In modern packet$-$switched networks, the source host splits long application$-$layer messages $($such as an image or a video file$)$ into smaller packets and sends the packets into the network. The receiver then reassembles the packets back into the original message. We refer to this process as message segmentation. Consider the path from a source host to a destination that includes $2$ routers. A message that is $5740$ bytes long is sent from the source to the destination. Suppose each link is $190$ Kbps$.$ Ignore propagation, queueing and processing delay.

Consider sending the message from source to destination without message segmentation.

What is the total time $($in seconds$)$ to move the message from the source host to the destination host? Keep in mind that each router uses store$-$and$-$forward packet switching.

Now suppose that the message is segmented into $70$ packets of the same length.

How many seconds does it take to move the whole message from the source host to the destination host?If a header is added to each packet before transmission, what is the minimum header size $($in bits$)$ that eliminates the benefit of message segmentation, i$.$e$.$ makes the message transfer time from the source to the destination with segmentation longer than that without segmentation? The result must be an integer.

If a packet has at least one bit corrupted, it has to be retransmitted. If the probability of a bit being corrupted during the transfer from the source to the destination is $10-5($which is unrealistically high but used for easier calculation$),$ what is the average number of retransmissions needed to transfer the message successfully without message segmentation and with segmentation respectively? $($Hint: check geometric distribution$).$

Kindly round the results to the nearest hundredth except specified otherwise.