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Question 1 (Delay, 18%). As shown in the figure below, a file of size F = 1000 + S bytes is transmitted on an end-to-end
connection over three links, where S is the last three digits of your student number. For example, if your student number is
490123456, then S = 456 and F = 1456 bytes.
Each link is 100 km. The signal prorogation speed is 2 × 108 m/s. Assume that a header of 40 bytes is added to each packet.
The bandwidth of all links is R = 1 Mbps at the beginning. The nodes use the store-and-forward scheme. (Ignore processing
delays at each node.)
(0) What is your student number? Warning: If you use another student’s number as S value to answer the question, the following
sub-questions will not be marked and you will get 0 in Question 1.
(1) How long does it take to transmit the file if the whole file is transmitted as a single packet.
Now assume that the bandwidth of link B ? C becomes 0.5 Mbps. Answer (2)–(4).
(2) Repeat (1).
(3) We would like to break the file into smaller packets to decrease the overall delay in the store-and-forward scheme. Assume
that each time you break the file to make a new packet, you have to add 40 bytes as the header of the new packet. Repeat (2)
when we break the file into N = 4 packets.
(4) What should be the optimal size of the packets to have the minimum overall delay to deliver the whole file? Find the overall
delay.
Hint: Since the link B ? C has a smaller bandwidth compared with A ? B, packets could be queued for some time!
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Question 2 (Equilibrium of Two Competing Transmissions, 18%). Consider the following scenario where two mobile phones
are competing to use the save channel (same scenario as Tutorial 1, Exercise 1).
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The utilities are as follows. (The two users have different utilities when its transmission is successful). Mixed strategy is used.
User 1 transmits with probability p1 and user 2 with probability p2. p1 and p2 are non-zero.
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(1) If the two users are selfish, compute the transmission probabilities of the two users at equilibrium. What are the utilities of
the two users at equilibrium?
(2) If the two users are cooperative and p1 = p2, compute the max average utility of two users, i.e., 0.5×average utility of user
1 + 0.5×average utility of user 2. What is the value of p1 (i.e., p2) when the average utility of two users is maximized?