A Study of Queues and Appointment Systems in Hospital Out-Patient Departments, with Special Reference to Waiting-Times

Summary An investigation, based on the use of random numbers, has been made into the kind of queueing process occurring in hospital out-patient departments. Special attention has been paid to the patients’ waiting time and also to the time which a consultant may waste waiting for the next patient. As compared with many appointment systems at present in use, it is concluded that by suitable choice of the system to be adopted a substantial amount of the patients’ waiting time may be eliminated without appreciably affecting the consultant. A recommended procedure is to give patients appointments at regular intervals, each equal to the average consultation time; the consultant commencing work when the second patient arrives. The effect of variations in the appointment interval, the number of patients attending the clinics, and the distribution of queue-size are discussed. The precision of the results obtained is also considered.