"Many people in that situation spend their coffee breaks calling their offices, trying to find out if they have any urgent messages waiting," said Dr. Julia Hirschberg, one of the researchers who developed the AT&T system.
Now, assume that at the start of week n we have w1 1-week semi-urgent slots and w2 2-week semi-urgent slots waiting.
Sally Greenbrook from Breakthrough Breast Cancer said the charity hoped the pilot would "lead to decisive action to tackle the problem of non-urgent referral waiting times" as some women were experiencing long waits between a non-urgent referral and diagnosis which could negatively impact upon treatment outcomes.
Furthermore, as mentioned in the introduction, if the number of semi-urgent slots waiting for treatment exceeds the weekly amount of OR slots available, semi-urgent surgeries have to be performed in overtime, which is very undesirable as well.
Therefore, when the number of 1-week semi-urgent slots waiting exceeds m, or when the sum of 1- and 2-week semi-urgent slots waiting exceeds 2 m, the surplus semi-urgent slots are performed in overtime.
We focus on the number of semi-urgent slots waiting at the start of week n (W n ).
An example of the progression in the number of semi-urgent slots waiting at the start of week n is given in Fig. 1.
The system state at the start of week n, (n = 0,1,..., ∞ ), is given by w n = (w1 n, w2 n ), where w1 n and w2 n are the number of 1- and 2-week semi-urgent slots waiting at that moment.
When considering all possible states, consisting of the number of one-, two- and three-slot semi-urgent surgeries waiting, this expectation equals 8.86 when taking into account the adjacency requirement (i.e. in the situation where we have four full OR days of three slots and a single slot on another OR day).
Unfortunately for Mr Emanuel, the problem is too urgent to wait for the courts.
