Example $10\mathrm{.}1$: Customers in Line

Western National Bank is considering opening a drive$-$through window for customer service. Management estimates that customers will arrive at the rate of $15$ per hour. The teller who will staff the window can service customers at the rate of one every three minutes.

Assuming Poisson arrivals and exponential service, find

Utilization of the teller

Average number in line

Average number in system

Average waiting time in line

On the basis of hour:

$20$

Average waiting time in system, including service