. Consider an open network with two nodes having a single exponential server at each of two nodes with service rates ui, i = 1,2. Suppose that arrivals to node 1 occur in accordance with a Poisson process having rate

À. After being served at node 1, the customer (job) goes to node 2 with probability p or leaves the system with probability (1 - p) = q. From node 2 it again goes to node 1. Assume that the system is at steady state.

Show that the queues at nodes 1 and 2 behave like independent M/ M/1 queues with intensities PI=

and Ap P2

(9M2)

and that the system state (n11, n2) with n, at node i, i = 1,2, has the probability p(m1, M2) = (1- P)p" (1 - p2)p2.

Show that the average response time at two nodes is given by E(R)= 1|1- P1 + 1- 2]

Pi Let E(B;) be the average service-time requirements at node i, i = 1,2, Then show that 2

E(B;)

E(R) =>

1 - XE (B;)