Models and Insights for Hospital Inpatient Operations: Time-Dependent ED Boarding Time

Abstract

O ne key factor contributing to emergency department (ED) overcrowding is prolonged waiting time for admission to inpatient wards, also known as ED boarding time. To gain insights into reducing this waiting time, we study operations in the inpatient wards and their interface with the ED. We focus on understanding the effect of inpatient discharge policies and other operational policies on the time-of-day waiting time performance, such as the fraction of patients waiting longer than six hours in the ED before being admitted. Based on an empirical study at a Singaporean hospital, we propose a novel stochastic processing network with the following characteristics to model inpatient operations: (1) A patient's service time in the inpatient wards depends on that patient's admission and discharge times and length of stay. The service times capture a two-time-scale phenomenon and are not independent and identically distributed.(2) Pre-and post-allocation delays model the extra amount of waiting caused by secondary bottlenecks other than bed unavailability, such as nurse shortage.(3) Patients waiting for a bed can overflow to a nonprimary ward when the waiting time reaches a threshold, where the threshold is time dependent. We show, via simulation studies, that our model is able to capture the inpatient flow dynamics at hourly resolution and can evaluate the impact of operational policies on both the daily and time-of-day waiting time performance. In particular, our model predicts that implementing a hypothetical policy can eliminate excessive waiting for those patients who request beds in mornings. This policy incorporates the following components: a discharge distribution with the first discharge peak between 8 a.m. and 9 a.m. and 26% of patients discharging before noon, and constant-mean allocation delays throughout the day. The insights gained from our model can help hospital managers to choose among different policies to implement depending on the choice of objective, such as to reduce the peak waiting in the morning or to reduce daily waiting time statistics.

Using a birth‐and‐death process to estimate the steady‐state distribution of a periodic queue

“…lengthof-stay random variables under the assumption that the length of stay should only depend on the patient's medical condition. The fitted death rates show that the length-of-stay distribution should be regarded as time-varying, which is consistent with the conclusions reached in [2,28,36]. In Section 6.4, we advocate the fitted BD process as a statistical test of the muchused M t /M/s + M Erlang-A model.…”

“…PROOF: First, we get (30) directly from Theorem 2.5 and formulas (27) and (28). The first term in (31) can be taken as a definition.…”

Queueing Models of Case Managers

“…This approach, however, has rarely been used to study service systems. Ramakrishnan et al (2005) and Shi et al (2016) examine patient flow between a hospital's ED and in-patient beds using a different type of two-time-scale analysis, one in which the speed of the fast time scale does not approach infinity, as it does in the approach we use. The approximation is related to Gilbert's (1996) "perpetual backlog" system, a finite-source model of a single case manager that assumes that the manager is always at the caseload limit.…”

Managing urgent care in hospitals

“…Given the nature of hospital wards, where patients spend some time both waiting and undergoing further treatment, these are modeled using queuing models [45,83,87,166,169,175,217,246,258,260], or simulation [18,22,33,50,51,71,90,97,109,142,150,151,157]. Complete hospital bed planning is also modeled [24,109,151,242], and when wards are evaluated elective patients may also be included [24,103,125,146].…”

“…Discharge policies are also a topic of research. [217] model an ED and inpatient wards to gain insight into waiting time reductions. They find that a discharge policy that focuses on better discharging patient throughout the day such that boarding and waiting times at the ED are reduced.…”