Let we have a queue of independent events. The events are processed in the order of arrival, processing one event takes $t$ time.
Events arrive in average $N$ events per identity time.
What it the average length of the queue?
I am waiting up to three days for a company to process my request and wonder why the queue is so long (three days), while obviously processing one item should not take much time (it can be done in a minute, I think). So I want to see a formula for this. I do not need a proof.