Predicting overflow in an emergency department

Au, L.; Byrnes, G. B.; Bain, C. A.; Fackrell, M.; Brand, C.; Campbell, D. A.; Taylor, P. G.
January 2009
IMA Journal of Management Mathematics;Jan2009, Vol. 20 Issue 1, p39
Academic Journal
Ambulance bypass occurs when the emergency department (ED) of a hospital becomes so busy that ambulances are requested to take their patients elsewhere, except in life-threatening cases. It is a major concern for hospitals in Victoria, Australia, and throughout most of the western world, not only from the point of view of patient safety but also financially-hospitals lose substantial performance bonuses if they go on ambulance bypass too often in a given period. We show that the main cause of ambulance bypass is the inability to move patients from the ED to a ward. In order to predict the onset of ambulance bypass, the ED is modelled as a queue for treatment followed by a queue for a ward bed. The queues are assumed to behave as inhomogeneous Poisson arrival processes. We calculate the probability of reaching some designated capacity C within time t, given the current time and number of patients waiting.


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