A production line consists of two single-machine stations in series. Jobs arrive to the first station according to a Poisson process with rate 20 jobs/hour. The service rate at each station is 30...

A production line consists of two single-machine stations in series. Jobs arrive to the first station according to a Poisson process with rate 20 jobs/hour. The service rate at each station is 30 jobs/hour. At each station, approximately 10% of the jobs are found to be defective and are scrapped.

(a) Approximate the buffer space needed for each station to ensure that all arriving jobs can be accommodated at least 95% of the time.

(b) Determine the expected number of jobs at station 2.

(c) Determine the utilization of the machine at station 2.

(d) Now suppose that there is a rework station associated with each machine station. Defective items from station 1 are reworked and then sent to station 2. Defective items from station 2 are reworked and then sent out. However, only 50% of the items sent to the rework stations can be salvaged; the others become scrap. The rework stations complete jobs at a rate of 4/hour. Develop a new model of this system, and answer the questions above.

(e) Suppose we pool the rework stations, meaning that there is one rework station with two servers, each working at rate 4/hour. Develop a new model, and again answer the first two questions.