Skill Builder #4
Problem 1: A fast-food franchise is considering opening a drive-up window food service operation. Assume that customer arrivals follow a Poisson distribution, with a mean arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive up to the service window to pay for and receive their order.
Compute the following operating characteristics for each of the four service alternatives are being considered below: a) Average number of cars waiting for service.
b) Average time a car waits for service.
c) Average time in the system.
d) Average number of cars in the system.
(1) A single channel operation where one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes.
(2) A single-channel operation where two employees work as a team to serve each customer. The average service time for this alternative is 1 minute.
(3) A two-channel operation with two service windows and two employees. Newly arriving customers join a queue which feeds both service windows. The employee stationed at each window fills the order and takes the money for customers arriving at the window. The average service time for each service window is 2 minutes.
(4) There are two service windows and two employees. There is a separate queue for each of the service windows. Newly arriving customers randomly choose one of two queues. The employee stationed at each window fills the order and takes the money for customers arriving at that window. The average service time for each service window is 2 minutes.
(5) The manager finds out that most customers do not mind waiting in line a little longer because they can listen to...