Collaborative Research: A Framework for Evaluation, Approximation, and Optimization of Time-Dependent Stochastic Service System Models having Deterministic/Scheduled Interventions

协作研究：具有确定性/预定干预的时间相关随机服务系统模型的评估、近似和优化框架

• 批准号: 1538055
• 负责人: Michael Taaffe
• 金额: $ 27万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-08-01 至 2019-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1538055&HistoricalAwards=false
• 关键词: Collaborative; Research; Framework; Evaluation; Approximation

This award supports establishing a mathematical framework for modeling, evaluating, approximating, and optimizing the performance of service systems featuring time-varying random as well as deterministic/scheduled input processes. Two important example problem classes are (1) optimizing efficiency and utilization while improving patient satisfaction in healthcare facilities that treat both time-varying randomly-arriving patients (e.g., emergent or walk-in) as well as patients having scheduled appointments (e.g., primary-care-physician referrals, school-required physical exams, or scheduled vaccinations), and (2) optimizing efficiency and utilization while improving flexibility and responsiveness to global competition in manufacturing facilities that operate in both a time-varying stochastic (e.g., production) environment as well as a deterministic/scheduled (e.g., job-release schedule) environment. The solution to a unified abstraction of both problem classes requires modeling and analysis methods that allow rich variations in model-input processes, and model logic, while adequately capturing the time-dependent evolution of the resulting probabilistic network. Traditional (exact) time-dependent differential-difference equation modeling of such networks is infeasible since the number of differential-difference equations describing even modest-sized networks can be of the order of hundreds of thousands (or more). Monte Carlo (MC) computer simulation, the natural alternative choice, is convenient but burdened with slow convergence rates and additional mathematically technical inefficiencies. Methods investigated by the research team will assist healthcare (and other) service and manufacturing sector industries to increase their economic competitiveness and patient/customer, satisfaction.The research will result in closure-equipped partial moment differential equations (PMDEs) for numerically approximating the time-dependent evolution of general stochastic networks having scheduled interventions. By exploiting the structure of PMDEs, and then strategically using closure approximations, the research team will be able to efficiently describe the time-dependent evolution of very general networks. Preliminary evidence indicates that the time-dependent evolution of modest stochastic networks can be approximated to machine accuracy within a few seconds on a typical laptop computer. Moreover, higher order derivatives, which often require significant effort in the Monte Carlo context, can be obtained with little to no extra effort by exploiting the rich structure inherent in the approximations.

该奖项支持建立一个数学框架，用于建模、评估、近似和优化具有时变随机以及确定性/预定输入过程的服务系统的性能。 两个重要的示例问题类别是 (1) 优化效率和利用率，同时提高医疗机构的患者满意度，这些医疗机构治疗随时间变化的随机到达的患者（例如急诊或预约）以及预定预约的患者（例如初级保健医生转诊、学校要求的体检或预定的疫苗接种），以及 (2) 优化效率和利用率，同时提高灵活性和 在时变随机（例如生产）环境和确定性/预定（例如工作发布时间表）环境中运行的制造设施对全球竞争的响应能力。 两个问题类的统一抽象的解决方案需要建模和分析方法，这些方法允许模型输入过程和模型逻辑的丰富变化，同时充分捕获所得概率网络的时间相关演化。这种网络的传统（精确）时间相关微分方程建模是不可行的，因为即使描述中等规模的网络，微分方程的数量也可能达到数十万（或更多）的量级。蒙特卡罗 (MC) 计算机模拟是自然的替代选择，虽然很方便，但收敛速度慢且数学技术效率低下。 研究团队研究的方法将帮助医疗保健（和其他）服务业和制造业提高其经济竞争力和患者/客户满意度。该研究将产生配备闭包的偏矩微分方程（PMDE），用于数值近似具有预定干预措施的一般随机网络的时间相关演化。通过利用 PMDE 的结构，然后策略性地使用闭包近似，研究团队将能够有效地描述非常通用的网络的时间相关演化。 初步证据表明，在典型的笔记本电脑上，适度随机网络的时间相关演化可以在几秒钟内近似于机器精度。 此外，在蒙特卡罗背景下通常需要大量努力的高阶导数可以通过利用近似中固有的丰富结构而无需额外努力即可获得。