An earlier article, inspired by overflow models in telecommunication systems with multiple streams of telephone calls, proposed a new analytical model for a network of intensive care units (ICUs), and a new patient referral policy for such networks to reduce the blocking probability of external emergency patients without degrading the quality of service (QoS) of canceled elective operations, due to the more efficient use of ICU capacity overall. In this work, we use additional concepts and insights from traditional teletraffic theory, including resource sharing, trunk reservation, and mutual overflow, to design a new patient referral policy to further improve ICU network efficiency. Numerical results based on the analytical model demonstrate that our proposed policy can achieve a higher acceptance level than the original policy with a smaller number of beds, resulting in improved service for all patients. In particular, our proposed policy can always achieve much lower blocking probabilities for external emergency patients while still providing sufficient service for internal emergency and elective patients. In addition, we provide new accurate and computationally efficient analytical approximations for QoS evaluation of ICU networks using our proposed policy. We demonstrate numerically that our new approximation method yields more accurate, robust and conservative results overall than the traditional approximation. Finally, we demonstrate how our proposed approximation method can be applied to solve resource planning and optimization problems for ICU networks in a scalable and computationally efficient manner.
Keywords: Analytical approximation; Intensive care units; Optimization; Overflow networks.