NSF Award
2308120
Networks of queueing systems have broad applications in applied probability and operations research, such as in the design of call centers, factories, shops, offices, hospitals, public transportation services, and cloud computing systems. The goal of this project is to understand the impact of the network on the performance of large interacting queueing systems, in both typical scenarios and rare and unexpected scenarios with significant consequences. This research will help system managers design the queueing network and queueing policies, which will lead to better system efficiency and stability. The project will also develop new mathematical techniques for problems of networks of interacting queues, and the results will be beneficial to the study of areas beyond queueing systems, such as social science and epidemiology. This research project includes training undergraduate students, graduate students, and postdoctoral researchers.<br/><br/>This project focuses mainly on the analysis of asymptotic behavior of large-scale load balancing queueing systems on random graphs, including join-the-shortest-queue, join-the-idle-queue and power-of-d policies. Three classes of graphs will be considered: classic complete graphs, random graphs with homogeneous limits, and heterogeneous random graphs. The research objectives are to rigorously understand the crucial and challenging impacts of stochastic networks on the system performance, in particular the significant deviation from the classic complete graph setup, via obtaining various scaling limits, including laws of large numbers, central limit theorems, long-time stability, large deviation principles and moderate deviation principles, together with analyzing the associated accelerated Monte-Carlo schemes of numerical estimation of rare event probabilities. The study of typical asymptotic behaviors will require a combination of tools from the theory of weakly interacting particle systems and random graph/graphon theory. The main challenges of obtaining large and moderate deviation principles arise from system features of infinite dimensional dynamics, vanishing transition rates, and discontinuous statistics. Besides using classic large deviation approaches and weak convergence approaches, the study of atypical asymptotic behaviors will also require the development of new techniques, involving a combination of tools from stochastic analysis and differential equations.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
