AbstractAn arbitrary policy of fixing the number of outpatient appointments specifying the dates (and not the exact times) of appointments created long queues and large waiting times in some departments of the Ibn-Rochd health centre, but considerable idle time for the consulting doctors in others. After narrating in detail these circumstances and examining a number of possible options, this paper describes the scientific approaches made to determine the number of appointments, the corresponding parameters of the queue and the system and the service per cent occupation.Finite source size, a random number of initial patients, group arrivals, non-exponential service time distribution, late start-up of the servicing unit and many other factors combined to render available theoretical results difficult to apply and results obtained by applying approximately equivalent theoretical models unreliable as compared with those observed in real life. It is shown that simulation could be more profitably applied in such situations.