1 At a manufacturing assembly line, 30 jobs arrive per hour. Each job must pass through two production stages:

stage 1 and stage 2. Stage 1 takes an average of 1 minute to complete, and 1 worker is available to perform stage 1.

After completing stage 1, the job immediately passes to stage 2. Stage 2 takes an average of 2 minutes to complete, and 2 workers are available to work on stage 2. After completing stage 2, each job is inspected. Inspection takes an average of 3 minutes, and 3 workers are available to perform inspection. After inspection, 10% of the jobs must be returned to stage 1, and they then repeat both stages 1 and 2. After inspection, 20% of all jobs return to stage 2 and repeat stage 2. Assume that interarrival times and service times are exponential.

a What is the average time a job spends in the system from arrival to completion?

b What percentage of the time is each worker busy?