P$13.($a$)$ Suppose $N$ packets arrive simultaneously to a link at which no packets are currently being transmitted or queued. Each packet is of length $L$ and the link has transmission rate $R.$ What is the average queuing delay for the $N$ packets?

$($b$)$ Now suppose that $N$ such packets arrive to the link every $L\frac{N}{R}$ seconds. What is the average queuing delay of a packet?

$($What is the stability limit$,$ i$.$e$.,$ how often can a batch of $N$ packets arrive to ensure that the queue does not grow to infinity$)$