Queueing Models and Optimization for Healthcare System Design and Improvement

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Simulation has been the dominant tool for healthcare operations management for the last two decades. Despite its ability to model complex stochastic systems by incorporating all the details into a single model, simulation models are mainly useful for validation and actual implementation. Queueing models are good for developing valuable insights into operational decision making in situations with inherent uncertainty, and have been increasingly used to address complex problems in areas such as telecommunications, flexible manufacturing, and inventory management. Queueing models have been proven to generate reliable results for general settings with minimum input data. Despite its obvious advantages, queueing theory has been underutilized in solving healthcare system operational problems because of the required modeling assumptions and the difficulty encountered in solving those models. The focus of this research is stochastic modeling and optimization of healthcare systems. I will develop and analyze queueing models for complex stochastic systems with state dependent service in which service time depends on some exogenous or indigenous factors of the system. These models exhibit some special structure e.g. Quasi-Birth and Death process that enables their solution by numerical analysis methods, such as matrix analytic methods or by analytical approximations. I will develop specialized algorithms and optimization models that can be used to design sustainable healthcare systems and solve operational problems. Two application areas will be investigated: healthcare service systems with state dependent service, and appointment scheduling. In both areas, queueing models will be developed and analyzed. Explicit formula solutions will be derived to solve different healthcare operational problems. The goal is to find an optimal design and sustainable practices that optimize classical objectives such as patient wait-time, access to care, and resource utilization.