$1)(40$ points$)$ Consider a packet switched network for the communication of two end points A and

B$.$ There are two switching nodes, X and Y$,$ between A and B$.$ The capacity of the link between A

and X is $10$ Mbps $(10,000,000$ bps$).$ The capacity of the link between X and Y is $5$ Mbps

$(5,000,000$ bps$).$ The capacity of the link between Y and B is $2$ Mbps $(2,000,000$ bps$).$

A wants to send a file of $50$ Kbytes $(50,000$ bytes$)$ to B using this packet switching network. One

packet has $5000$ bytes of data and $100$ bytes of header. After receiving the entire file, B sends an

acknowledgment back to A through the same network. The recipient B imposes $0\mathrm{.}001$ sec

processing delay before sending the acknowledgment after receiving the last packet $($no other

processing delays in the network$).$ Assume there is no transmission time for the acknowledgment.

The network is not used for another communication until acknowledgment is received.

The distance between A and X is $60$ km: The distance between X and Y is $60$ km$.$ Finally, the

distance between Y and B is $30$ km$.$ The speed of signal is $300,000$ km$/$s$.$

a$)$ What is the round$-$trip time for sending the file and receiving its acknowledgment in the

abovementioned scenario? Show your work.

Hint: draw the packets as we did in class to understand the scenario.

b$)$ What is the throughput of this system? Show your work.

Notice: be aware of bit and byte conversion.

$2)(30$ points$)$ In a production line, three robots work with the following job descriptions and

performance figures. RobotA carries the items to RobotB for inspection. After RobotB finishes the

inspection, it puts the item on a conveyor band. At the end of the band, RobotC gets the item and

pack it$.$ The rate of RobotA to carry the items is $3$ items$/$min$.$ RobotB spends $15$ seconds for the

inspection of an item and another $10$ seconds to put the item on the band. The travel time for an

item on the conveyor band is $150$ seconds. Finally, RobotC packs one item in $15$ seconds. Assume

there is enough storage area for all of the robots if the items need to wait.

What is the total production time for $10$ items? Explain your answer.

$3)(30$ points$)$ Consider a direct link with capacity $25$ Kbps $(25000$ bits per second$)$ between two

end points A and B$.$ The link layer protocol between A and B is that A sends two packets

consecutively. Then A waits for an acknowledgment from B in order to send the next two packets.

There is no processing delay at B to send an acknowledgement after receiving the second packet.

The length of one packet is $4750$ bits of data and $250$ bits of header. The length of the

acknowledgment packet is $50$ bits with no extra header. The length of this link is $10$ km and the

speed of signal is $200,000$ km$/$s$.$

What is the utilization of this link at the steady state?