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In a network of 3 service stations 1, 2, 3 customers arrive 1, 2, 3 from outside in accordance with Poisson Process having rates 5,

In a network of 3 service stations 1, 2, 3 customers arrive 1, 2, 3 from outside in accordance with Poisson Process having rates 5, 10, 15 respectively. The service times at the 3 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 (c) leave the system. A customer departing from service at station 2 always goes to station 3. A departure from service at station 3 is equally likely to go to station 2 or leave the system. What is the average number of customers in the system consisting of all the three stations? What is the average time a customer spends in the system?

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