1. SELECT item_id WHERE expire = 0. If this is empty, no items are available.
2. UPDATE SET expire = some_future_time WHERE item_id = $selected_item_id AND expire = 0. Then check whether UPDATE affected any rows. If it did, item_id is yours. If not, loop. If the database has a sane optimizer it'll note at most one document needs locking as the primary id is given.
All this needs is a very weak property: document level atomic UPDATE which can return whether it changed anything. (How weak? MongoDB could do that in 2009.)
Source code at https://git.drupalcode.org/project/drupal/-/blob/9.2.x/core/... (We cooked this up for Drupal in 2009 but I am reasonably sure we didn't invent anything new.)
Of course, this is not the fastest job queue there is but it is quite often good enough.
As always, there are trade offs, no silver bullets.
It's a little insane that a highly rated thread on HN is telling people to use postgres as their queuing solution. The world is wide, I'm sure that somewhere out there there is a situation where using postgres of a queue makes sense, but in 99% of all cases, this is a terrible idea.
Also, SQS and nsq are simple.
As long as you don't need clustering (even a single node can handle some pretty heavy load), it's actually really simple to setup and use - way easier than Postgres itself, for example.
My biggest beefs with it have historically been the Erlang-style config files (which are basically unreadable), and the ridiculous spiel of error messages you get if you have an invalid configuration. But thankfully RabbitMQ switched to a much simpler config file format one or two years back, and I understand the Erlang OTP is working on better error messages and stack traces.