A computer consists of three processors. Their main task is to execute jobs from users.

These jobs arrive according to a Poisson process with rate 15 jobs per minute. The execution time is exponentially distributed with mean 10 seconds. When a processor completes a job and there are no other jobs waiting to be executed, the processor starts to execute maintenance jobs. These jobs are always available and they take an exponential time with mean 5 seconds. But as soon as a job from a user arrives, the processor interrupts the execution of the maintenance job and starts to execute the new job. The execution of the maintenance job will be resumed later (at the point where it was interrupted).

(i) What is the mean number of processors busy with executing jobs from users?

(ii) How many maintenance jobs are on average completed per minute?

(iii) What is the probability that a job from a user has to wait?

(iv) Determine the mean waiting time of a job from a user.