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

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

customers an hour. The respective mean service times at the nodes are 4, 2 and 1 [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.