Stochastic Convexity in Queueing Networks and its Applications

该项目是与J.乔治Shanthikumar合作， 加州大学伯克利分校。 主要研究者 发展了强随机凸性的概念， 方向凸性，这是基于样本路径的结构 分析和优化设计所必需的性能 一般随机离散事件系统与离散网络 特别是。 该项目的重点是有关的财产， 网络的结构和政策变化。 进行建模和 理解这些变化，单调性和凸性的概念 不直接应用。 沿着 随机重排和随机优化线将 发展。 这些概念提供了数学支持， “成对交换”参数，广泛用于 调度、控制和资源分配。 初步研究 已经证明了它们在处理 结构和政策的变化。 此外，这些属性 是随机凸性的自然扩展。 一个新的，统一的（基于样本路径的）二阶 网络中的属性似乎正在出现。 这些属性一起将支持（静态）参数化 调度网络的设计、动态调度和控制。

This project is collaborative with J. George Shanthikumar of University of California at Berkeley. The principal investigator's developed the notions of strong stochastic convexity and directional convexity, which are sample- path based structural properties essential to the analysis and optimal design of stochastic discrete event systems in general and queueing networks in particular. This project focuses on properties relating to structural and policy changes in queueing networks. To model and understand these changes, notions of monotonicity and convexity do not apply directly. New concepts and new machineries along the lines of stochastic rearrangement and stochastic majorization will be developed. These notions provide mathematical support for "pairwise interchange" arguments that are widely used in scheduling, control, and resource allocation. Preliminary studies have demonstrated their usefulness and effectiveness in dealing with structural and policy changes. Furthermore, these properties are natural extensions of stochastic convexity. A new, unified hierarchy of (sample-path based) second-order properties in queueing networks appears to be now emerging. Together, these properties will support the (static) parametric design of queueing networks, and dynamic scheduling and control.