Stochastic Convexity in Queueing Networks and its Applications

该项目是与加州大学伯克利分校的J.George Shanthikumar合作完成的。主要研究人员提出了强随机凸性和方向凸性的概念，它们是基于样本路径的结构性质，对于一般的随机离散事件系统，特别是排队网络的分析和优化设计是必不可少的。这个项目集中在与排队网络中的结构和策略改变相关的性质。要模拟和理解这些变化，单调性和凸性的概念并不直接适用。将沿着随机重排和随机优化的路线开发新的概念和新的机制。这些概念为在调度、控制和资源分配中广泛使用的“成对交换”参数提供了数学支持。初步研究表明，它们在处理结构和政策变化方面是有用和有效的。此外，这些性质是随机凸性的自然推广。排队网络中一种新的、统一的(基于样本路径的)二阶性质层级现在似乎正在出现。综合起来，这些性质将支持排队网络的(静态)参数设计，以及动态调度和控制。

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.