Sep 19, 2017

# CONSIDER A CLOSED QUEUEING NETWORK IN WHICH ONLY TWO IDENTICAL CUSTOMERS CIRCULATE. THE NETWORK…

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Consider a closed queueing network in which only two identical customers circulate. The network is composed of four nodes; the first node contains two exponential servers each of which provides service at rate μ1 = 1; node 2 is an infinite-server node, in which each server provides exponentially distributed service at rate μ2 = 0.5; nodes 3 and 4 both contain a single exponential server with rates μ3= 0.8 and μ= 0.4, respectively. On exiting from node 1, all customers go to node 2; on exiting node 2 customers will next go to node 3 with probability 0.4 or to node 4 with probability 0.6. On exiting either node 3 or 4, customers return to node 1. Use Buzen’s algorithm to find the marginal distribution at nodes 1 and 2 and the mean number of customers at each of the four nodes.

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