Stochastic Convexity in Queueing Networks and its Applications

排队网络中的随机凸性及其应用

• 批准号: 9108540
• 负责人: David Yao
• 金额: $ 12万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-09-01 至 1994-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9108540&HistoricalAwards=false
• 关键词: Stochastic; Convexity; Queueing; Networks; its

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.

该项目是与加州大学伯克利分校的 J. George Shanthikumar 合作的。 主要研究者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特性，对于一般随机离散事件系统（特别是排队网络）的分析和优化设计至关重要。 该项目重点关注与排队网络结构和政策变化相关的属性。 为了建模和理解这些变化，单调性和凸性的概念并不直接适用。 将开发沿着随机重排和随机主要化的新概念和新机制。 这些概念为广泛应用于调度、控制和资源分配的“成对交换”论点提供了数学支持。 初步研究已经证明它们在应对结构和政策变化方面的有用性和有效性。 此外，这些属性是随机凸性的自然延伸。 排队网络中一种新的、统一的（基于样本路径的）二阶属性的层次结构现在似乎正在出现。 这些属性共同支持排队网络的（静态）参数化设计以及动态调度和控制。