Estimating the waiting time of multi-priority emergency patients with downstream blocking

Abstract

To characterize the coupling effect between patient flow to access the emergency department (ED) and that to access the inpatient unit (IU), we develop a model with two connected queues: one upstream queue for the patient flow to access the ED and one downstream queue for the patient flow to access the IU. Building on this patient flow model, we employ queueing theory to estimate the average waiting time across patients. Using priority specific wait time targets, we further estimate the necessary number of ED and IU resources. Finally, we investigate how an alternative way of accessing ED (Fast Track) impacts the average waiting time of patients as well as the necessary number of ED/IU resources. This model as well as the analysis on patient flow can help the designer or manager of a hospital make decisions on the allocation of ED/IU resources in a hospital.

Managing urgent care in hospitals

“…The other departments where non-elective care is offered also treat elective patients, and limited attention is given to non-elective patient planning and scheduling, as this is intrinsically more difficult, especially for the operating theater where elective patients must be scheduled well in advance. If multiple departments are taken into account, this is mainly done through patient flow modeling (61%), for example by modeling the entire care pathway of patients through ED and wards (e.g., [33,97,166]). As there are limitations to modeling approaches, direct model expansions to include Chapter 2.…”

“…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].…”

“…For example, [166] use a queuing approach to model both ED and downstream inpatient units. They link the size of inpatient units, and patient length of stay to the required capacity at the ED, and suggest threshold sizes for inpatient units, after which additional capacity has no effects.…”

“…The coupling effect between ED boarding and ward sizes is also investigated [142,166,175,246], where the size of downstream hospital wards influences the possibility of ED patients to be admitted to wards without waiting (at the ED) for a bed to become available. Similar to ED boarding, the sizing of wards downstream from ORs influences their per-…”

“…There are various triage systems being used at emergency departments. Of these, the Australian Triage Scale (ATS) [55], Canadian Emergency Department Triage and Acuity Scale (CTAS) [132,166,166], Manchester Triage Scale (MTS) [29,193], and Emergency Severity Index (ESI) [12,13,36,62,72,145,161,206,206,208,211,243,261], and are most seen in practice [15,65,80,189,254]. These triage systems all categorize 2.3.…”