For a small computing system the processing time per job is exponentially distributed with an average

time of $3$ minutes. Jobs arrive randomly at an average rate of $1$ job every $4$ minutes

$($a$)$ What is the mean time in the system?

$($b$)$ Compute the server utilization.

$($c$)$ What is the mean number of jobs in the system?

$($d$)$ It is decided that, when the workload increases to the level such that the mean system time in

the system reaches $30$ minutes, the system capacity will be increased. What is the mean arrival

rate at which this will occur?