Stochastic Convexity in Queueing Networks and Its Applications

这个项目是与大卫D.哥伦比亚的姚 大学 主要的研究者提出了 强随机凸性和方向凸性 分析所必需的基于样本路径的结构特性 随机离散事件系统的最优设计 尤其是网络。 该项目的重点是 与住房结构和政策变化有关的财产 网络. 为了模拟和理解这些变化， 单调性和凸性不直接适用。 新概念和 沿着随机重新排列的路线， 将开发随机优化。 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。 初步研究表明，它们是有用的， 有效地处理结构和政策变化。 此外，这些性质是随机性的自然推广， 凸性 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 David D. Yao of Columbia University. The principal investigators 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 extension 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.