Queues with Time-Varying Arrivals and Inspections with Applications to Hospital Discharge Policies
In 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) the amount of time between subsequent inspections should be uniform throughout a day, and 3) the marginal improvements of adding additional inspection times is decreasing.
Based on joint work with Jing Dong and Linda Green.
Carri Chan is an Associate Professor in the Decision, Risk and Operations Division at Columbia Business School. Her research interests are in data-driven modeling and analysis of service systems with an emphasis on healthcare operations management. Her current focus is on combining empirical approaches with mathematical modeling to develop evidence-based approaches to improving patient flow through hospitals. She is the recipient of a 2014 NSF CAREER award, an NSF/AHRQ grant, as well as a number of best paper awards. She received her BS from MIT in 2004 and MS and PhD from Stanford University in 2006 and 2010, all in Electrical Engineering.