RIA: Alternate Representations of Stochastic Processes and Perturbation Analysis of Discrete-Event Dynamic Systems

本研究的目的是将无穷小摄动分析（IPA）方法推广到新的大型离散事件动态系统（DEDS）中，从而使其成为分析和控制DEDS的实用工具。目前研究界的共识是，IPA是一种有效的工具，但其可应用的系统范围相当有限。例如，它通常不适用于具有多类客户的系统或具有有限容量缓冲区的系统。但是这些特性是许多应用程序的核心。因此，IPA被广泛认为是一种有趣的技术，但没有实际用途。我们认为这是不正确的，国际音标法可以相当普遍地应用。我们已经为这一说法提供了理论支持；本研究的目的是将这一理论转化为实施IPA的实际“机制”。我们的方法是基于使用过程的适当表示（构造）在样本路径空间上构造连续的度量变化映射。一个关键因素是，我们只需要对感兴趣的性能度量进行连续性，而不是对整个性能度量类进行连续性。这就大大削弱了适用国际音标的现有条件。本研究的成功将代表着DEDS性能导向分析与控制的突破，并对该领域的实际成功做出重大贡献。

The goal of this research is to extend the method of infinitesimal perturbation analysis (IPA) to large new classes of discrete-event dynamic systems (DEDS), and thus make it a practical tool for analysis and control of DEDS. The current consensus of the research community is that IPA is an effective tool, but quite limited in the range of systems to which it can be applied. For example, it is generally inapplicable to systems with multiple classes of customers or systems with finite-capacity buffers. But these features are central in many applications. Thus IPA is widely regarded as an interesting technique, but not practically useful. We claim that this is incorrect and that IPA can be applied quite generally. We have developed theoretical support for this claim; the purpose of this research is to translate this theory into a practical "machinery" for implementing IPA. Our approach is based on constructing continuous measure-changing mappings on the sample path space using an appropriate representation (construction) of the process. A key element is that we require continuity only for the performance measure of interest, rather than an entire class of performance measures. This allows a substantial weakening of the existing conditions for the applicability of IPA. The success of this research will represent a breakthrough in the performance- oriented analysis and control of DEDS, and contribute substantially toward practical success in this area.