Using queuing theory to analyse completion times in accident and emergency departments in the light of the UK Government’s 4-hour target

This paper uses a queuing model to evaluate completion times in accident and emergency (A&E) departments in the light of the UK Government’s target of completing and discharging 98% of patients inside 4 hours. It illustrates how flows though an A&E can be very accurately represented as a queuing process, how the outputs of a queuing model can be used to visualise and interpret the 4-hour hour Government target in a simple way and how queuing models can be used to assess the practical achievability of A&E targets in the future. The paper finds that A&E targets have resulted in significant improvements in completion times and thus deal with a major source of complaint by users of the National Health Service. It finds that whilst some of this improvement is attributable to better management, some is also due to the way some patients in A&E are designated and therefore counted. It finds for example that the current target would not have been possible without some form of patient re-designation or re-labelling taking place. Further it finds that the current target is so demanding that the integrity of reported performance is open to question and that a different approach is needed. Related incentives and demand management issues resulting from this Government target are also briefly discussed.