A manufacturing process always has 8 parts in process.A part must successfully complete two steps (step 1 and step 2) to be completed. A single machine performs step 1 and can process an average of 8 parts per minute. A single machine performs step 2 and can process 11 parts per minute. Unfortunately, step 2 is not totally reliable. (Step 1 is totally reliable, however.) Each time a part is sent through step 2, there is a 10% chance that step 2 must be repeated.
a) Find the steady-state distribution of parts at each machine.
b) Find the average number of parts at each machine.
c) Find the probability that each machine is busy.
d) Find the number of parts per minute successfully completing service at each machine.