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.