The U of A computer center is equipped with four identical mainframe computers. The number of users at any time is 25. Each user is capable of submitting a job from a terminal every 15 minutes, on the average, but the actual time between submissions is exponential.

Arriving jobs will automatically go to the first available computer. The execution time per submission is exponential with mean 2 minutes. Compute the following:

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(a) The probability that a job is not executed immediately upon submission.

(b) The average time until the output of a job is returned to the user.

(c) The average number of jobs awaiting execution.

(d) The percentage of time the entire computer center is idle.

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(e) The average number of idle computers.