基于排队模型的重症医疗系统的最优设计与控制

The Optimal Design and Control for the Intensive Health Care System Based on Queueing Models

摘要: 针对重症病人在就诊时处于等待状态和治疗状态需要昂贵的医疗资源这一现状，本文实现了针对不同的病人到达速率的重症医疗系统的最优设计与控制。首先，利用具有随机性的排队模型对主要进行两阶段治疗的重症医疗系统进行建模和刻画；其次，使用离散时间马尔可夫链的平衡方程来分析该二阶段随机系统的稳态分布的形式，利用具有乘积解的扰动随机游动和基于马尔可夫报酬过程的逼近策略来对每个治疗阶段平均等待的病人数进行逼近，并确定该重症医疗系统的最优病床数；然后，在医疗资源确定的情形下，利用排队博弈理论，确定该重症医疗系统最优的病人到达率来控制该随机系统的繁忙程度；最后通过数值实验分析，验证了基于排队模型的重症医疗系统的最优设计与控制的有效性，研究结果可为二阶段且等待花费很高的随机服务系统提供系统设计与控制的理论与技术支持。

Abstract: Due to the high cost for the health care resources for the patients in serious condition which require intensive health care either in waiting or treatment state, this paper aims for optimal design and control for this intensive health care system with a given patients’ arrival rate. Firstly, this stochas-tic two-stage intensive health care system has been characterized by a two-node queueing model. Secondly, based on the balance equations of the discrete-time Markov chain, the form of the sta-tionary distribution of this two-stage stochastic system has been analyzed. Deploying the perturbed random walk which has a product-form solution and the Markov reward process based approxima-tion scheme, this paper finds the mean number of patients waiting in each stage, which can be used to determine the optimal design for the beds in the intensive health care system. Thirdly, when the medical resources are determined, using the queueing game theory, the equilibrium arrive rate for the intensive health care system has been determined; finally, based on the numerical example, it has been shown that our approach can be used to design and control for the intensive health care system effectively. Our results can also be applied to the optimal design and control for other two-stage stochastic system with high cost in waiting.