The 85% bed occupancy fallacy: The use, misuse and insights of queuing theory

Abstract

Queuing theory can and has been used to inform bed pool capacity decision making, though rarely by managers themselves. The insights it brings are also not widely and properly understood by healthcare managers. These two shortcomings lead to the persistent fallacy of there being a globally applicable optimum average occupancy target, for example 85%, which can in turn lead to over- or under-provision of resources. Through this paper, we aim both to make queuing models more accessible and to provide visual demonstrations of the general insights managers should absorb from queuing theory. Occupancy is a consequence of the patient arrival rate and ‘treatment’ rate (the number of beds and length of stay). There is a trade-off between the average occupancy and access to beds (measured by, for example, the risk of access block due to all beds being full or the average waiting time for a bed). Managerially, the decision-making input should be the level of access to beds required, and so bed occupancy should be an output. Queuing models are useful to quickly draw the shape of these access-occupancy trade-off curves. Moreover, they can explicitly show the effect that variation (lack of regularity) in the times between arrivals and in the lengths of stay of individual patients has on the shape of the trade-off curves. In particular, with the same level of access, bed pools subject to lower variation can operate at higher average occupancy. Further, to improve access to a bed pool, reducing variation should be considered.

Were the hospital bed reductions proposed by English Clinical Commissioning Groups (CCGs) in the sustainability and transformation plans (STPs) achievable? Insights from a new model to compare international bed numbers

“…In addition, the surgical group only accounts for 30% of acute adult daytime occupied beds (and declining) – hence there is little scope for large reductions. Indeed, it could be argued that more surgical beds are needed to provide an adequate occupancy margin to minimize cancelled operations 30–32 …”

“…Note that the volatility in average LOS over time (Figure 8) is part of a generous occupancy margin which must be applied to ensure that a bed is available for the next arriving patient at all times of the year. In the absence of this occupancy margin, patients are consigned to queues in the emergency department (especially in winter) or the elective waiting list which is a characteristic of the NHS across all parts of the United Kingdom 30–32,72 …”

“…It must be categorically stated that the much quoted 85% occupancy margin for hospitals has no theoretical or real‐world basis 96 . It is widely recognized that queuing theory and Poisson statistics gives profound insight into the bed occupancy rate applicable to hospitals of different size and complexity 30–32 . However, it is also important to realize that queuing theory only encapsulates statistical variation and does not inform regarding the environment‐based variation in the occupancy margin.…”

“…A limitation of this model is that it used available beds rather than occupied beds, 29 which measures the demand for beds while available beds reflect multiple factors relating to the average bed occupancy margin, the most important of which is hospital size 30–32 . In addition, some countries like the United States and Germany have a very high proportion of hospitals with fewer than 100 beds, 45% in the United States and 35% in Germany 33,34 …”

Discrete-Event Simulation Modeling of Critical Care Flow: New Hospital, Old Challenges

“…In the past, queuing theory analysis was applied to a variety of hospital activities, including critical care units, obstetric services, operating rooms, and emergency departments, as a mean of directing the allocation of increasingly scarce resources ( 14 , 15 ). Unfortunately, most proposed queuing models lack real-world validation and, perhaps for this reason, have yet to be embraced by physicians and hospital administrators ( 16 ). An early study using these methods was used to model accurately a large ICU within Microsoft Excel (Microsoft Corp., Redmond, WA) ( 14 ).…”