Queueing Models and Optimization for Healthcare System Design and Improvement

在过去的二十年里，模拟一直是医疗保健运营管理的主导工具。尽管它能够通过将所有细节整合到一个模型中来对复杂的随机系统进行建模，但仿真模型主要用于验证和实际实施。排队模型有助于在具有内在不确定性的情况下对运营决策提供有价值的见解，并已越来越多地被用于解决电信、柔性制造和库存管理等领域的复杂问题。排队模型已被证明可以用最少的输入数据为一般设置生成可靠的结果。尽管排队论具有明显的优势，但由于所需的建模假设和在求解这些模型时遇到的困难，排队论在解决医疗保健系统操作问题方面一直没有得到充分的利用。 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排队模型，其中服务时间取决于系统的某些外生或内在因素。这些模型表现出一些特殊的结构，例如准生灭过程，这使得它们可以用数值分析方法来求解，如矩阵分析方法或解析近似。我将开发专门的算法和优化模型，用于设计可持续的医疗保健系统并解决运营问题。将调查两个应用领域：具有状态依赖服务的医疗服务系统和预约安排。在这两个领域，将开发和分析排队模型。将推导出明确的公式解决方案，以解决不同的医疗保健运营问题。我们的目标是找到一个优化的设计和可持续的实践，以优化经典的目标，如患者等待时间、获得护理的机会和资源利用。

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.