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

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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 these 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.