Design, Performance Evaluation, and Optimization for Intensive Care Networks Based on Non-Hierarchical Overflow Loss Systems

In design and optimization of intensive care unit (ICU) networks, one common practice is to prioritize the treatment for patients of higher emergency levels, while ensuring fairness to other patients by guaranteeing a certain Quality of Service (QoS) level. One common approach to realize such priority arrangement is bed reservation policy, which designates a certain number of last occupied beds in each hospital to be exclusively used by certain patient classes. In this paper, we propose an approach that can significantly improve the computational efficiency in obtaining the optimal reservation thresholds for each patient class, given their respective requirements, in a non-hierarchical ICU model (where the external emergency patients can possibly be allocated to any ICU hospital), which has been shown to be computationally challenging in performance evaluation and optimization. Specifically, we apply the Information Exchange Surrogate Approximation (IESA) to analytically approximate the key QoS metrics under given reservation thresholds, and the integer Particle Swarm Optimization (PSO) algorithm to search for the optimal threshold based on the approximation results by IESA. We demonstrate numerically, with real data from ICUs in Hong Kong, that IESA can obtain reasonably accurate results for QoS metrics, and thus lead to accurate optimal reservation thresholds. In addition, our proposed approach combining IESA and PSO can significantly reduce the computation time by more than four orders of magnitude compared to the state-of-the-art evaluation and optimization methods in existing research for similar problems, especially for ICU networks with practical sizes.