Please solve manually, do not use excel. Thanks. 1 (10) Suppose jobs arrive at a single-machine work

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1 (10) Suppose jobs arrive at a single-machine workstation at a rate of 29 per hour and the average process time is 1.75 minutes What is the utilization of the machine? Suppose that inter-arrival and process times are exponential, a. b. i) What is the average time a job spends at the station (i.e. waiting plus process time)? ii) What is the average number ofjobs at the station? iii) What is the long run probability of finding more than three Jobs at the station? c. Process times are not exponential, but instead have a mean of 2 minutes and a standard deviation of five minutes, i) What is the average time a job spends at the station? i) What is the average number ofjobs at the station? ii) What is the average number of jobs in the queue? Please solve manually, do not use excel. Thanks. 1 (10) Suppose jobs arrive at a single-machine workstation at a rate of 29 per hour and the average process time is 1.75 minutes What is the utilization of the machine? Suppose that inter-arrival and process times are exponential, a. b. i) What is the average time a job spends at the station (i.e. waiting plus process time)? ii) What is the average number ofjobs at the station? iii) What is the long run probability of finding more than three Jobs at the station? c. Process times are not exponential, but instead have a mean of 2 minutes and a standard deviation of five minutes, i) What is the average time a job spends at the station? i) What is the average number ofjobs at the station? ii) What is the average number of jobs in the queue?

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