A fast food franchise is considering a drive-up window food-service operation. Assume that


customer arrivals follow a Poisson probability 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. The following three service


alternatives are being considered:


a) 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.


b) A single-channel operation where one employee fills the order while a second employee


takes the money from the customer. The average service time for this alternative is 1. 25


minutes.


c) A two-channel operation with two service windows and a single employee at each


window. The employee stationed at each window fills the order and takes the money


from the customer. The average service time for this alternative is 2 minutes for each


channel.


Compute the following operating characteristics for each alternative and recommend an


alternative design for the fast food franchise.


(i) What is the probability that there are no customers in the system?


(ii) What is the average number of cars waiting for service?


(iii)What is the average time a car waits for service?


(iv)What is the average time in the system?


(v) What is the average number of cars in the system?


(vi)What is the probability an arriving car will have to wait for service?