Interesting. My gut reaction is that this is true in reverse: infinite wait time leads to 100% utilization. However, I feel like you can also have 100% utilization with any queue length if input=output. Is that theory just a result of a first order approximation or am I missing something?
That's right, this is true no matter the queue length. If input=output on average, there is no limit on how long your queue will grow, and therefore no limit on how long queued task will wait.
The average queue length is still infinity. Whatever the queue length happens to be at the start, it will stay there, and it could be any positive number up to infinity.
