The waiting equilibrium

Marina Krakovsky in Slate suggests that long US doctor appointment waiting times (weeks!) are a consequence of a bad equilibrium. She doesn’t say it in those terms but that doesn’t stop it being true.

When a patient calls in the morning asking to see a doctor who uses open access, the office offers an appointment for that same day. Why are there openings available? Well, the main reason most doctors defer today’s work to some time in the future is that today’s schedule is clogged with appointments made weeks ago. Doctors following the same-day scheduling model, on the other hand, are free today because they saw yesterday’s patients yesterday. Using open access, doctors might still schedule some early-morning appointments in advance, for follow-up visits or for patients who actually prefer a future appointment. But the key is that they keep most of their time free for same-day visits and fill up their schedules as the day goes.

So in one equilibrium, there are long waiting lists which mean that schedules are set weeks in advance. In another, that isn’t done and so everyday there are openings. Each outcomes feeds on itself. So to get out of the bad waiting equilibrium you need a big push to clear the lists and then you can move to the good no-waiting situation. Of course, this makes for a hard transition.

Of course, the no-waiting equilibrium is also fragile unless you have sufficient slack in the system — that is, on average more slots available than there is demand. This is because if you have a bad day, that creates a backlog and this can feed back on itself so that waiting times slowly increase. The slack reduces the chances of that but means that someone has to pay for the unused doctor capacity.

[Update: The Aplia blog looks at this issue]

3 thoughts on “The waiting equilibrium”

  1. You’ve gotta wonder whether this system is necessarily better for resources. When appointments aren’t on the same day as booking, 30% drop out. The crucial question is whether some of this 30% drop out because their problem went away on its own. Depending on the numbers – and what happened to the remainder of the dropouts – the same day system may increase the number of pointless consultations. (The effect – good or bad – may be still larger if some people who don’t get a same day appointment simply decide not to see a doctor at all.)

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  2. I’ve considered this a lot. I think queueing theory is one field which is simple enough for a year 12 to understand, but with so many applications which society stubbornly ignores to its peril.

    In the case of doctors, I suspect some people (as Jeremy said) don’t go because of the long wait, so you get something like a price/demand curve. If not for that, there would simply be too many patients.

    But there is no excuse for hospital waiting lists of a year, even though that’s partly due to urgent cases jumping the queue. The hospital system’s equilibrium is relying on people dying in the queue or getting treated elsewhere.

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  3. I just read the article. It’s a great idea, just what I’d been advocating for a long time. They don’t go into any detail though about how they keep their workload to an appropriate level.
    (Only once I’ve had the pleasure of ringing the doctor to say I was better and no longer needed my appointment.)

    Another similar situation is when tickets are being sold to a big event and hundreds of people camp overnight outside the ticket office. No one gains from this scenario; the house does not make more money and the same number of people get tickets as would have if they’d come and bought them without the wait (though some might enjoy the overnighter). I don’t understand why in such cases the house doesn’t anticipate the popularity of the event and hike the price a little bit. The same number of patrons will get tickets and the same number will miss out, no one will spend a night camped out, and the house makes more money.

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