Queues with Time-Varying Arrivals and Inspections with Applications to Hospital Discharge Policies

AbstractIn order for a patient to be discharged from a hospital unit, a physician must first perform a physical examination and review the pertinent medical information to determine that the patient is stable enough to be transferred to a lower level of care or be discharged home. Requiring an inspection of a patient's "readiness for discharge" introduces an interesting dynamic where patients may occupy a bed longer than medically necessary. Motivated by this phenomenon, we introduce a queueing system with time-varying arrival rates in which servers who have completed service cannot be released until an inspection occurs. We examine how such a dynamic impacts common system measures such as stability, expected number of customers in the system, probability of waiting, and expected waiting time. Leveraging insights from an infinite-server model, we're able to optimize the timing of inspections and find via theoretical and numerical analysis that 1 optimizing a single inspection time could lead to significant improvements in system performance when the amplitude of the arrival rate function is large, 2 multiple inspections should be uniformly distributed throughout the day, and 3 the marginal improvements of adding additional inspection times is decreasing.