1. a fast-food franchise is considering opening a drive-up window 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. three service alternatives are being considered:

(i) a single-channel, single-phase operation in which one employee both fills the order and takes the money from the customer. the average service time for this alternative is 2 minutes.

(ii) a single-channel, two-phase operation in which one employee at one window takes the money from the customer and a second employee stationed at a second window fills the order. the average service time for this alternative is 1,25 minutes for each window

(iii) a two-channel, single-phase operation with two service windows. (in other words, there is one line that feeds each of two windows.) the employee stationed at each window both fills the order and takes the money for customers arriving at his window. the average service time for this alternative is 2 minutes.

compute the following operating characteristics for each alternative, and if applicable, determine the total for all phases (hint: you may need little's law to you out:
(a) average number of cars waiting for service.
(b) average time a car waits for service.
(c) average time in the process.
(d) average number of cars in the process