Foundations for Discrete Event Stochastic Systems

在模拟一般排队网络的资源循环时，系统状态可以用整数数组表示。运行这些模拟相当于在特定事件时间增加和减少这些数组中元素的值。许多这些模拟的动力学可以用线性和混合整数程序来表示。数学程序的解与运行仿真生成的状态轨迹相同。这些数学程序中的变量是事件时间。系统事件之间的关系约束了这些事件时间。与系统仿真一样，数学程序的目标是在系统的逻辑和动力学所施加的约束下尽快执行事件。该项目的目标是产生一种方法来建模离散事件动态系统作为组合优化问题。该方法来源于一种模拟建模技术，该技术是为解决特定的大规模工程问题而以一种特殊的方式开发的。本研究将在一般情况下研究这种建模方法的理论和实践基础。许多复杂的系统，包括卫生保健提供、运输、通信和生产系统，可以有效地建模为在特定事件发生时发生的离散变化。这些系统可以通过在计算机上调度事件来模拟真实系统中这些事件的发生。在本研究中，离散事件系统将使用运筹学的优化工具和技术建模。这将允许数学和随机规划的丰富理论和算法应用于这类大型和重要的动态系统的建模和分析。

In simulating the resource cycles in general queuing networks, the system state can be represented by integer arrays. Running these simulations amounts to increasing and decreasing the values of elements in these arrays at specific event times. The dynamics of many of these simulations can be formulated as linear and mixed-integer programs. The solutions to the mathematical programs are identical to the state trajectories generated by running the simulation. The variables in these mathematical programs are the event times. Relationships between system events constrain these event times. The objective of the mathematical program, like in a system simulation, is to execute events as soon as possible subject to the constraints imposed by the logic and dynamics of the system. The project objective is to produce a methodology for modeling discrete event dynamic systems as combinatorial optimization problems. The approach is derived from a simulation modeling technique that was developed in an ad-hoc manner to solve specific large-scale engineering problems. This research will study the theoretical and practical foundations of this modeling methodology in a generic context.Many complex systems, including health care delivery, transportation, communication and production systems, can be effectively modeled as undergoing discrete changes that take place when particular events occur. These systems can be simulated by scheduling events on a computer that mimic the occurrences of these events in the real system. In this research, discrete event systems will be modeled using the optimization tools and techniques of operations research. This will allow the rich theory and algorithms of mathematical and stochastic programming to be applied to the modeling and analysis of this large and important class of dynamic systems.