Jobs arrive to a facility 24/7 according to a Poisson process with mean rate of 3 per hour. Upon arrival to the system, jobs move from the unloading dock to the first machine workstation which is 50 meters away at a speed between 100 and 200 meters per hour. Jobs are not allowed to cut in line; that is, a job cannot pass another job that is ahead. Jobs are processed by a single-server workstation (i. e., processes jobs one at a time) with the service time per job being exponentially distributed with mean of 9 minutes, the workstation requires a setup time before processing a job between 0 and 2 minutes and a teardown time after processing a job randomly distributed according to a triangular distribution between 1 and 3 minutes with a most likely time of 2 minutes. When jobs finish with the first machine workstation, approximately 40% of them are sent to a second machine station with two identical servers (with one queue). The mean service time for each job is random and is between 0.75 hour and 1.25 hours. Approximately 60% of the jobs leaving the first machine station are sent to a third machine station containing a single server with mean processing time 20 minutes and standard deviation 10 minutes. There is no time between jobs leaving the first machine and arriving to the second and third machines. After a job has been processed by the second or third machines, it takes the job exactly 12 minutes to leave the system. (Add several symbols with different colors to the model entity and randomly chose the color to see your model working).

Give the theoretical long-run utilizations:
Utilization of first machine station:
Utilization of second machine station:
Utilization of third machine station: