CAREER: Robust Design and Control of Parallel Server Systems: Analysis via Augmented Fluid Models and Heavy-Traffic Asymptotic Regimes

本学院早期职业发展（Career）项目的研究目标是确定有效的控制政策，并建立新的理论工具来分析这些政策和其他在需求不确定性下运行的复杂系统中常用的政策。本研究主要包括两个部分。在第一部分中，将建立一个新的框架，称为增强流体模型，来研究常用的控制策略的稳定性，如静态优先级策略和基于队列长度的策略。增强流体模型使人们能够使用更简单的确定性流体模型来建立这种系统的稳定性，并扩展了传统流体模型的应用领域。在研究的第二部分，重点将放在面对需求率不确定性的排队系统的容量和控制的联合确定，目标是提供期望的服务质量水平。新的控制策略将被开发出来，不需要任何到达率信息，在制定调度决策时不使用任何明确的统计学习。将使用多服务器渐近分析来确定所建议策略的有效性。如果成功，该项目将为实践中常用政策的稳定区域提供明确的解决方案。这将反过来改善现代服务业、制造业和通信网络中出现的系统设计。由此产生的策略有可能应用于面临时间依赖和随机到达率的各种应用程序以及可能变得过载的应用程序。在业务系统和通信网络中的应用将导致在具有不同特征的用户之间实时有效地利用和分配可用资源。本研究结果将纳入本科及研究生课程。通过与行业公司的合作，将现代应用，特别是来自服务系统的应用纳入教学活动。

The research objective of this Faculty Early Career Development (CAREER) project is to identify effective control policies and build new theoretical tools for the analysis of these and other commonly used policies in complex systems operating under demand uncertainty. The research consists of two main parts. In the first part, a new framework, referred to as augmented fluid models, will be established to study the stability of commonly used control policies such as static priority policies and queue length based policies. Augmented fluid models enable one to establish the stability of such systems using much simpler deterministic fluid models and they extend the application domain of traditional fluid models. In the second part of the research, the focus will be on joint determination of capacity and control of queueing systems facing demand-rate uncertainty with the objective of providing a desired level of quality of service. New control policies will be developed that do not require any arrival-rate information and that do not use any explicit statistical learning when making scheduling decisions. Effectiveness of the proposed policies will be established using a many-server asymptotic analysis.If successful, this project will provide explicit solutions for the stability region of commonly used policies in practice. This will in turn improve the design of systems arising in modern service, manufacturing and communication networks. The resulting policies have the potential to be applied in a variety of applications facing time-dependent and random arrival rates as well as in those applications that may become overloaded. Applications in service systems and communications networks will result in effective use and distribution of available resources on a real time basis among users with different characteristics. The findings of this research will be integrated into undergraduate and graduate courses. Contemporary applications, especially from service systems, will be incorporated into teaching activities via collaborations with companies from the industry.