How much surplus capacity is required to maintain low waiting times?

Random fluctuations in demand make it impossible to see all patients in a very short time scale unless capacity exceeds the mean demand. We describe a model to estimate the capacity levels required as a function of mean demand. Random fluctuations were assumed to follow a Poisson distribution. A Monte Carlo analysis was used to model variations in length of waiting times. To see patients without a waiting list the capacity must exceed mean demand by an amount proportional to the square root of the mean; if capacity equals mean demand, then actual demand will exceed capacity almost half the time. The smaller the mean demand, the greater the percentage increase in capacity that is required. Thus, subdivision of numbers, for subspecialization or fast-tracking, demands greater overall capacity. When multiple serial steps are required, each step must have spare capacity if a waiting list is to be avoided. When capacity is only slightly greater than mean demand, random fluctuations mean that targets can be met for long stretches of time, but these are interspersed with periods when the waiting list rises substantially. Allowing a small waiting time (2-4 weeks) considerably reduces the excess capacity required. Targets such as the 2-week wait for cancer referrals can be achieved only if resource levels are set to give considerably more patient slots per week than mean demand. The level of spare capacity required depends on the level of demand and the maximum waiting time permitted. Without surplus capacity, waiting targets cannot be met. To meet the 2-week waiting target, capacity must exceed mean demand by two patient slots per week for 99% success, or by one slot per week for 90% success.