Consider a single server queue. Initially, there is no customer in the system. Suppose that the inter$-$

arrival time of the first $5$ customers u$1,$ u$2,$ u$3,$ u$4,$ u$5$ are given as follows: u$1=2,$ u$2=5,$ u$3=7,$

u$4=3,$ u$5=1.$ In other words, the first customer will arrive in $2$ minutes, and the second will arrive

in $2+5$ minutes, and so on$.$ Also, suppose that the service time of the first $5$ customers v$1,$ v$2,$ v$3,$ v$4,$

v$5$ are given as follows: v$1=1,$ v$2=4,$ v$3=2,$ v$4=8,$ v$5=3.$

$($a$)$ Compute the average waiting time of the first $5$ customers.

$($b$)$ Compute the average system time $($waiting time plus service time$)$ of the first $5$ customers.

$($c$)$ Compute the average queue size during the first $20$ minutes.

$($d$)$ Does the Little$$s law hold for the average queue size in the first $20$ minutes?