Queue theory and the National Health Service; the application thereof as a way of reducing waiting list times. There are two types of ways of moving people through a queue: push, and pull.

"In a push system, transferring patients from one step of the process to the next is the responsibility of the earlier part of the process. They will 'push' the patient to the next stage. For instance, GPs 'push' urgent referrals to cancer units. Cancer units 'push' patients requiring specialist radiotherapy to cancer centres. [...] The trouble is that patient flow stops when it reaches a bottleneck where queues and waiting lists (backlog) build up."

Bottlenecks come in two varieties, process and functional. The two tricks to reducing waiting list are to redesign the process such that both push and pull are present in the system - I'll get to that in a second - and that bottlenecks aren't caused by inspectors. Needing people to inspect forms is a process bottleneck and not in the critical path. So what's pull?

"In a pull system, the bottleneck governs the rate that patients flow through the whole process. In this system it is the responsibility of the later parts of the process to pull patients towards them by asking for the work when they have the capacity to do it. [...] One non-healthcare example of a pull system is the use of chevrons on motorways. The rule is to keep two chevrons between you and the car in front. Therefore all cars go at the rate of the slowest car but if that car speeds up so will the whole system."

So pull is a way of making sure that your queue goes as fast as the bottleneck (ie, that the bottleneck itself isn't causing more bottlenecks, for instance shortage of beds at other previously fine stages of the process), and ensuring that any speed-ups you make to the process immediately cascade and are felt everywhere.

So far so good. This information, by the way, is taken from the NHS Modernising Agency Improvement Guides. They're PDFs. The particular document I've been referring to is Managing Capacity and Demand [HTML version], by Paul Zollinger Read, a leading light in NHS queue theory. (Thanks Andrew for pointing me that way.) In that document you'll also find a dice game to model queue systems, examples and ideas on how to change your systems.

Where it gets interesting is where push/pull is put into practice. Have a look at another Modernising Agency document: Improving the flow of emergency admissions [HTML version].

The traditional process to get people out of hospital is push based. Once they've had their treatment, they're lie in a bed until they're fit enough to go home. At that point they're pushed into a discharge lounge (another area of the hospital) to hang around for a couple of days before they go home. Beds in wards, incidentally, are an enormous bottleneck and always running out.

"Redbridge Hospital (Redbridge Health Care NHS Trust) changed its working philosophy to a 'pull' rather than 'push' system where staff working in the discharge lounge proactivity recruit new patients. Use of the lounge increased by 50% freeing up beds in the wards more quickly."

These are important and serious numbers, affecting throughput of patients (and increasing care) without spending more money -- just changing the process. The story behind this:

There was previously no incentive for nurses to move patients to the discharge lounge. The wards are full, so moving relatively healthy patients who require little work out frees up beds that are immediately going to be filled with still-sick high maintenance, high work patients. So in the traditional process there's an actual incentive for the nurses to tighten the bottleneck and slow the process.

Pull stops this. It's the duty of the discharge lounge nurses to move people away from the functional bottleneck and free up valuable resources. The bottleneck instead becomes the number of nurses available which is a fixable problem by employing more nurses. And that's the magic of queue theory.

Now there are applications here, outside the health industry I'm sure of it. And one day I'll figure out what they are.