Problem 5: (Queueing Networks) [20 points] Consider a network of three stations with a single server at each station. Customers arrive at stations A, B, C 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 A is equally likely to (i) go to station B, (ii) go to station C, or (iii) leave the system. A customer departing service at station B always goes to station C. A departure from service at station 3 is equally likely to either go to station B or leave the system. (a) (5 points) Draw the flow diagram of the system. Indicate the corresponding rates. (b) (5 points) Compute the total arrival rates at each station. (c) (5 points) Compute the expected number of customers in the whole system? (d) (5 points) Compute the expected time a customer spends in the system