Capacity and demand models for radiotherapy treatment machines.

Models to predict the number of linear accelerators (linacs) required usually assume that capacity needs to equal demand. Queuing theory shows that capacity needs to exceed mean demand, to avoid the build-up of waiting times. A model has been developed, using Monte-Carlo modelling, to calculate the percentage of spare capacity required to keep waiting times to treatment short. For a matched pair of linacs, in a department that closes on bank holidays and compensates for category 1 patients by treating twice before or after the break, about 10% spare capacity is required to ensure that 86% of patients are able to start radiotherapy within a week of completing the treatment planning process. If a machine is booked as a single (unmatched machine), an additional 3% spare capacity is needed. If all bank holidays in the year are worked, then about 3% less is needed.