A manufacturing cell has 4 operators (working independently in parallel) and a shared buffer space that can fit at most 6 incoming jobs. During a production period, jobs arrive to the cell with rate of 10 jobs per hour (Poisson arrival, i.e., exponential inter-arrival time). The average processing time of a job is 30 minutes (exponentially distributed service time). Answer the following questions using the analytical formulas learned in class. (a) Which queueing model should be used to model this problem? (b) What is the long-term average waiting time of a job in the buffer? (c) What is the probability that an arriving job cannot be admitted into the cell due to full occupancy? (d) If the desired the rejection probability is no more than 10% in this case, what would you suggest? Use calculations to justify your answer.
A manufacturing cell has 4 operators (working independently in parallel) and a shared buffer space that can fit at most 6 incoming jobs. During a production period, jobs arrive to the cell with rate of 10 jobs per hour (Poisson arrival, i.e., exponential inter-arrival time). The average processing time of a job is 30 minutes (exponentially distributed service time). Answer the following questions using the analytical formulas learned in class. (a) Which queueing model should be used to model this problem? (b) What is the long-term average waiting time of a job in the buffer? (c) What is the probability that an arriving job cannot be admitted into the cell due to full occupancy? (d) If the desired the rejection probability is no more than 10% in this case, what would you suggest? Use calculations to justify your answer.
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