Problem $1$

Consider a source and a destination connected by $N$ links $($i$.$e$.,N-1$ packet switches$).$ Each link has capacity $R$ bps$,$ and propagation delay $d_{\text{p}\text{r}\text{o}\text{p}}$ seconds. Ignore processing delays and assume that initially all the buffers are empty.

a$)$ Give a formula for the end$-$to$-$end delay of sending one packet of length $L$ bits.

b$)$ Generalize the formula for sending $P$ packets of $L$ bits each.

c$)$ Now suppose the links $($in the order from source to destination$)$ have capacities $d_1,d_2,$dots,$d_{N}PL{R}_1>R_2>$dots$>R_N{d}_1,d_2,$dots,$d_N{R}_1,$ and propagation delays $d_1,d_2,$dots,$d_N(with$ arbitrary values$).$ Give formula for the end$-to-$end delay $of$ sending $P$ packets $ofL$ bits each.

$d$