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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.
Six Operators are to be assigned to five jobs with the cost of assignment in Rs. given in the matrix below. Determine the optimal assignment. Which operator will have no assignment
max z 60x1+50x2 Sab to 4x1+10x2 2x1+2x2 3x1+2x2 X1+x2. >_ o
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