Queueing Models and Optimization for Healthcare System Design and Improvement

在过去的二十年里，模拟一直是医疗运营管理的主要工具。尽管它能够通过将所有细节合并到单个模型中来建模复杂的随机系统，但仿真模型主要用于验证和实际实施。在具有内在不确定性的情况下，决策模型有助于对运营决策制定进行有价值的见解，并且越来越多地用于解决电信，柔性制造和库存管理等领域的复杂问题。实践证明，在一般情况下，使用最少的输入数据就可以生成可靠的结果。尽管有明显的优势，但由于所需的建模假设和解决这些模型时遇到的困难，因此在解决医疗保健系统运营问题时，模糊理论一直未得到充分利用。本研究的重点是医疗保健系统的随机建模和优化。我将建立和分析具有状态依赖服务的复杂随机系统的调度模型，其中服务时间取决于系统的一些外部或内部因素。这些模型表现出一些特殊的结构，如拟生灭过程，使其解决方案的数值分析方法，如矩阵分析方法或分析近似。我将开发专门的算法和优化模型，可用于设计可持续的医疗保健系统和解决运营问题。两个应用领域将被调查：医疗服务系统与状态相关的服务，预约调度。在这两个领域中，将开发和分析模型。显式公式的解决方案将被导出，以解决不同的医疗保健业务问题。目标是找到最佳设计和可持续实践，以优化患者等待时间、获得护理和资源利用等经典目标。**

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.**