"No Waiting Room" and Queuing Theory

I just read Nat Friedman's post, No Waiting Room, about his experiences in a hospital in Germany vs. one in Boston:

I hadn't been asked to sit in a waiting room for 8 hours like the time I had a concussion in Boston. A few hours later, after my abdominal ultrasound was clear, I poked around the hallway near the main entrance just to confirm what I'd been wondering about. There was no waiting room.

He then goes on to relate this experience to health insurance models in the U.S. vs. Germany, how people respond to them, the number of ER vs. scheduled visits, and so on.

Now, there are surely lots of things to say about the difference between U.S. and German (and Canadian, for that matter) health insurance systems. But I don't think this actually provides a data point either way.

In any system, long-but-not-growing queues are a sign of a very specific kind of failure. People like to oversimplify and assume that a long queue means there aren't enough doctors (for example), but that's not right; if there are more people arriving at the hospital than are being treated, the queue would keep growing. But as far as I know, the queue at the hospital in Boston wasn't ever-growing,¹ it was just really really long. That's a totally different condition. An ever-growing queue is a bandwidth problem; a long-but-constant queue is a latency problem.²

Somewhere in this system is an ineffective queue. What's the optimal route through the hospital queue, and how many people follow non-optimal routes? Does the optimal route involve filling out paperwork for two hours? If so, then your minimum stay is two hours. Does a typical route involve three layers of nurses pre-checking you so they can put you into the right doctor's queue? Each of those layers adds a delay (and probably another delay as you wait your turn for the following stage). Is the traffic bursty, ie. do more people arrive at certain times of day, so that you get an 8-hour queue built up at rush hour, and it empties out by 4am, so the "average bandwidth" is sane but the peak bandwidth is crazy? (Surely people don't get sick only during certain hours, so why would it happen?)

Interestingly, this sort of problem is almost always solvable without spending a lot of money. Upgrading bandwidth requires money; improving latency only requires cleverness. It's a variant of Just in Time manufacturing, where instead of "excess inventory" you have "patients in the waiting room." Companies that do JIT - German manufacturers come to mind - produce efficiency without spending more money.

I'm not an expert in hospitals; not in the slightest. In fact, I live in Canada, so I can't provide useful input on the U.S. healthcare system or the German one, having never experienced either.

But I know a law of the universe when I see one.

Footnote

¹ Why I think the queues aren't overflowing: because if they did, you'd be turning away customers. You might complain about the U.S. health care system being run by profit-seeking corporations and individuals, and I'm sure that has its problems. But if there's one thing profit-seeking entities never want to do, it's turn away paying customers. If the problem were insufficient doctors, for example, you'd be much more likely to see it in socialized systems like Canada's, where doctors' salaries are capped and there's no supply-and-demand effect.

² I wrote about BitTorrent and transmit queues a while ago, and that's another example of the same phenomenon. No matter how fast your network link is, BitTorrent can destroy your performance if you don't speed-limit it; if you do speed limit your BitTorrent, say to 90% of your max bandwidth, whatever your max bandwidth might be, then your latency won't suffer at all. That's the magic of queuing theory. It matters for hospitals just like it matters for networks and highways.