23. Consider a network of three stations. Customers arrive at stations 1, 2, 3 in accordance with Poisson processes having respective rates 5, 10, 15.

The service times at the three stations are exponential with respective rates 10, 50, 100. A customer completing service at station 1 is equally likely to

(a) go to station 2,

(b) go to station 3, or

(c) leave the system. A customer departing service at station 2 always goes to station 3. A departure from service at station 3 is equally likely to either go to station 2 or leave the system.

(i) What is the average number of customers in the system (consisting of all three stations)?

(ii) What is the average time a customer spends in the system?