The control of communication and power networks through regulation and deregulated market mechanisms presents tremendous challenges and affects almost every citizen of the United States. Theoretical understanding in this area is built on the mathematical field called stochastic networks, a field whose growth has been closely tied to the Institute for Mathematics and its Applications (IMA). In March 2004 the IMA brought together experts in fields as diverse as probability theory, statistics, electrical engineering, computer science, and economics, at a workshop entitled Control and Pricing in Communication and Power Networks. A topic of intense interest at the workshop was the rash of blackouts experienced in California a few years before, and its connection to the Enron scandal. Electricity prices in California had shown far more volatility than predicted by the simple static models that had been used to study the deregulated power market, and hence the prevailing view was that the explanation must lie in illegal market manipulation.
Sean Meyn, an electrical engineer from University of Illinois attending the workshop, was suspicious of this explanation and suggested that a good understanding of the physical characteristics of electrical generation together with a dynamic model of the electricity market might provide a better explanation of the observed volatility. The problem was to arrive at a model including the relevant factors, but still simple enough to analyze. Meyn engaged the diverse group of experts meeting at the IMA such as Marija Ilic, an expert in electric power systems modeling from Carnegie Mellon University. Lively discussions led Meyn, his economist collaborator In-Koo Cho, and Meyn's student Mike Chen (who was also at the IMA workshop, and whose thesis grew out of this work), to a new model. Their model, while still ignoring many of the complex details of power generation, captured the essential features: rapidly changing and unpredictable demand, constraints on the rate of increase of electricity generation, the lack of an economical method for storing electricity in quantity for later use, the availability from multiple sources, and the astronomical costs of failing to meet demand (think blackouts). Their analysis of the model demonstrates convincingly that volatility and high prices can be expected in a deregulated power market whenever the market achieves an efficient allocation. This striking result not only requires a rethinking of what put out the lights in California in 2000, but also opens the way for a new understanding of the implications of deregulation for other commodities.
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