Modeling and Simulation of Stochastic Systems

该研究项目涉及涉及不确定性的复杂系统(随机系统)的模拟和优化。随机建模和数值模拟现在是科学、工程、管理和其他几个领域的主要工具。仿真往往是处理复杂系统真实模型的唯一实用工具，这些系统通常是动态、随机和非线性的。建立具有足够代表性的随机模拟模型，设计高效、可靠的模拟方法，并利用模拟来优化这些系统中的决策/运营策略，是具有巨大现实意义的任务，但仍然具有很大的挑战性。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、软件实现和特定现实应用程序的适应)提供新的想法和方法来应对这些挑战。我从事一般方法论方面的工作，以及在不同领域的选定应用程序，如金融、风险分析、通信、可靠性和服务系统中的运营管理。我目前和今后五年的主要研究方向是：(1)研究和改进计算机产生(伪)随机数的方法，用于各种用途(模拟、游戏、彩票等)。(2)开发和研究用于多变量集成和优化的随机准蒙特卡罗(RQMC)方法；(3)开发更逼真的方法来建模复杂的随机系统，如呼叫中心、医疗保健系统、收入管理系统及其他类型的运营管理系统；(4)设计用于模拟的效率提高(方差减少)的方法，包括罕见事件模拟；(5)开发基于随机模拟的优化方法，用于运营管理中的决策。

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.