This research is aimed at using mathematical optimization to solve a wide range of problems, including improving internet routing protocols, devising efficient methods of pricing telecommunications bandwidth, and inferring traffic flows in real-time from anonymous cell phone data. The most common intra-domain internet routing protocol requires creating fictitious "costs" for each link in the network. The standard heuristic method for doing that may lead to unnecessary network congestion. Observations of the bandwidth market show that there is often inefficiency in pricing, which allows arbitrage: clever purchasers can often construct more valuable connectivity than they pay for. A National Highway Traffic Safety Administration study estimated that 3% of American drivers are talking on cell phones at any given time; by anonymously tracking the progression of each call from one cell tower to another, it may be possible to estimate traffic patterns in the area without violating any individual caller's privacy. Although seemingly unrelated, these problems all have similar underlying mathematical structure. The shared mathematical structure of these optimization problems will be investigated and the knowledge gained will be used to develop ways of obtaining better solutions to each of these problems, as well as others which share the same properties. Practical outcomes include a decrease in network congestion, increased efficiency in the bandwidth marketplace, and real-time methods for deducing and responding to roadway congestion.
