Timing-Waiting Lines

Joe Hammer is thinking about setting up a special counter for the do-it-yourself customers at which they can get, not only help where to find products in the store, but also some quick advice about the best way to handle their upcoming projects. Experience has taught Joe that six minutes is a good figure to allow for the average time required to serve a do-it-yourselfer and that these customers will arrive every 15 minutes throughout the day.

a.) If joe sets up the counter under these conditions, what operating characteristics might he expect?

b.) What might Joe do to avoid the costs of idleness?

c.) What is the likelihood(probability) that three or more customers will be at the counter, either waiting or being served, at any given time?

Calculate the Utilization rate, idleness rate, Average time in queue, Average time in system, Average number in queue, Average number in system, and probability that three or more customers will be in the counter system at the same time.

Please show calculation for each question, thank you.