Queuing Systems with Dependencies: Theory and Applications

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Queuing models provide important methods for studying customer flow in many service industries. Patient flow in hospitals and calls to large-scale call centers provide examples of systems where waiting time in queue and service time may exhibit a complicated dependance structure not typically accounted for in existing models. This project will provide fundamental new theoretical understanding as well as efficient computational approaches for queueing systems where service requirements may exhibit certain types of dependance with waiting times in the queue. The project will specifically seek better models and policies for critical care service systems, for example, in hospital emergency departments where patient health can deteriorate significantly while waiting for service. This research will support graduate students in developing new quantitative skills and to use these to solve challenging operational problems.The dependence of the service times on the delay in queue (endogenous dependence) or the patience distribution (exogenous dependence) gives rise to substantial empirical and mathematical difficulties due to the fact that the queue processes do not admit a (finite-dimensional) Markov representation. Even limiting approximations for infinite-dimensional Markov (measure-valued) representations require new techniques, because existing techniques rely heavily on the service times being independent of other primitive distributions. This project will develop rigorous new tools to overcome these difficulties. In particular, novel stochastic-process approximations and limiting techniques will be employed in order to provide effective approximations for the complex queueing dynamics, and in turn, to optimize operations. To facilitate the implementation of the project's models in practice, the empirical challenges will be addressed as well, in order to appropriately fit the models to real-world systems.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.