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.
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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.