The Poisson process is a random distribution. Just because its average is 1.1 per minute doesn't mean you can't have 2 people show up at virtually the same time

The Poisson process is a random distribution. Just because its average is 1.1 per minute doesn't mean you can't have 2 people show up at virtually the same time, it's just pretty rare. Or there's like a 10^-100 chance a million people show up at the same second, etc etc. You'll always have some nonzero average queuing time if you calculate it across the whole distribution for that reason.