Alfredo Garcia

A Game-Theoretic Approach to Efficient Power Management in Sensor Networks

Wireless sensor networks pose numerous fundamental coordination problems. For example, in a number of application domains including homeland security, environmental monitoring, and surveillance for military operations, a networks ability to efficiently manage power consumption is extremely critical because direct user intervention after initial deployment is severely limited. In these settings, limited battery life gives rise to the basic coordination problem of maintaining coverage while maximizing the networks lifetime. In this paper, we propose a distributed scheme for efficient power management in sensor networks that is guaranteed to identify suboptimal topologies in an online fashion. Our scheme is based on a general (game-theoretic) mathematical structure that induces a natural mapping between the informational layer and the physical layer. We provide sufficient conditions for the convergence of the algorithm to a pure Nash equilibrium and characterize the performance of the algorithm in terms of coverage. We also present encouraging performance results on a MicaZ testbed as well as on large-scale topologies (obtained via simulation).

Market power analysis for the Colombian electricity market

Abstract In this paper, a dynamic Cournot model is used to evaluate the likely impacts of possible mergers in the Colombian wholesale market for electricity. Our simulations showed that a substantial degree of energy withholding resulted in spot prices that on average were 24% above pre-merger levels. However, when high levels of ex-ante contracting were incorporated into the model, post-merger prices did not increase substantially or even drop below pre-merger prices. A short discussion on how these results were used for policy making at the regulatory commission is presented.

Dynamic Incentives for Congestion Control

We introduce a new dynamic pricing mechanism for controlling congestion in a network shared by non-cooperative users. The network exhibits a congestion externality and users have private information regarding their willingness to pay for network use. The externalities imply that many simple uniform price adjustment processes (e.g., tatonnement) either fail to effectively control flow demands and/or are subject to strategic manipulation. We propose a dynamic discriminatory pricing mechanism design and show that it effectively controls congestion while ensuring the efficient allocation of network capacity. We show the proposed mechanism is robust to strategic manipulation. To the best of our knowledge, there is no other dynamic pricing mechanism in the literature with these properties.

Equilibrium Capacity Expansion Under Stochastic Demand Growth

In critical energy infrastructure sectors (e.g., electric power generation, natural gas transportation, oil-refining capacity), maintaining a certain level of excess capacity is socially valuable (because it serves to protect against unexpected market conditions) but not necessarily compatible with the incentives for individual firms in the market. In this paper, we develop a dynamic oligopoly model with a stochastically growing demand to analyze the inherent tension in market-based incentives for capacity expansion where capacity additions take place over long time lags. Our results indicate that the market fails to induce the socially optimal level of capacity. However, the magnitude of this failure varies greatly as a function of entry costs and the relative profitability of investments in the market (as measured by the ratio of maximum markup over production costs and investment costs). In general, the likelihood of insufficient capacity in equilibrium increases with decreasing probability of demand growth, increasing discount and depreciation rates, and/or increasing investment and/or production costs. We discuss the public policy implications of our results.

Distributed Synchronization Control of Multiagent Systems With Unknown Nonlinearities

This paper revisits the distributed adaptive control problem for synchronization of multiagent systems where the dynamics of the agents are nonlinear, nonidentical, unknown, and subject to external disturbances. Two communication topologies, represented, respectively, by a fixed strongly-connected directed graph and by a switching connected undirected graph, are considered. Under both of these communication topologies, we use distributed neural networks to approximate the uncertain dynamics. Decentralized adaptive control protocols are then constructed to solve the cooperative tracker problem, the problem of synchronization of all follower agents to a leader agent. In particular, we show that, under the proposed decentralized control protocols, the synchronization errors are ultimately bounded, and their ultimate bounds can be reduced arbitrarily by choosing the control parameter appropriately. Simulation study verifies the effectiveness of our proposed protocols.

Joint distributed access point selection and power allocation in cognitive radio networks

Spectrum management has been identified as a crucial step towards enabling the technology of the cognitive radio network (CRN). Most of the current works dealing with spectrum management in the CRN focus on a single task of the problem, e.g., spectrum sensing, spectrum decision, spectrum sharing or spectrum mobility. In this work, we argue that for certain network configurations, jointly performing several tasks of the spectrum management improves the spectrum efficiency. Specifically, we study the uplink resource management problem in a CRN where there exist multiple cognitive users (CUs) and access points (APs), with each AP operates on a set of non-overlapping channels. The CUs, in order to maximize their uplink transmission rates, have to associate to a suitable AP (spectrum decision), and to share the channels belong to this AP with other CUs (spectrum sharing). These tasks are clearly interdependent, and the problem of how they should be carried out efficiently and distributedly is still open in the literature. In this work we formulate this joint spectrum decision and spectrum sharing problem into a non-cooperative game, in which the feasible strategy of a player contains a discrete variable and a continuous vector. The structure of the game is hence very different from most non-cooperative spectrum management game proposed in the literature. We provide characterization of the Nash Equilibrium (NE) of this game, and present a set of novel algorithms that allow the CUs to distributively and efficiently select the suitable AP and share the channels with other CUs. Finally, we study the properties of the proposed algorithms as well as their performance via extensive simulations.

Averaged Iterative Water-Filling Algorithm: Robustness and Convergence

The convergence properties of the iterative water-filling (IWF) based algorithms have been derived in the ideal situation where the transmitters in the network are able to obtain the exact value of the interference plus noise (IPN) experienced at the corresponding receivers in each iteration of the algorithm. However, these algorithms are not robust because they diverge when there is time-varying estimation error of the IPN, a situation that arises in real communication system. In this correspondence, we propose an algorithm that possesses convergence guarantees in the presence of various forms of such time-varying error. Moreover, we also show by simulation that in scenarios where the interference is strong, the conventional IWF diverges while our proposed algorithm still converges.

Joint Access Point Selection and Power Allocation for Uplink Wireless Networks

We consider the distributed uplink resource allocation problem in a multi-carrier wireless network with multiple access points (APs). Each mobile user can optimize its own transmission rate by selecting a suitable AP and by controlling its transmit power. Our objective is to devise suitable algorithms by which mobile users can jointly perform these tasks in a distributed manner. Our approach relies on a game theoretic formulation of the joint power control and AP selection problem. In the proposed game, each user is a player with an associated strategy containing a discrete variable (the AP selection decision) and a continuous vector (the power allocation among multiple channels). We provide characterizations of the Nash Equilibrium of the proposed game. We present a novel algorithm named Joint Access Point Selection and Power Allocation (JASPA) and its various extensions (with different update schedules) that allow the users to efficiently optimize their rates. Finally, we study the properties of the proposed algorithms as well as their performance via extensive simulations.

Solution and Forecast Horizons for Infinite-Horizon Nonhomogeneous Markov Decision Processes

We consider a nonhomogeneous infinite-horizon Markov Decision Process (MDP) problem with multiple optimal first-period policies. We seek an algorithm that, given finite data, delivers an optimal first-period policy. Such an algorithm can thus recursively generate, within a rolling-horizon procedure, an infinite-horizon optimal solution to the original problem. However, it can happen that no such algorithm exists, i.e., the MDP is not well posed. Equivalently, it is impossible to solve the problem with a finite amount of data. Assuming increasing marginal returns in actions (with respect to states) and stochastically increasing state transitions (with respect to actions), we provide an algorithm that is guaranteed to solve the given MDP whenever it is well posed. This algorithm determines, in finite time, a forecast horizon for which an optimal solution delivers an optimal first-period policy. As an application, we solve all well-posed instances of the time-varying version of the classic asset-selling problem.

Dynamic Auctions for On-Demand Services

In this paper, we consider a market in which a finite number of firms compete in prices for the incoming demand for service. Upon every customer arrival, an independent auctioneer gathers bids from each one of the competing queuing systems and assigns the incoming customer to the system that submitted the lowest bid. We provide a simple characterization of Markov Perfect equilibrium in terms of ldquoindifference prices,rdquo i.e., price levels at which players are indifferent between committing available capacity or withholding it. We identify sufficient conditions for socially efficient performance in equilibrium.