Problem:

The local Quick Burger fast food restaurant has a drivethrough window. Customers in cars arrive at the window at the rate of 10 per hour (Poisson distributed). It requires an average of four minutes (exponentially distributed) to take and fill an order. The restaurant chain has a service goal of an average waiting time of three minutes.

Required:

Question 1) Will the current system meet the restaurant's service goal?

Question 2) If the restaurant is not meeting its service goal, it can add a second drive-in window that will reduce the service time per customer to 2.5 minutes. Will the additional window enable the restaurant to meet its service goal?

Question 3) During the two-hour lunch period the arrival rate of drive-in customers increases to 20 per hour. Will the two-window system be able to achieve the restaurant's service goal during the rush period?

Provide thorough explanation of the given question.