[kqr]

Many electronic queueing systems in hospitals etc. show you how many customers are ahead of you. If you observe the time it takes for a few people to receive service you can estimate how long you'll be stuck waiting. This is a number they rarely show you because it's often not encouraging...

It's the most primitive application but immediately useful for anyone.

I've used similar methods to estimate work lag: https://two-wrongs.com/estimating-work-lag.html

And to argue for concurrency limits in latency-sensitive backend serviced.