Predicting overflow in an emergency department.

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. [ABSTRACT FROM AUTHOR]