projection algorithm. A numerical study on a
toy network illustrates the effectiveness of the tolling strategy and reveals a
Braess-type paradox in the context of traffic-derived emission.Comment: 23 pages, 9 figures, 5 tables. Current version to appear in the
Proceedings of the 20th International Symposium on Transportation and Traffic
Theory, 2013, the Netherland
Understanding Braess’ Paradox in power grids
The ongoing energy transition requires power grid extensions to connect renewable generators to consumers and to transfer power among distant areas. The process of grid extension requires a large investment of resources and is supposed to make grid operation more robust. Yet, counter-intuitively, increasing the capacity of existing lines or adding new lines may also reduce the overall system performance and even promote blackouts due to Braess\u27 paradox. Braess\u27 paradox was theoretically modeled but not yet proven in realistically scaled power grids. Here, we present an experimental setup demonstrating Braess\u27 paradox in an AC power grid and show how it constrains ongoing large-scale grid extension projects. We present a topological theory that reveals the key mechanism and predicts Braessian grid extensions from the network structure. These results offer a theoretical method to understand and practical guidelines in support of preventing unsuitable infrastructures and the systemic planning of grid extensions
Macroscopic modeling and simulations of room evacuation
We analyze numerically two macroscopic models of crowd dynamics: the
classical Hughes model and the second order model being an extension to
pedestrian motion of the Payne-Whitham vehicular traffic model. The desired
direction of motion is determined by solving an eikonal equation with density
dependent running cost, which results in minimization of the travel time and
avoidance of congested areas. We apply a mixed finite volume-finite element
method to solve the problems and present error analysis for the eikonal solver,
gradient computation and the second order model yielding a first order
convergence. We show that Hughes' model is incapable of reproducing complex
crowd dynamics such as stop-and-go waves and clogging at bottlenecks. Finally,
using the second order model, we study numerically the evacuation of
pedestrians from a room through a narrow exit.Comment: 22 page
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