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Jobs arrive at a computer server according to a Poisson process with a rate of 5 jobs per hour. The server can complete one job
Jobs arrive at a computer server according to a Poisson process with a rate of 5 jobs per hour. The server can complete one job at a time, and the time that it takes for each job to be completed follows an Exponential distribution with a mean of 10 minutes. If the computer server is actively completing a job, then any additional jobs that arrive are added to a queue.
(a) On average, in the long term, how many jobs are there in the queue?
(b) Compute the probability, in the long term, that there at least 3 jobs in the queue.
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