What service discipline is best for testing queues?

First in, first out (FIFO) is the service discipline that we are all most familiar with. If I get in line at the cafe before you do, I get to place my order first. Simple. Fair. But is that the best scheme for running the queue for covid tests?

That’s basically the question asked by a recent post on Marginal Revolution (Stack-Push-Pop COVID Testing, Aug 7). The basic complaint is that delayed test results are useless test results. Hence, there should be an emphasis on turning around results quickly while not wasting resources on past-due samples. Deviating from FIFO is one way of achieving this.

One way of thinking about this is to use a stack or last-in first-out (LIFO) model for testing. In a stack model the newest test request is pushed onto the top of the stack and the next test to be processed is popped off the top of the stack. One disadvantage of this model is that some test requests will never be processed (they should be removed from the bottom of the stack and returned as null results). Some people will be angry.

But the stack model of testing has a huge advantage over first-come, first-served. Namely, just as many tests will be completed as under the current model but the tests results will all come back faster and be much more useful.

There are, of course, other ways of running the queue that would achieve similar results without being fully LIFO. For example, one could run FIFO but with a simple rule that any sample waiting more than X hours is not processed. That would maintain some sense of fairness while avoiding spending resources on old samples.

Some comments on the post note that LIFO has some perverse incentives. In particular, if don’t hear quickly, why not submit another? (That, of course, assumes you don’t have to pay until you successfully get results.) The commenters suggest randomly pulling people from the queue as one solution to that since the original sample still has some chance of delivering results. (We’ve written about random queues or lotteries before.)

A different take on this is to note that not all tests are the same. If an elderly resident of an assisted living center is ill, nailing down the diagnosis quickly could be essentially for protecting a vulnerable population. On the other hand, if you are a college sophomore whose school insist that you get tested before moving back to campus, you’ve got more time and indeed could love with a slightly stale result. That all suggests that someone should be prioritizing the test that get submitted.

(Finally, a hat tip to Rob Bray for sending me this one.)