A queueing network consists of three nodes (queueing systems) 1,2 , and 3 , each of type \(M / M / 1 / \infty\). The external inputs into the nodes have respective intensities

\[\lambda_{1}=4, \lambda_{2}=8, \text { and } \lambda_{3}=12 \text { [customers per hour]. }\]

The respective mean service times at the nodes are \[4,2, \text { and } 1[\mathrm{~min}]\]
After having been served by node 1 , a customer goes to nodes 2 or 3 with equal probabilities 0.4 or leaves the system with probability 0.2 . From node 2 , a customer goes to node 3 with probability 0.9 or leaves the system with probability 0.1 . From node 3 , a customer goes to node 1 with probability 0.2 or leaves the system with probability 0.8 . The external inputs and the service times are independent.
(1) Check whether this queueing network is a Jackson network.
(2) Determine the stationary state probabilities of the network.