Queuing at doctors and movie theaters

| Misc
Over at Yglesias, people are discussing this anti-universal health care ad:

A number of the commentors observe that this is a bit inartful, since movie theaters are not exactly bastions of state ownership. For instance:

Soooo...movie lines are government run? Movie tickets are Federally subsidized and not a matter of free-market supply and demand?

OK, so this is sort of a fair cop, since the advertisers brought up the comparison, but at some level these are different situations, or at least maybe are.

Queues serve two primary social purposes: exerting backpressure on demand and distributing load over time.

Exerting Backpressure on Demand
It doesn't take a queueing theorist to see that if a system can service 10 users an hour, then if the aggregate number of aggregate customers entering the system is 20 an hour on a permanent basis, then not all of them are going to be served. There are a lot of different ways to deal with this (rationing, auctions, etc.), but one is simply to implement a first-come-first-served policy. Everyone who can't be served immediately just has to wait in the queue. Now, if your aggregate demand exceeds your aggregate service capability, that means that the queue gets longer and longer. At some point, new users decide that they're not going to get served in any reasonable time and don't even bother to enter the queue. This provides a form of load management, sorting users to some extent by their willingness to wait. So, making people queue is one way of dealing with demand which would otherwise exceed capacity.

Load Distribution
The other major purpose queueing is load distribution. Lots of systems have extremely uneven demand profiles. If you average demand over time, it's less than the capacity of the system, but over short periods of time it significantly exceeds demand. You can of course deal with this by increasing capacity, but generally you just make people wait during periods of high demand and then catch up when demand is low. This lets you handle a plausible level of service even when you can't handle peak demand.

The flip side of load distribution—and this is where we get back to movie theaters—is that there are systems where the rate of service provision is extremely variable. In particular, any given movie theater room is only showing one movie at a time and people are only admitted every two hours or so. If that's at 12 PM, 2PM, 4PM, etc., and someone shows up at 1PM, they have to wait till 2 to get into the theater. This is true even if aggregate capacity far exceeds demand, i.e., the theater is always half empty. Even if people all show up at 1.59, only so many people can fit through the theater door at once, so you still end up queuing a bit. Now, obviously you could have 10 times as many movie theaters, thus reducing the amount of queuing, but nobody expects theaters to operate at 100x levels of overcapacity. It is worth noting, though, that there's a tradeoff between overcapacity (i.e., idleness) and forcing users to queue.

Now let's take the case of medical service, which is more complicated. When people talk about waiting for medical service, they're mostly using queuing as synechdoche for the system being overloaded and queuing as a form of pushback on demand. The implied claim, of course, is that free markets don't have this. Whether that's true or not (and if you were in Palo Alto on iDay you know it's not) queuing at movie theaters isn't that great a counterexample.