JACPR Inc. is a company that operates with two servers. An average of 8 customers per hour arrive from outside at server 1, and an average of 15 customers per hour arrive from outside at server 2. Interarrival time are exponential. Server1 can serve at an exponential rate of 20 customers per hour, and server 2 can serve at an exponential rate of 30 customers per hour. After completing service at server 1, half of the customers leaves the system, and half go to server 2. After completing service at server 2, 0.75 of the customers complete service, and 0.24 return to server 1.
i. What fraction of the time is server 1 idle?
ii. Find the expected number of customers at each server.
iii. Find the average time a customer spends in the system.
iv. How would the answer to parts 1-3 change if server 2 could serve only an average of 20 customers per hour?