Modeling and Simulation of Stochastic Systems

这个研究项目涉及不确定性（随机系统）的复杂系统的模拟和优化。随机建模和数值模拟现在是科学、工程、管理和其他一些领域的主要工具。模拟通常是处理复杂系统的现实模型的唯一实用工具，这些模型通常是动态的、随机的和非线性的。建立具有足够代表性的随机仿真模型，设计高效可靠的仿真方法，并利用仿真优化这些系统中的决策/操作策略，是具有巨大现实意义的任务，但仍然非常具有挑战性。我的目标是从理论角度（例如，算法的收敛分析和随机数生成器结构的数学分析）和实践角度（经验实验，软件实现和适应特定的现实生活应用）贡献新的想法和方法来解决这些挑战。我研究一般的方法，以及在各个领域的选择应用，如金融、风险分析、通信、可靠性和服务系统的运营管理。我目前和未来五年的主要研究方向是：(1)研究和改进计算机生成（伪）随机数的方法，用于各种用途（模拟、游戏、彩票等）和计算平台（例如本地内存有限的高度并行通用处理器）；(2)开发和研究随机拟蒙特卡罗（RQMC）多元积分与优化方法；(3)开发更现实的方法来建模复杂的随机系统，如呼叫中心、医疗保健系统、收益管理系统和其他类型的运营管理系统；(4)设计效率改进（方差减少）模拟方法，包括罕见事件模拟；(5)发展基于随机模拟的运营管理决策优化方法。

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.