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，近似和优化具有随机变化的随机以及确定性/计划的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，同时提高患者在医疗机构中的满意度，这些设施可以治疗随机差异的患者（例如，出现或步入式）以及计划预约的患者（例如，初级医生 - 物理学转诊，辅助体格检查效率及其效率），以及（2），或（2）对全球制造设施竞争的反应能力，这些竞争在随机变化的随机性（例如生产）环境以及确定性/计划的（例如，工作释放计划）环境中。 对两个问题类别的统一抽象的解决方案都需要建模和分析方法，以使模型输入过程和模型逻辑有丰富的变化，同时充分捕获所得概率网络的时间依赖性演变。此类网络的传统（精确）时间相关的差分方程建模是不可行的，因为描述甚至适度网络的差分差分方程的数量可能是数十万（或更多）的顺序。蒙特卡洛（MC）计算机模拟是自然的替代选择，很方便，但由于收敛速度缓慢和额外的数学技术低效率而负担重大。 研究团队研究的方法将帮助医疗保健（以及其他）服务和制造业行业提高其经济竞争力和患者/客户的满意度。该研究将导致具有封闭式的局部矩微分方程（PMDES），以在数值上近似于计划进行干预措施的一般随机网络的时间依赖时间依赖时间。通过利用PMDE的结构，然后从战略上使用闭合近似值，研究团队将能够有效地描述非常通用网络的时间依赖性演变。 初步证据表明，在典型的笔记本电脑上，可以在几秒钟内将适中随机网络的时间依赖性演变近似于机器的精度。 此外，通过利用近似值中固有的丰富结构，几乎没有额外的努力，通常需要在蒙特卡洛语境中进行大量努力的高阶衍生物。