Mathematical Sciences: Several Questions in Probability

数学科学：概率中的几个问题

• 批准号: 9209586
• 负责人: Jiangang Dai
• 金额: $ 10.5万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-01 至 1996-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9209586&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Several; Questions; Probability

This research involves the mathematical theory of probability and its application, and consists of largely independent investigations by two principal investigator, Professors Dai and Hill. Professor Dai's research will mainly focus on queueing networks, which arise from computer networks and manufacturing systems. It includes justification of the Brownian approximation for multiclass queueing networks, understanding network performance when it is heavily loaded, and computation of stationary distribution of a reflected Brownian motion. The ultimate goal is to develop a robust set of computer software tools that can accurately and efficiently predict the performance of a wide class of queueing networks. Professor Hill's research includes: optimal stopping problems, especially order selection and minimax rules; partitioning or fair-division problems in probability and statistics; one-sided limit laws and probability bounds, especially for means and quantiles; and fusions of probabilities and their relationship to dilation, convex domination and martingales. The principal investigators will carry out research in both theoretical and applied aspects of probability. The more applied topics include investigating the performance of queueing networks (inter-connected service facilities populated by randomly arriving customers with random amounts of service requirements) which arise from computer networks and manufacturing systems, and investigating optimal stopping theory (sequential analysis of time dependent random processes such as pollution levels in a city or stock prices). At one extreme, this research is aimed at developing practical computer software tools that can accurately and efficiently predict the performance of a wide class of random systems, and at the other extreme it is aimed at discovering new basic mathematical theorems in abstract spaces and settings.

这项研究涉及的数学理论， 概率及其应用，主要包括 由两名主要调查员进行独立调查， 戴教授和希尔教授 戴教授的研究将主要 专注于互联网，它源于计算机网络 和制造系统。 它包括理由， 多类神经网络的布朗近似， 了解网络在重负载时的性能，以及 反射布朗运动平稳分布的计算 议案 最终目标是开发一套强大的计算机 软件工具，可以准确和有效地预测 一个广泛的类嵌入式网络的性能。 教授 希尔的研究包括：最优停止问题，特别是 序选择和极大极小规则;划分或公平划分 概率和统计中的问题;片面极限定律和 概率界限，尤其是均值和分位数;以及 概率的融合及其与膨胀的关系， 凸控制和鞅 主要研究人员将在这两个领域开展研究。 概率的理论和应用方面。 应用越多 主题包括研究路由网络的性能 （随机分布的互联服务设施） 随机服务需求量的到达客户） 它产生于计算机网络和制造系统， 研究最佳停止理论（顺序分析） 时间依赖的随机过程，如污染水平， 市或股票价格）。 在一个极端，这项研究旨在 开发实用的计算机软件工具， 并有效地预测各种随机 在另一个极端，它旨在发现新的 抽象空间和背景中的基本数学定理。