a router receives delay senesitive traffic based. The router's queue can hold up to $5$ packets. It's arrival process is described as a poisson process with a rate lambda $=30$ packet$/$s$.$ The inter$-$packet service completion time is expotenitally distributed with $1/$mew $=20$ms

$($i$)$calculate the blocking probaility for the queue

$($ii$)$calculate the average delay of packets in the queue

$($iii$)$calculate the proportion of time the queue is empty