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

本研究的目的是扩展 无穷小扰动分析（IPA） 一类新的离散事件动态系统 （DEDS），从而使其成为一个实用的工具， DEDS的分析和控制。 当前 研究界的共识是，IPA是 一个有效的工具，但在范围内相当有限， 可以应用的系统。 例如它 通常不适用于具有多个 有限容量的一类用户或系统 缓冲器。 但这些特征在许多 应用. 因此，IPA被广泛认为是 有趣的技术，但实际上没有用。 我们 声称这是不正确的，IPA可以 应用相当普遍。 我们已经开发 这一主张的理论支持; 这项研究是将这一理论转化为 执行《投资促进机构协定》的实际"机制"。 我们 方法基于构造连续的 样本路径上的变测度映射 空间使用适当的表示 （建设）过程。 一个关键因素是， 我们只要求表演的连续性 而不是一个完整的阶级， 业绩计量。 这使得大量的 现有条件的削弱， IPA的适用性。 这项研究的成功 将代表着表演上的突破 面向DEDS的分析和控制，以及 为实际成功作出重大贡献 这方面

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.