The steady state is like Big-O notation; it’s already talking about the edge (as time grows to infinity). A single day deviation doesn’t really matter — your queue might shrink and grow a little day-to-day, but on average it’ll grow more than it shrinks, and you’re ultimately fucked.

If your utilization looked like 100% on one day, 0% on another, and flipping back and forth (allowing the queue to clear) then by definition your steady state isn’t 100%, its more like 50%.

And of course if your time bound is limited, or your potential customers is limited, then naturally everything is limited. But like big-O, the notion is to describe what happens when your inputs grows to infinity