35. Consider a network of three stations with a single server at each station. Customers arrive at stationsI mage in accordance with Poisson processes having respective ratesI mage, and 15. The service times at the three stations are exponential with respective ratesI mage, 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?