(i) The scheduled patients may be classified into two groups (out patients and inpatients) as these two classes of patients have different mean service times, different levels of punctuality and different show-up probabilities. In addition, there is a stream of walk-in outpatients. The service times for walk-ins and scheduled outpatients are considered to be the same. The characteristics specific to the inpatient and outpatient classes of patients are summarized in Table 1 (ii) The patients may be classified on the basis of the type of study or investigation to be undertaken as well as the source of arrival (inpatient or outpatient). These two characteristics are known to affect the time taken for an MRI investigation. The type of study in this paper refers to the body part to be investigated and the type of scan (MRI scan, only screening, and MR Angiogram)