Managing Queues with Reentrant Customers in Support of Hybrid Healthcare

The COVID-19 pandemic has profoundly boosted the use of hybrid healthcare settings, which orchestrate face-to-face services together with virtual ones. The advantages of virtual healthcare services are clear: they are less costly and less disruptive for patients who can receive the service in the comfort of their home and reduce patients’ exposure to illnesses prevalent in healthcare facilities. Nevertheless, there is evidence that patients are likely to require a supplementary in-person service upon completion of their virtual service. Motivated by such settings, we study a multiservice queueing system with face-to-face, virtual, and supplementary service channels. The service operator needs to allocate service capacity among the three classes and decide how to prioritize the patients when a service provider becomes available. The strong dependency between virtual and supplementary visits makes the problem challenging. Based on a fluid relaxation, we develop an index-based policy, the [Formula: see text] rule (or the [Formula: see text] rule in short), which, in addition to the holding cost, service time, abandonment rate, and service reward, also carefully balances the return probability and associated penalty. The theoretical results along with numerical experiments demonstrate the effectiveness of the proposed policy and the importance of capacity coordination when managing hybrid service settings. Our work provides insights on the trade-off between convenience and the value of care when offering virtual healthcare services. Funding: The author was supported in part by an Israel Science Foundation [Grant 277/21] and the Israel National Institute for Health Policy Research [Grant 2021/160/R].