The following closed network has 3 nodes and 2 jobs circulating. From node 1, with probability 1/3 a job visits node 2, otherwise it visits node 3.

After processing at nodes 2 or 3, a job returns to node 1.

The processing times are all exponentially distributed, with mean 10 seconds at node 1, and 20 seconds at both nodes 2 and 3.

(a) Find the throughput at the bottleneck node.

(b) Removing the constraint that there are 2 jobs circulating, what is the maximum possible throughput at node 1?