9,820 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
Planning with Information-Processing Constraints and Model Uncertainty in Markov Decision Processes
Information-theoretic principles for learning and acting have been proposed
to solve particular classes of Markov Decision Problems. Mathematically, such
approaches are governed by a variational free energy principle and allow
solving MDP planning problems with information-processing constraints expressed
in terms of a Kullback-Leibler divergence with respect to a reference
distribution. Here we consider a generalization of such MDP planners by taking
model uncertainty into account. As model uncertainty can also be formalized as
an information-processing constraint, we can derive a unified solution from a
single generalized variational principle. We provide a generalized value
iteration scheme together with a convergence proof. As limit cases, this
generalized scheme includes standard value iteration with a known model,
Bayesian MDP planning, and robust planning. We demonstrate the benefits of this
approach in a grid world simulation.Comment: 16 pages, 3 figure
Some numerical methods for solving stochastic impulse control in natural gas storage facilities
The valuation of gas storage facilities is characterized as a stochastic impulse control problem with finite horizon resulting in Hamilton-Jacobi-Bellman (HJB) equations for the value function. In this context the two catagories of solving schemes for optimal switching are discussed in a stochastic control framework. We reviewed some numerical methods which include approaches related to partial differential equations (PDEs), Markov chain approximation, nonparametric regression, quantization method and some practitioners’ methods. This paper considers optimal switching problem arising in valuation of gas storage contracts for leasing the storage facilities, and investigates the recent developments as well as their advantages and disadvantages of each scheme based on dynamic programming principle (DPP
Distributed stochastic optimization via matrix exponential learning
In this paper, we investigate a distributed learning scheme for a broad class
of stochastic optimization problems and games that arise in signal processing
and wireless communications. The proposed algorithm relies on the method of
matrix exponential learning (MXL) and only requires locally computable gradient
observations that are possibly imperfect and/or obsolete. To analyze it, we
introduce the notion of a stable Nash equilibrium and we show that the
algorithm is globally convergent to such equilibria - or locally convergent
when an equilibrium is only locally stable. We also derive an explicit linear
bound for the algorithm's convergence speed, which remains valid under
measurement errors and uncertainty of arbitrarily high variance. To validate
our theoretical analysis, we test the algorithm in realistic
multi-carrier/multiple-antenna wireless scenarios where several users seek to
maximize their energy efficiency. Our results show that learning allows users
to attain a net increase between 100% and 500% in energy efficiency, even under
very high uncertainty.Comment: 31 pages, 3 figure
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