Problem: The Fast Shop Market has a single checkout counter and one employee to serve customers. An average of 24 customers arrives each hour with a Poisson distribution (and therefore, exponentially distributed interarrival times). Customer checkout times are exponentially distributed with a mean of 2 minutes. Customers are checked out according to their order line.
Question 1: Calculate the average length of the checkout line and the average time (minutes) that customers spend waiting in line prior to checkout.
Question 2: The owner of Fast Shop is considering adding a "bagger" to speed up the checkout process. Experiments show that 40 customers can be served per hour with a bagger (exponentially distributed). Recalculate the average length of the checkout line and the average time (minutes) that customers spend waiting in queue for service.
Question 3: The bagger will cost the store employee $300 per week. The national office has done research that indicates that for each additional minute the average customer waits in line costs a Fast Shop store $150 per week in lost sales. Is the bagger worth her/his wages?
Question 4: Suppose that Fast Shop finds that in addition to reducing mean processing times, the use of a bagger also reduces the standard deviation of checkout times by 50%. By what percent will customer in-line waiting times be reduced?