Stability, Sensitivity and Optimization of Stochastic Systems

随机系统的稳定性、敏感性和优化

• 批准号: 1234100
• 负责人: Kavita Ramanan
• 金额: $ 28万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1234100&HistoricalAwards=false
• 关键词: Stability; Sensitivity; Optimization; Stochastic; Systems

This award provides funding for the development of analytical and computational tools for determining the sensitivity to system parameters of both transient and steady-state performance measures in queueing networks. Standard numerical methods to calculate sensitivity of performance measures with a high level of accuracy are usually computationally prohibitive because they involve a two-step approach of first obtaining numerical approximations of expectations of performance measures at different parameter values and then numerical differentiation of these approximate expectations. This work aims to provide a more tractable analytical characterization of the sensitivity in terms of a single expectation, and to then use this characterization to develop efficient one-step algorithms for the computation of sensitivities. In particular, this extends approaches that have been used in finance and other domains to queueing networks, where the issue is far more subtle due to the presence of boundaries. This award also supports research in the study of many-server queues, with the goal of obtaining tractable approximations for transient and steady-state performance measures associated with many-server queues. New tools will be developed for the analysis of stability in such systems and obtaining tractable approximations of steady state and transient performance measures and applied for optimal system design.Due to uncertainty in parameters, computation of sensitivities are very important for design and capacity allocation in queueing networks. The development of efficient computational tools would greatly enhance the planning capabilities of companies with manufacturing processes governed by queueing networks. Many-server queues arise in diverse applications such as call centers, health-care and data centers. In applications, knowledge of steady state and transient performance measures are required for staffing and decisions, the efficiency of which can have significant economic and social impact. In addition, this research will also develop new mathematical tools that will be applicable in a broader setting.

该奖项为开发分析和计算工具提供资金，以确定对排队网络​​中瞬态和稳态性能测量的系统参数的敏感性。 计算高准确性的性能度量敏感性的标准数值方法通常在计算上是过度的，因为它们涉及两步方法，即首先获得以不同参数值的绩效测量值的数值近似值，然后对这些近似期望的数值差异。 这项工作旨在根据单个期望来提供更容易触觉的分析表征，然后使用此表征来开发有效的一步算法来计算灵敏度。 特别是，这扩展了已在金融和其他领域中使用的方法排队网络，由于存在边界，因此问题更加微妙。 该奖项还支持研究多个服务队列的研究，目的是获得与多个服务队列相关的瞬态和稳态绩效指标的可拖动近似值。 将开发新工具，以分析此类系统中的稳定性，并获得稳态和瞬态性能度量的可拖动近似值，并应用于最佳系统设计。对于参数的不确定性，敏感性的计算对于排队网络的设计和容量分配非常重要。 有效的计算工具的开发将大大增强由排队网络控制的制造过程的公司的计划能力。 多个服务器队列在呼叫中心，医疗保健和数据中心等不同应用中出现。 在应用程序中，人员配备和决策需要了解稳态和瞬态绩效指标，其效率可能会产生重大的经济和社会影响。 此外，这项研究还将开发新的数学工具，这些工具将适用于更广泛的环境。