Stability, Sensitivity and Optimization of Stochastic Systems

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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.