Telehealth Control Policies: Bridging the Gap Between Patients and Doctors

Abstract

This paper studies a sequential decision-making problem in a two-stage queueing system modeled after operations in CVS MinuteClinics, where nurse practitioners (NPs) oversee patient care throughout the entire visit. All services are non-preemptive, and NPs cannot begin treating a new patient until the current patient has completed both stages of care. Following an initial diagnosis in the upstream phase, NPs must decide for low-acuity patients whether to proceed with treatment independently through immediate service, or to collaborate with a dedicated general physician (GP) via telemedicine. While collaboration typically improves service quality and is preferred by individual patients, it may introduce delays as the NP-patient pair waits for a GP to become available. This work explores the structural properties of optimal policies under different system parameters, with a focus on large initial upstream queues, revealing unconventional and complex policy behaviors. Leveraging these structural insights and supporting theoretical results, we design simple and effective heuristics that are computable in linear time and suitable for practical implementation. These heuristics are robust across the entire parameter space of interest, and offer clear, actionable guidance for NPs as system parameters vary. They also achieve near-optimal performance, averaging within 0.1% of the optimal, while commonly used benchmark policies are highly sensitive to parameter shifts and can incur costs more than 100% higher than optimal. The work provides applicable insights for decision-makers on improving policy robustness and effectiveness, as well as recommendations for stakeholders on the value of investing in telemedicine infrastructure. For instance, we identify scenarios where such investments may be either unnecessary or essential based on specific system parameters.