A computer consists of three processors. Their main task is to execute jobs from users, which arrive according to a Poisson process with rate $15$ jobs per minute and have execution times that are exponentially distrifuted with mean $10$ seconds. When a processor completes at user's job and there are no other users' jobs waiting to be executed, the processor starts to execute maintenance jobs. Maintenance jobs are always available and take an exponentially distributed amount of time with mean $5$ seconds, however, as soon as a job from a user arrives, the processor interrupts the execution of the maintenance job and starts to execute the nem job; the execution of the maintenance job will be resumed later at the point where it was interrupted.

$($a$)$ What type of queueing system is this for the jobs from users?

$($b$)$ What is the mean number of processors bray with executing jobs from users? $(2\mathrm{.}5$ processors$)$

$($c$)$ What is the probability that a job from a werr has to wait? $(0\mathrm{.}2978)$

$($d$)$ Determine the mean waiting time of a job from a user. $(3\mathrm{.}51$ min$)$

$($e$)$ What is the mean number of processors busy with executing maintenance jobs? $(0\mathrm{.}5$ processors$)$

$($f$)$ Ou average, how many maintenance joho are completed per minute? $(6/$min$)$