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

Abstract

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) multiple inspections should be uniformly distributed throughout the day, and 3) the marginal improvements of adding additional inspection times is decreasing.

Queueing Models for Patient-Flow Dynamics in Inpatient Wards

“…The most closely related works to ours are Chan et al (2017) and the series of papers Dai and Shi (2017), Shi et al (2016), Dai and Shi (2018). In Shi et al (2016), the authors build a detailed simulation model to study the effects of operational policies in the IW on ED boarding times.…”

“…We next prove Theorem 1. We note that the stability of the embedded DTMC when D = 0 follows from Lemma 1 in Chan et al (2017), but a new proof is needed for the general case (with D > 0). To prove the theorem, we employ a more involved Lyapunov argument than the one in Chan et al (2017), building on the theory developed in Foss and Konstantopoulos (2006).…”

“…In Chan et al (2017) a time-varying queueing model with periodic inspection rounds, but no discharge delays, is analyzed. The main goal is to study the impacts of adding more inspection rounds on the system's performance, as well as to characterize the optimal times to perform those inspection rounds.…”

“…The main goal is to study the impacts of adding more inspection rounds on the system's performance, as well as to characterize the optimal times to perform those inspection rounds. Chan et al (2017) consider hospital units which are relatively lightly-loaded (e.g., ICUs), and thus employs highly-tractable infinite-server approximations for their analysis.…”

“…Furthermore, unlike Chan et al (2017), which focus on small units for which it is feasible to add inspection rounds, more than one inspection round is unlikely to take place in large IWs due to the number of people that are involved and the time that those inspection rounds consume. Thus, our model, goals and analyses are different than those in Chan et al (2017). In particular, we employ a fluid model to approximate the system's dynamics and key performance measures.…”