On Fair Routing from Emergency Departments to Hospital Wards: QED Queues with Heterogeneous Servers

The interface between an emergency department and internal wards is often a hospital's bottleneck. Motivated by this interaction in an anonymous hospital, we analyze queueing systems with heterogeneous server pools, where the pools represent the wards, and the servers are beds. Our queueing system, with a single centralized queue and several server pools, forms an inverted-<i>V</i> model. We introduce the randomized most-idle (RMI) routing policy and analyze it in the quality- and efficiency-driven regime, which is natural in our setting. The RMI policy results in the same server fairness (measured by idleness ratios) as the longest-idle-server-first (LISF) policy, which is commonly used in call centers and considered fair. However, the RMI policy utilizes only the information on the number of idle servers in different pools, whereas the LISF policy requires information that is unavailable in hospitals on a real-time basis. <i>This paper was accepted by Assaf Zeevi, stochastic models and simulation.</i>