. Consider a closed network with three nodes and K circulating jobs. Sup-

pose that the service times at the nodes are independent exponential RVs with rates u1, U2, and u3, respectively. Suppose that after receipt of ser-

vice at node 1, the job is fed back into node 1 with probability pi or goes to nodes 2 (or 3) with probability p2 (or p3), with ( Pi + P2 + p3 =1).

Draw a diagram and find a = ((1, @2, 3). Show that the probability that the system is at state (n1, n2, n3), Z; , ni = K is given by 1

Pzl p(n1, H2, H3) =

A(K)

12 H3 where PZL 712 A(K) = X II 1.2 13 020 1=0 EM1=K Show that the server utilization at node 1 equals A(K-1)
W = > ПР(М), n2, n3) =2 A(K)
1,20 i=0 En ,- x