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

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.