Stability, Sensitivity and Optimization of Stochastic Systems

该奖项提供资金，用于开发分析和计算工具，以确定对瞬态和稳态性能测量的系统参数的灵敏度。 标准的数值方法来计算灵敏度的性能指标具有高水平的准确性通常是计算上禁止的，因为它们涉及一个两步的方法，首先获得数值近似的期望值的性能指标在不同的参数值，然后数值微分这些近似的期望。 这项工作的目的是提供一个更易于处理的分析表征的灵敏度在一个单一的期望，然后使用此特性开发有效的一步算法的灵敏度的计算。 特别是，这将金融和其他领域中使用的方法扩展到了社交网络，由于边界的存在，这个问题要微妙得多。 该奖项还支持多服务器队列的研究，目标是获得易于处理的 与多服务器队列相关的瞬态和稳态性能度量的近似值。 由于参数的不确定性，灵敏度的计算对于配电网的设计和容量分配是非常重要的。 有效的计算工具的发展将大大提高公司的规划能力，制造过程由制造网络管理。 多服务器队列出现在呼叫中心、医疗保健和数据中心等各种应用中。 在应用程序中，稳态和瞬态性能的措施的知识需要人员配置和决策，其效率可以有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，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.