The goal of the project is to study complex stochastic systems, with one particular focus on cascading failures. Systems such as the electric power grid and fault-tolerant computing systems suffer from such failures, and the effective design and operation of these systems critically depend on accurate modeling and effcient analysis techniques. The investigators plan to produce effcient analytical and simulation methods for analyzing such systems. Because these systems are designed to fail only very rarely, standard simulation methods are ineffective, necessitating the use of effciency-improvement techniques, which the investigators plan to develop. Another aspect of the project is producing simulation methods with properties that make them appropriate to use within stochastic optimization algorithms. In addition to having low bias and variance, these estimators will use a bounded amount of memory and will not require an a priorixed simulation run length. Cascading failures affict many complex systems, including those that make up the nation's critical infrastructure, such as the electric power grid and communication networks.
The techniques that the investigators propose to develop will lead to a better understanding of this potentially devastating phenomenon and more generally will aid in designing and optimizing systems operating under uncertainty. The investigators will enhance a software package they developed to incorporate the new modeling and analysis advances, taking into account special structure inherent to some of these infrastructures, such as the electric power grid. Other broader impacts of the proposed work include educating and including in research underrepresented minorities and undergraduates and outreach to local high schools.
The goals of the grant are to develop mathematical and computer-based methods to analyze complex stochastic systems. One main focus is on studying systems that are subject to cascading failures, as occur in the electric power grid and large networks of computing systems. The project has produced efficient Monte Carlo simulation and analytical methodologies to analyze such systems. The grant has also supported research on efficient simulation techniques to evaluate risk, such as portfolio risk for financial institutions and as needed for safety and uncertainty analyses of nuclear power plants. The intellectual merit of the supported research stems from the innovative models and analysis techniques developed. One project supported from the grant efficiently estimates the failure probability of a distribution network, and the asymptotic efficiency of the proposed algorithms is rigorously established. Another project develops efficient algorithms and data structures to analyze complex stochastic systems with cascading failures, reducing computation times by orders of magnitude. Other grant work devises new methods to construct asymptotically valid confidence intervals for a quantile, which has applications in analyzing risk. Also, the project has provided new algorithms for simulation-based optimization and rigorously analyzed them. The grant work has had many broader impacts in addition to addressing the application areas described above. The research on confidence intervals for quantiles is useful for safety analyses and probabilistic risk assessments of nuclear power plants (NPPs). Federal regulations require NPP licensees to establish, with high confidence, that the risks from hypothesized accidents are acceptably low. Currently, only simple random sampling is applied for these analyses, but this approach can result in unusably noisy estimates. The new results on confidence intervals for quantiles when applying variance-reduction techniques has the potential to alter policies governing how safety analyses are performed on NPPs. The grant has supported both graduate and undergraduate students, one through a Research Experience for Undergraduates Supplement. The PI has visited high schools in New Jersey to discuss career opportunities in science, technology, engineering and mathematics disciplines, and to discuss his research. The new techniques developed in the project have also been incorporated in undergraduate and graduate courses at the investigators' university.
