$1.$Consider sending a single message of F$=200,000$ bytes from one host to another with N$=4$ intermediate routers. Assume that the message will wait for M$=3$ other same size messages to finish transmission at each intermediate router. Also assume that the total distance between the sender and the receiver is $3000$ km $(0\mathrm{.}3$ km$/\backslash$mu sec$)$ and the transmission capacity is C$=20$ Mbps along the path.

a$.$Calculate the time from the first bit being sent out from the sender and the last bit received by the receiver. Specify clearly the different delay components and any assumption made in your calculations.

b$.$ If the above total delay cannot exceed $200$ ms$,$ what is the minimal transmission capacity Cmin needed to achieve this requirement? Assuming everything else remains the same.

c$.$ Repeat b$.$ above but assess what N and M combination$($s$)$ could satisfy the requirement?

d$.$Calculate the BW$-$Delay Product for Part a$.$ Please be careful on the exact $$delay$$ value you will use? It may not be the exact number you found in Part a$.$ How do you think this BW$-$Delay Product will change for Part b$.$ or Part c$.?$ Explain