Consider a network with $3$ hops shown in Figure $3.$ Packets at node $2$ sent toward node $3($or vice versa$)$ will take link u with probability $0\mathrm{.}25$ and link v with probability $0\mathrm{.}75.$ Retransmissions take the same path as the original packet. The propagation delays on links $(1,2),$ u$,$ v$,(3,4)$ are $1$ms$,50$ms$,2$ms$,$ and $1$ ms respectively. Assume that propagation delay dominates.

a$.$ What is the long$-$term average RTT observed by the sender transmitting TCP segments to the destination? Explain your calculations clearly.

b$.$ If a stop$-$and$-$wait transport layer protocol is used, and a $1\mathrm{.}5$ GB file, broken into $1500$ byte segments is sent, how much time $($in hours$)$ would it take for the file to be received at the destination if there are no lost packets and no errors? Ignore lower layer effects. Assume $25\%$ of the packets take link u and $75\%$ take link v$.$

c$.$ Next consider layering ignored in $($b$).$ Let Ethernet frames be transmitted on each link and are $1500$ bytes long.. They carry the IP datagram and TCP segments. TCP adds $160$ bits as header for each Layer $4$ segment. Each TCP segment is carried by an IP datagram with a $160$ bit header. The IP datagrams form the payload of Ethernet, which has a $176$ bit header and a $32$ bit CRC$.$ How many bits of data are sent on the physical medium to complete the transmission of all of the application data $($the $1\mathrm{.}5$ GB file$)?$ And how long $($in hours$)$ would it take to deliver the $1\mathrm{.}5$ GB file to the destination? Again, assume $25\%$ of the packets take link u and $75\%$ take link v$.$ Comment on how$/$why this result is different from that in Q$3($b$).$

d$.$ Explain in six or fewer sentences how a Go$-$Back$-$N or Selective Repeat protocol helps reduce the time taken to deliver the file $($use an example data rate of $100$ Mbps on all links$).$