Customers arrive according to a Poisson process with rate λ = 5 per hour in a system with two servers. The probability that an arbitrary customer goes to server no. 1 (respectively, no. 2) is equal to 3/4 (resp., 1/4). The service times (in hours) are independent exponential random variables with parameters 𝜇1 = 6 and 𝜇2 - 4, respectively. A customer who goes to server no. 2 immediately leaves the system after having been served. On the other hand, after having been served by server no. 1, a customer (independently from one time to another)
Moreover, there is no limit on the number of customers who can be in the system at any time.
Let (n, m) be the state of the system when there are n customers in front of server no. 1 and m customers in front of server no. 2.
(b) Calculate the average number of customers in the system at a large enough time instant, given that the system is not empty at the time in question.
(c) What is the average time that an arbitrary customer who arrives in the system and goes to server no. 1 will spend being served by this server before leaving the system if we suppose that the customer in question never goes to server.no.2?