There is a queuing system consisting of 3 service stations.

Stations 1 and 2 have a single service, which can process an average of 20 jobs / h, Station 3 has 3 servers, each takes 10 minutes to process a job. 

Processing times at each station are exponential.  

An average of 6 jobs per hour at Station 1, 4 jobs per hour at Station 2, and two jobs per hour at Station 3. When a job ends its service at Station 2, 15% randomly arrive from outside the system.  of them must return to station 1 for adjustments and 80% continue to station 

3. When a job ends its service at station 3, 20% returns to station 2 for adjustments and 76% becomes finished product .  

All jobs ending their service at station 1 go to station 2 (with the exception of defective ones).  Defective jobs at each station must be reprocessed right there;  from station 1 there are 5% defects, from station 2 also 5% and 4% from station 

a) Calculate the fraction of time that each server in each station is unoccupied 

b) Determine the average size of the inventory in process at each station.

c) Estimate the average process time for the jobs d) How efficiently the line is working

e) Is the line well balanced? If not, what would you do to balance it.