You are in the Post Office, queueing to send a parcel. A Post Office queue is ruthlessly fair: there is only one of it, and when you get to the front it’s your turn. If the queue is long then you have a long wait ahead of you, and so does everybody else who comes in. If the queue is short, then you and the others have a short wait. In the Post Office, your waiting time is all about the length of the queue, the imbalance between capacity and demand.

A cheeky young man comes in, glances at the long queue snaking around the barriers, and walks straight up to a counter. “Can I just get a passport application form? I’m in a hurry”, he butts in. The clerk sniffs, but reaches around for the form anyway. “How much is the Check & Send service?”, the young man asks. He’s pushing his luck now. People in the queue start to look annoyed.

Why are they annoyed? Because the cheeky young man has pushed in, and so everybody else has to wait longer as a result. If his friend comes in next and does the same thing, there will be complaints. If lots of people push in, the whole system will start to break down; the pushiest will wait no time at all, and the meekest will wait for ages. How long will the meekest wait exactly? That depends on the length of the queue. But it also depends on the amount of queue-jumping.

Queue-jumping doesn’t feature much in real-life Post Offices. But it does feature very strongly in the NHS, and rightly so: clinical priorities such as cancer patients have an excellent reason to jump the queue and they do. So do other patients with deteriorating or dangerous conditions. Nobody minds, because the benefit to the urgent patients (who jump the queue) far outweighs the detriment to the routine patients (who wait longer as a direct result).

Other things happen in the NHS as well. Perhaps a clinic is chock-a-block for the next three weeks, and a cancer referral comes in. Or a patient is booked in for an operation next month but changes her mind, leaving a gap in the session. Or a patient comes in for day surgery and confesses he had a slice of toast for breakfast, so he is sent home and rebooked for another day. It doesn’t happen in the Post Office, but it does in the NHS, and it all jumbles up the order.

What does all this have to do with yin and yang? In Chinese philosophy yin and yang are contrasts, like warm and cool, soft and hard, feminine and masculine. In the NHS, the number of patients waiting is easily measured and simply stated, yang-style. But the order in which they come in is complex, difficult to define, and subtle to justify, more yin.

But yin and yang are also two sides of the same coin, two aspects of the same truth, two parts that form a whole. NHS waiting times depend on the yin as well as the yang: the order in which patients come in, as well as the number of patients waiting. To achieve your waiting time targets, you must manage both. Let either one go, and you may fail.

Waiting lists are a longstanding NHS preoccupation. But scheduling patients in the right order? Not so much. It may be complex, difficult, and subtle, but that does not mean we can leave it to chance. Waiting time targets, and more importantly patient safety, depend on it.

That’s why I thought it would be worth taking a few years to study it properly, to work out the best ways to schedule patients, and to come up with rules of thumb that quantify the effects of each kind of disorder. Now that the work is done, you can learn all about it in just a few hours here.