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Consider the closed network of the following figure. The number at the arrows give the transition probabilities for a customer leaving the queue to route to a subsequent queue. Every station contains a single server, and all arriving customers may enter the station.
Service is in order of arrival. The service times have an exponential distribution with with: m1=4, m2=3, m3=2, m4=1.
a) Give the joint stationary distribution for the number of customers in the four stations for m=1, 2, and 3 (m=total number of customers in the network).
b) Obtain using Mean Value Analyse the average number of customers and the average sojourn time in the four queues for m=1, 2 and 3.
c) Determine for m=1 the average time for a customer to return for the first time to station 1.
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