# 15-441: Computer Networks Homework 2 Solution

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4 7 7 Replacing with bps I 7 and simplifying we get I Solution 2 (accepted with full points): I to From previous answer, I. -:- -:- I Replacing with I and simplifying we get -:- I I:I bps 5 ongestion ontrol Harry Bovik thinks that if the sources in the Internet use additive increase additive decrease (AIAD) the system should still converge to fairness and efficiency. onnection 2 throughput Region I Region II Region III Region IV onnection throughput Figure 2: TP Phase-plot Harry decides to use phase-plots (see pg. 269 of the book) to check his intuition for the two-user case. Figure 2 shows a simple phase plot. In the graph, the state of the system is represented by a point (x, x2), where x is stream s current rate and x2 is stream 2 s current rate. The total capacity of the link is bits/s. Assume that after the packet loss the window sizes have been reduced according to AIAD and now the system state is in either one of the labelled regions.. On the figure, for each of the labelled regions, I, II, III, and IV, draw vectors indicating the direction in which the system will move next i.e., after the AIAD response to the packet loss. Answer: See Figure In each of the following regions, does the response after the packet loss increase, reduce or keep fairness the same? Region I: Answer: Increases Region II: Answer: Decreases 4

6 3. Harry Bovik says that since there are negligible losses within the US, the streaming multimedia applications do not need to have a playback buffer in US. What would be your response? Answer: The playback buffer is required to smooth out the video. Delay variance causes packets to arrive after their playout time and hence are missed. The playback buffer is needed even if there are no losses. 7 Reliability For all parts of this question, refer to figure 4. The graph shows the packets sent and AKs received by a TP Reno sender. The x-axis shows the time in seconds and the y-axis shows the sequence number of the packet (or AK) being sent (or received). Assume that all packets that are not lost will arrive in order at both the sender and receiver. Also assume that receiver keeps all the out of order received packets. Seqno Sender view of packets and AKs in TP Reno Packets AKs Time Figure 4: Reno : Fast Retransmission. Mark on the x-axis of the graph, the time interval when the connection is in slow-start. Answer: Slow start is approximately from time 0 to.4sec, 2.2 to 3. sec, and 3.5 to 3.7 (though it is fine if you missed this last one). 2. Mark the packets (if any) with that are lost. Answer: Packet Numbers: 25, 26, 27, 29, 32, 36, 4, 46, 47, 48, 49 6

7 3. Mark the duplicate packets received by the receiver (if any) with a. Answer: Packet Numbers: 28(2nd), 30(2nd), 3(2nd), 33(2nd), 34(2nd), 35(2nd), 36(3rd), 37(2nd), 38(2nd), 39(2nd), 40(2nd), 4(3rd), 42(2nd), 43(2nd), 44(2nd), 45(2nd), 46(3rd), 50(2nd) 4. Mark the timed out packet (if any) with a T. Answer: Packet Number: Draw on the graph an approximate curve showing how a Tahoe TP Sender would behave. Answer: Tahoe will behave the same as Reno for the first.5sec. Then while Reno would wait for a timeout, Tahoe will start slow start around.5sec and continue roughly parallel to Reno but being about sec earlier than Reno. 7

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