Steven A. Gabriel - US grants

The objective of this work is to examine systems with micro-level data for which an equilibrium of some sort is to be reached. One important example is the Gas Systems Analysis Model (GSAM), a modular, reservoir-based model of the North American natural gas system developed for the U. S. Department of Energy. In its current form, GSAM is a large-scale nonlinear program that computes estimates of market equilibrium prices, quantities, flows, and other values based on the notion of maximizing total surplus less transportation costs. Unlike the classical approach in which supply curves are known in closed form, GSAM builds supply curves from the "bottom up" using a data base of over 17,000 natural gas reservoirs taking into account both the interregional as well as intertemporal interdependence of these curves. While this "bottom up" feature provides a good deal of realism, it renders the equilibrium computations much more difficult due to the lack of closed form supply curves. The proposed work has two main objectives. First, analyze the GSAM market equilibrium problem more generally by noting the functional relationships between seasonal market prices (Lagrange multipliers) and demand for gas, storage activity levels, investment decisions, etc. using the variational inequality problem (VIP) and nonlinear complementarity problem (NCP) formats. The second main task is to develop efficient methods to reach a solution to GSAM-type problems exploiting the particular problem structure. Iterative methods from optimization and equation solving is used to develop appropriate algorithms for this task.

Due to recent advances in information technology, it is now possible to model the activities of individual agents in rather complicated systems. Examples of applications in scientific and engineering settings using micro-level data abound. While simulations of these systems can be rather elaborate using for example, complicated "if-then" type rules, determining equilibrium behavior of the system in a rigorous manner can be challenging. Part of the difficulty is due to a lack of closed form expressions for describing the system. The proposed work will examine one such system in its general form and develop both a theory for equilibrium as well as efficient mathematical algorithms to compute such a solution. The anticipated impact of this work is to greatly advance the state of the art in solving large-scale equilibrium problems that use micro-level data for modeling the economic behavior of individual agents. This is significant since many similar systems are now modeled that contain no closed form expressions for key elements but for which an equilibrium solution is desirable.

The project will develop energy market equilibrium models with probabilistic components and analyze conditions that ensure existence and uniqueness of solutions. Two modes will be considered, the first one in which a specific sector such as natural gas will be examined and the second one corresponding to the overall energy market where sectors (e.g., the coal market) will be modeled from a high-level perspective. In the sector-specific approach, individual market players (e.g., natural gas producers, electric power generators) will be depicted as solving profit maximization problems subject to operational constraints as well as uncertain demand or other stochastic elements. These market participants will either be modeled as Nash-Cournot players and thereby have the potential to assert market power, or perfectly competitive players that take market prices as given. The simultaneous solution of each of these optimization problems along with market clearing conditions will lead to a nonlinear complementarity or variational inequality problem whose solution will be sought. In the second mode considered, the overall energy sector will be modeled allowing for certain key elements (e.g., pipeline capacity) to be uncertain due to man-made or natural occurrences. Existence and uniqueness issues for the related market equilibria also based on a nonlinear complementarity/variational inequality approach will be examined. The project will also develop and analyze efficient algorithms to solve these stochastic market equilibrium problems making use of decomposition, matrix factorizations, or recourse approaches. As such, the project will join the two important disciplines of stochastic optimization and equilibrium modeling. Lastly, the project will analyze key energy policy scenarios using these models.

Modern society depends heavily on many types of infrastructure to operate efficiently. This infrastructure is in many forms such as the electric power grid, transportation networks, water treatment facilities, etc. However, many of these infrastructure elements face risks that threaten to seriously degrade the societal benefits. For example, recent energy market deregulation and restructuring have in some cases contributed to large volatility in energy prices which have adversely affected society. The instability in certain aspects of the energy sector is troublesome since energy is vital to many parts of the economy. Thus, risk management in energy can benefit many areas. To combat these energy infrastructure problems, one can develop mathematical models to predict how the energy sector will function under a wide range of scenarios and then plan accordingly by building redundant systems, using financial instruments or other measures. This project will both develop and analyze energy market equilibrium models as well as build and analyze efficient algorithms to solve such problems. These models will directly take into account uncertain demand or other probabilistic elements to more accurately reflect the market players' actions when faced with uncertainty. These models will then be used to analyze certain key energy policy scenarios in consultation with U.S. energy officials as well as those of other countries as appropriate.

NeTS-ProWiN: Broadband Optical/RF Wireless Networks with Topology and Diversity Control

Award 0435206

Stuart Milner, Univ. of Maryland - College Park

Abstract

Optical fiber backbones provide gigabit per second data rates enabling end-to-end multimedia services to homes, offices, classrooms and even mobile users. However, there is a significant gap between such backbones and end users both in availability and capacity. This has been referred to as "the last (or first) mile problem" and continues to be the greatest obstacle we face in implementing broadband networks from anywhere to anywhere.

In this project, software for autonomous network reconfiguration (topology control) is being developed, which will promote survivability (bi-connectedness), scalable autonomous physical and logical reconfiguration, maximum data rate and maximum availability at all times and everywhere in a wireless backbone.

In a unique manner, reconfigurable optical wireless communications, with up to gigabit per second transmission rates are used in combination with directional RF communications. This offers the capability for autonomous physical and logical reconfiguration. This is referred to as topology control, uniquely combining autonomous backbone formation with assured, agile, optical wireless and RF links.

Innovative advanced software methodologies and techniques for topology control are being developed. The software includes: traffic engineering and reconfiguration algorithms; multi-objective optimization; and topology discovery, dissemination, and survivability. Software and methodologies designed to respond to degradation in the network link(s) as well as for network recovery will include: traffic engineering; multi-objective optimization techniques with embedded uncertainty modeling; and topology discovery, dissemination and survivability. Evaluation of the algorithms and software will be achieved using analytical and discrete event simulation techniques.

The objective of this EArly-Concept Grant for Exploratory Research (EAGER) award is to explore the engineering design decision aspects of Design For Bundling (DFB) and address the challenge of bringing together the three related areas of engineering design, marketing and public policy into a unified DFB decision framework. DFB is defined as the process of integrating the design elements of multiple complementary product categories into a single product and selling it to the customers for one price. The product categories can be physical, service, software or a combination. The approach will explore two main research questions. The first research question explores the issues of representation, generation and evaluation of a bundled design purely from an engineering design perspective. The second research question investigates the implications of marketing and public policy in a design decision making context in DFB. The answer to these questions will produce the research ingredients necessary for a systematic decision making in DFB that can be used for physical, service, and software product categories under market competition, public policy regulations and uncertainty considerations.

If successful, this exploratory research will have important implications for United States manufacturers in creating successful product bundling innovations for national and international markets that take competition and regulatory aspects into account. It will also enable manufacturers to understand the impact of uncertainties in developing bundled products and functionalities that compete with foreign brands. The design method will contribute to the area of interface of engineering design, consumer markets, and public policy by taking into account structural complexities. The DFB approach here will also promote a new product innovation model which can reshape the market structures because DFB essentially blurs the established boundaries of existing product markets. Wide adoption of the methodology will open up new markets and redefine the competitions among the manufacturers. The research award involves active participation of one Ph.D. student. The PIs plan to transfer research results and engage students in their respective undergraduate and graduate courses in engineering design decision making, marketing research and public policy. Additionally, it is expected that the successful completion of this EAGER research will provide the necessary foundations for launching a full-scale research effort that will lead the way for other researchers in the community.

This grant will support the modeling of novel management approaches for improved cooperation among independent water resources users and stakeholders. Such cooperation is not naturally incentivized because the actions beneficial to upstream users can often negatively impact downstream users. These asymmetrical benefits create the potential for non-cooperative behavior in three key areas: 1) water withdrawal rights, 2) water quality responsibilities, and 3) risks associated with flooding. Historically, cooperative agreements among independent entities have required static legal agreements that created barriers to adaptation or policy improvement. This research will explore novel management approaches, such as market-based mechanisms, to overcome these challenges to cooperation. The anticipated efficiency and equity gains in these systems will advance prosperity and welfare for municipal, industrial, and agricultural water users; treatment plant and network operators; and the natural environment. Two contrasting use cases will be considered in this research: urban river restoration in the Anacostia Watershed (Use Case #1) in the metropolitan Washington, DC, area and economic development and ecological preservation in the Duck River Watershed (Use Case #2) in Tennessee. The work will establish new interdisciplinary collaborations between experts in operations research and water resources management, which will promote the progress of science and intellectual merit.

The work will use rigorous mathematical techniques to model deterministic and stochastic water infrastructure systems from a one-level and two-level equilibrium problem perspective based on non-cooperative game theory. The developed models combine engineering, water policy, machine learning, risk analysis, resilience planning and economic elements. The novelty of this work is that it accounts for risk and benefits in a systematic, unified, and endogenous manner across all entities and their interactions and allows the system operator/regulator to effectively balance risk and cost under uncertain and/or changing conditions. Furthermore, it is anticipated that the work will lead to algorithmic advances in decomposition methods for water equilibrium problems as well as stochastic equilibrium models for this general class of infrastructure equilibrium problems. Also, a rolling-horizon, stochastic mathematical program with equilibrium constraints will develop strategic learning algorithms for water stakeholders to improve their decision-making over time.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.