Consider a $20-$minute session on a single$-$server queuing system. Arrivals and

service times are:

Customer #$1$ arrives at $t=1$ minute and requires $5$ minutes of service time

Customer #$2$ arrives at $t=1$ minute and requires $2$ minutes of service time

Customer #$3$ arrives at $t=2$ minutes and requires $3$ minutes of service time

Customer #$4$ arrives at $t=12$ minutes and requires $6$ minutes of service time

Calculate the following:

i$.$ System throughput: $($X$)($ii$)$ totai busy time $($B$),($iii$)$mean service time $($Ts$),($iv$)$ Utilizition $($U$),($v$)$Mean system time $($delay in system$)($W$).$

and $($vi$)$ Mean mumber in the system $($L$).$