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Question

Consider a network of three stations- Customers arrive at stations 1, 2, 3 in accordance with Poimon processes having respective rates 5, ll}, 15. The service times at the three stations are
exponential with respective rates ID, 50, lilﬂ. 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?

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