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Mathematics, 19.02.2020 04:34 lesli4115
A production line has two machines, Machine A and Machine B, that are arranged in series. Each jol needs to processed by Machine A first. Once it finishes the processing by Machine A, it moves to the next station, to be processed by Machine B. Once it finishes the processing by Machine B, it leaves the production line. Each machine can process one job at a time. An arriving job that finds the machine busy waits in a buffer. (The buffer sizes are assumed to be infinite.) The processing times for Machine A are iid having exponential distribution with mean 4 minutes. The processing times for Machine B are iid with mean 2 minutes. Assume that the interarrival times of jobs arriving at the production line are iid, having exponential distribution with mean of 5 minutes (a) What is the utilization of Machine A? What is the utilization of Machine B?(b) What is the throughput of the production system?(c) What is the average waiting time at Machine A, excluding the service time?(d) It is known the average time in the entire production line is 30 minutes per job. What is the long-run average number of jobs in the entire production line?(e) Suppose that the mean interarrival time is changed to 1 minute. What are the utilizations for Machine A and Machine B, respectively? What is the throughput of the production system?
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A production line has two machines, Machine A and Machine B, that are arranged in series. Each jol n...
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