12,844 research outputs found
Stochastic Differential Games and Energy-Efficient Power Control
One of the contributions of this work is to formulate the problem of
energy-efficient power control in multiple access channels (namely, channels
which comprise several transmitters and one receiver) as a stochastic
differential game. The players are the transmitters who adapt their power level
to the quality of their time-varying link with the receiver, their battery
level, and the strategy updates of the others. The proposed model not only
allows one to take into account long-term strategic interactions but also
long-term energy constraints. A simple sufficient condition for the existence
of a Nash equilibrium in this game is provided and shown to be verified in a
typical scenario. As the uniqueness and determination of equilibria are
difficult issues in general, especially when the number of players goes large,
we move to two special cases: the single player case which gives us some useful
insights of practical interest and allows one to make connections with the case
of large number of players. The latter case is treated with a mean-field game
approach for which reasonable sufficient conditions for convergence and
uniqueness are provided. Remarkably, this recent approach for large system
analysis shows how scalability can be dealt with in large games and only relies
on the individual state information assumption.Comment: The final publication is available at
http://www.springerlink.com/openurl.asp?genre=article\&id=doi:10.1007/s13235-012-0068-
Mean Field Energy Games in Wireless Networks
This work tackles the problem of energy-efficient distributed power control
in wireless networks with a large number of transmitters. The problem is
modeled by a dynamic game. Each transmitter-receiver communication is
characterized by a state given by the available energy and/or the individual
channel state and whose evolution is governed by certain dynamics. Since
equilibrium analysis in such a (stochastic) game is generally difficult and
even impossible, the problem is approximated by exploiting the large system
assumption. Under an appropriate exchangeability assumption, the corresponding
mean field game is well defined and studied in detail for special cases. The
main contribution of this work is to show how mean field games can be applied
to the problem under investigation and provide illustrative numerical results.
Our results indicate that this approach can lead to significant gains in terms
of energy-efficiency at the resulting equilibrium.Comment: IEEE Proc. of Asilomar Conf. on Signals, Systems, and Computers, Nov.
2012, Pacific Grove, CA, US
An Extended Mean Field Game for Storage in Smart Grids
We consider a stylized model for a power network with distributed local power
generation and storage. This system is modeled as network connection a large
number of nodes, where each node is characterized by a local electricity
consumption, has a local electricity production (e.g. photovoltaic panels), and
manages a local storage device. Depending on its instantaneous consumption and
production rates as well as its storage management decision, each node may
either buy or sell electricity, impacting the electricity spot price. The
objective at each node is to minimize energy and storage costs by optimally
controlling the storage device. In a non-cooperative game setting, we are led
to the analysis of a non-zero sum stochastic game with players where the
interaction takes place through the spot price mechanism. For an infinite
number of agents, our model corresponds to an Extended Mean-Field Game (EMFG).
In a linear quadratic setting, we obtain and explicit solution to the EMFG, we
show that it provides an approximate Nash-equilibrium for -player game, and
we compare this solution to the optimal strategy of a central planner.Comment: 27 pages, 5 figures. arXiv admin note: text overlap with
arXiv:1607.02130 by other author
Boltzmann meets Nash: Energy-efficient routing in optical networks under uncertainty
Motivated by the massive deployment of power-hungry data centers for service
provisioning, we examine the problem of routing in optical networks with the
aim of minimizing traffic-driven power consumption. To tackle this issue,
routing must take into account energy efficiency as well as capacity
considerations; moreover, in rapidly-varying network environments, this must be
accomplished in a real-time, distributed manner that remains robust in the
presence of random disturbances and noise. In view of this, we derive a pricing
scheme whose Nash equilibria coincide with the network's socially optimum
states, and we propose a distributed learning method based on the Boltzmann
distribution of statistical mechanics. Using tools from stochastic calculus, we
show that the resulting Boltzmann routing scheme exhibits remarkable
convergence properties under uncertainty: specifically, the long-term average
of the network's power consumption converges within of its
minimum value in time which is at most ,
irrespective of the fluctuations' magnitude; additionally, if the network
admits a strict, non-mixing optimum state, the algorithm converges to it -
again, no matter the noise level. Our analysis is supplemented by extensive
numerical simulations which show that Boltzmann routing can lead to a
significant decrease in power consumption over basic, shortest-path routing
schemes in realistic network conditions.Comment: 24 pages, 4 figure
Applications of Repeated Games in Wireless Networks: A Survey
A repeated game is an effective tool to model interactions and conflicts for
players aiming to achieve their objectives in a long-term basis. Contrary to
static noncooperative games that model an interaction among players in only one
period, in repeated games, interactions of players repeat for multiple periods;
and thus the players become aware of other players' past behaviors and their
future benefits, and will adapt their behavior accordingly. In wireless
networks, conflicts among wireless nodes can lead to selfish behaviors,
resulting in poor network performances and detrimental individual payoffs. In
this paper, we survey the applications of repeated games in different wireless
networks. The main goal is to demonstrate the use of repeated games to
encourage wireless nodes to cooperate, thereby improving network performances
and avoiding network disruption due to selfish behaviors. Furthermore, various
problems in wireless networks and variations of repeated game models together
with the corresponding solutions are discussed in this survey. Finally, we
outline some open issues and future research directions.Comment: 32 pages, 15 figures, 5 tables, 168 reference
Game-theoretical control with continuous action sets
Motivated by the recent applications of game-theoretical learning techniques
to the design of distributed control systems, we study a class of control
problems that can be formulated as potential games with continuous action sets,
and we propose an actor-critic reinforcement learning algorithm that provably
converges to equilibrium in this class of problems. The method employed is to
analyse the learning process under study through a mean-field dynamical system
that evolves in an infinite-dimensional function space (the space of
probability distributions over the players' continuous controls). To do so, we
extend the theory of finite-dimensional two-timescale stochastic approximation
to an infinite-dimensional, Banach space setting, and we prove that the
continuous dynamics of the process converge to equilibrium in the case of
potential games. These results combine to give a provably-convergent learning
algorithm in which players do not need to keep track of the controls selected
by the other agents.Comment: 19 page
Ultra Dense Small Cell Networks: Turning Density into Energy Efficiency
In this paper, a novel approach for joint power control and user scheduling
is proposed for optimizing energy efficiency (EE), in terms of bits per unit
energy, in ultra dense small cell networks (UDNs). Due to severe coupling in
interference, this problem is formulated as a dynamic stochastic game (DSG)
between small cell base stations (SBSs). This game enables to capture the
dynamics of both the queues and channel states of the system. To solve this
game, assuming a large homogeneous UDN deployment, the problem is cast as a
mean-field game (MFG) in which the MFG equilibrium is analyzed with the aid of
low-complexity tractable partial differential equations. Exploiting the
stochastic nature of the problem, user scheduling is formulated as a stochastic
optimization problem and solved using the drift plus penalty (DPP) approach in
the framework of Lyapunov optimization. Remarkably, it is shown that by weaving
notions from Lyapunov optimization and mean-field theory, the proposed solution
yields an equilibrium control policy per SBS which maximizes the network
utility while ensuring users' quality-of-service. Simulation results show that
the proposed approach achieves up to 70.7% gains in EE and 99.5% reductions in
the network's outage probabilities compared to a baseline model which focuses
on improving EE while attempting to satisfy the users' instantaneous
quality-of-service requirements.Comment: 15 pages, 21 figures (sub-figures are counted separately), IEEE
Journal on Selected Areas in Communications - Series on Green Communications
and Networking (Issue 2
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