Optimal Control of a Medical Waiting System with Autonomous Patients

Waiting systems for medical services have two distinctive features that differentiate them from queueing systems commonly studied in Operations Management: variability in the quality of service, and patient autonomy. That is, patients in these systems recognize that waiting has an option value and, hence, are willing to decline a service offer if they expect future offers to be more attractive. In order to capture this behavior and identify mechanisms that alleviate the resulting externalities, we develop and analyze a stylized competitive queueing model. The model is an M/M/1 queue with reneging with the additional assumptions that patients may decline a service offer in order to maximize their own welfare, and that the quality of service is random and highly variable. Under an assumption of perfect and complete information we show that the queueing discipline is a potent instrument that can be used by the medical planner overseeing the waiting system in order to maximize social welfare. In particular, while the commonly used First-Come First-Serve (FCFS) discipline is found to be inefficient, Last-Come First-Serve (LCFS) achieves the socially optimal outcome. A numerical example demonstrates that the welfare losses from FCFS can be substantial.