Modeling and Simulation of Stochastic Systems

点击翻译按钮获取中文摘要

This research program concerns the simulation and optimization of complex systems that involve uncertainty (stochastic systems). Stochastic modeling and numerical simulation are now primary tools in science, engineering, management, and several other areas. Simulation is often the only practical tool to deal with realistic models of complex systems, which are typically dynamic, stochastic, and nonlinear. Building sufficiently representative stochastic simulation models, designing efficient and reliable simulation methods, and using simulation to optimize decision/operation strategies in these systems, are tasks with enormous practical importance, but which remain very challenging. My goal is to contribute new ideas and methods to address these challenges both from theoretical viewpoints (for example, convergence analysis of algorithms and mathematical analysis of the structure of random number generators) and practical ones (empirical experimentation, software implementation, and adaptation to specific real-life applications). I work on general methodology as well as on selected applications in various fields such as finance, risk analysis, communications, reliability, and operations management in service systems. The main directions of my research, currently and over the next five years, are: (1) Study and improve the methods for generating (pseudo)random numbers by computer, for various usages (simulation, games, lotteries, etc.) and computing platforms (e.g., highly-parallel general-purpose processors with limited local memory); (2) develop and study randomized quasi-Monte Carlo (RQMC) methods for multivariate integration and optimization; (3) develop more realistic ways of modeling complex stochastic systems such as call centers, health-care systems, revenue management systems, and other types of operations management systems; (4) design efficiency-improvement (variance reduction) methods for simulation, including rare-event simulation; (5) develop stochastic simulation-based optimization methods for decision making in operations management.