CAREER: Approximations and Bounds for Stationary and Transient Characteristics of a Class of Queueing Networks

这项职业研究的目标是开发制造系统中普遍存在的排队网络的分析模型。具体地说，为这些排队网络的某些特征建立近似值和界。需要考虑的一些关键性能指标是暂态和平稳停留时间的均值、方差、尾概率以及暂态和平稳等待时间的协方差。不幸的是，除非网络具有非常简单的结构并且在非常严格的假设下运行，否则很难获得此类性能指标的闭合形式的表达式。为此，将提供可用于数值逼近这些特性的展开公式。在这个项目中开发的分析模型最终可以用于设计新的工作发布和调度策略，这些策略将导致制造操作的改善，并最终增加美国制造商的竞争力。这项职业教学计划旨在通过专注于新课程开发项目、案例研究和其他课程材料的开发，并让本科生和硕士学生参与研究来改善工程教育。特别是，教育工作将侧重于为重组的本科随机过程课程开发课程材料，并设计一门新的研究生水平课程，重点放在制造业的随机模型上。此外，它还将致力于通过设计主动学习技术和让本科生和硕士学生参与研究来丰富学生的教育经验。

The objective of this CAREER research is to develop analytical models of queuing networks that are prevalent in manufacturing systems. Specifically, develop approximations and bounds for certain characteristics of these queuing networks. Some key performance measures to be considered are mean, variance, tail probability of transient and stationary sojourn times and covariance of transient and stationary waiting times. Unfortunately, it is very hard to get closed-form expressions for such performance measures unless the network has a very simple structure and it is operating under very restrictive assumptions. To this end, expansion formulae will be provided that can be used to numerically approximate these characteristics. The analytical models developed during this project can be eventually used to design new job release and scheduling strategies that will lead to improvements in manufacturing operations and ultimately increase the competitiveness of U.S. manufacturers.This CAREER teaching plan aims to improve engineering education by focusing on new course development projects, development of case studies and other course materials and involving undergraduate and master's students in research. In particular, the educational effort will focus on the development of course materials for the restructured undergraduate stochastic processes course and the design of a new graduate level course that will focus on the stochastic models in manufacturing. In addition, it will concentrate on enriching the students' educational experience by devising active learning techniques and involving undergraduate and masters students in research.