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

该学院早期职业发展(CALEAR)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，用于在需求不确定的情况下运行的复杂系统中分析这些政策和其他常用政策。本研究由两个主要部分组成。在第一部分中，将建立一个新的框架，称为增广流体模型，以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。增广流体模型使人们能够使用简单得多的确定性流体模型来建立这类系统的稳定性，它们扩展了传统流体模型的应用领域。在研究的第二部分，重点将集中在联合确定能力和控制面临需求率不确定性的排队系统，目的是提供期望的服务质量水平。将开发新的控制策略，这些策略不需要任何到达率信息，并且在做出调度决策时不使用任何明确的统计学习。所提出的策略的有效性将通过多服务器渐近分析来确定。如果成功，该项目将为实际中常用策略的稳定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的设计。由此产生的策略有可能应用于面临时间依赖和随机到达速率的各种应用以及可能变得超载的那些应用。在服务系统和通信网络中的应用将导致在不同特征的用户之间实时有效地使用和分配可用资源。这项研究的结果将被整合到本科和研究生课程中。当代应用，特别是来自服务系统的应用，将通过与行业公司的合作，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.