$3.$ Host A has opened a TCP connection with Host B$.$ Host A then sends a long sequence of data segments to B$.$ Each data segment is $1000$ bytes long. Host A and B agree to use stop$-$and$-$wait protocol for reliable data transfer. The RTT is $1$ msec.

a$.$ If the channel is perfect, what is the throughput of the connection in bits per second$($bps$)?$

b$.$ If the channel is perfect and the link speed at Host A is $\backslash$alpha bps $.$At what value of $\backslash$alpha below which the throughput for sure cannot be achieved.

c$.$ How would you double the throughput?

d$.$ Assume the channel corrupts segments at the receiver $($Host B$)$ only. What version of rdt should be used?

e$.$ If on the average $1$ out $10$ segments are corrupted at the receiver, what is the throughput of the connection?

f$.$ Assume, if segments are not lost in the network, the RTT for these segments is a uniform distributed random variable between RTT$1$ and RTT$2.$ Would you choose a timeout value smaller than RTT$1$ and why?

g$.$ Refer to $3.$f$,$ would you choose a timeout value larger than RTT$2$ and why?

h$.$ Assume Host A and B agree to use a modified stop and wait protocol in which A is allowed to send $3$ back to back segments before the acknowledgment for the first segment is received. If the channel is perfect, what is the throughput?

i$.$ Assume the channel can corrupt segments with probability q$.$ The modified stop$-$and$-$wait protocol is such that if one or more of the three back$-$to$-$back segments are corrupted, all three segments must be discarded. What is the throughput?

j$.$ Let the modified stop$-$and$-$wait protocol allows n back$-$to$-$back segments sent before receiving any acknowledgment. The channel corrupts segments with probability q$.$ Write the equation for the TCP throughput in terms of n and q$.$ Given q$,$ find the optimal value of n$.$