Using queuing theory to analyse the government's 4-H completion time target in accident and emergency departments

This paper uses a queuing model to evaluate completion times in Accident and Emergency (A&E) departments in the light of the Government target of completing and discharging 98% of patients inside 4 h. It illustrates how flows though an A&E can be accurately represented as a queuing process, how outputs can be used to visualise and interpret the 4-h Government target in a simple way and how the model 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 in the U.K. It suggests 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 through the system. 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. Related incentives and demand management issues resulting from the target are also briefly discussed.