Stability, Sensitivity and Optimization of Stochastic Systems

该合同为分析和计算工具的开发提供资金，用于确定排队网络中瞬态和稳态性能测量对系统参数的敏感性。以高精确度计算性能指标灵敏度的标准数值方法通常在计算上令人望而却步，因为它们涉及两步方法：首先获得不同参数值下性能指标期望的数值近似值，然后对这些近似期望进行数值微分。这项工作的目的是提供一个更易于处理的灵敏度分析表征，在一个单一的期望，然后使用这种表征来开发有效的一步算法计算灵敏度。特别是，这将在金融和其他领域使用的方法扩展到排队网络，由于存在边界，问题要微妙得多。该奖项还支持对多服务器队列的研究，其目标是获得与多服务器队列相关的瞬态和稳态性能度量的可处理近似值。将开发新的工具来分析这些系统的稳定性，并获得稳态和瞬态性能测量的可处理近似值，并应用于最佳系统设计。由于参数的不确定性，灵敏度的计算对排队网络的设计和容量分配具有重要意义。高效计算工具的发展将极大地提高那些生产过程受排队网络控制的公司的计划能力。许多服务器队列出现在呼叫中心、医疗保健和数据中心等不同的应用程序中。在应用中，稳态和瞬态性能测量的知识是人员配置和决策所必需的，其效率可以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，将适用于更广泛的环境。

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.