Consider a network of three stations with a single server at each station. Customers arrive at stations 1, 2, 3 in accordance with Poisson processes having respective rates 5, 10, and 15. The service times at the three stations are exponential with respective rates 10, 50, and 100. A customer completing service at station 1 is equally likely to (i) go to station 2, (ii) go to station 3, or (iii) 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.

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

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