hw5-F23

ECE/CSC 570 – Sections 3 and 601, Computer Networks, Homework #5 Total 100 points, Due by 11:59PM on Dec. 1 (Friday), 2023 1. (5 points) State whether the following statements are true (T) or false (F). (i) (2 points) Diff-serv scales better than RSVP to a large number of flows. (ii) (3 points) For a TCP connection between A (sender) and B (receiver), A’s throughput does not depend on B’s CPU speed. Note: There will be some True/False questions in the final exam, just like the above. 2. (10 points) In TCP lecture note on Refinement (slide # 21), Suppose we use TCP-Reno and the sender’s timer expires at transmission round 11. Assume the receiver window size is large enough, i.e., rwnd = ∞ . What is the congestion window size ( cwnd ) of the sender at transmission round 15 then? Explain your steps leading to your answer. 7UDQVPLVVLRQ# URXQG#+577, FZQG#+LQ# 066 , 3 8 9 : 43 ; 49 48 4: 4; 83 88 89 < 43 =< 4< 83 8< =3 93 7&>15HQR 8: 9< +:/=8, +4:/98, +4?/84, +88/8:, +8=/4, +8:/;, Figure 1: TCP window size as a function of time, for Problem 3 3. (30 points, 3 points each) Consider Figure 1 that shows how the congestion window size changes un- der TCP-Reno, with several key coordinates info. Assume rwnd = ∞ . Answer the following questions. In all cases, you should provide a short discussion justifying your answer. (a) Identify the intervals of time (e.g., [x,y] in terms of transmission round) when TCP slow start is operating. (b) Identify the intervals of time when TCP congestion avoidance is operating. (c) After the 16th transmission round, is segment loss detected by a triple duplicate ACK or by a timeout? (d) After the 22nd transmission round, is segment loss detected by a triple duplicate ACK or by a timeout? (e) What is the initial value of ssthresh at the first transmission round? 1

(f) What is the initial value of ssthresh at the 18th transmission round? (g) What is the initial value of ssthresh at the 24th transmission round? (h) During what transmission round is the 70th segment sent? (i) Assuming a packet loss is detected after the 26th round by the receipt of a triple duplicate ACK, what will be the value of the congestion window size ( cwnd ) and of ssthresh ? (j) Suppose TCP Tahoe is used (instead of TCP Reno), and assume that triple duplicate ACKs are received at the 16th round. What are the ssthresh and cwnd at the 19th round? 4. (10 points) Recall the idealized model for the steady-state dynamics of TCP. In the period of time from when the connection’s window size varies from W/ 2 to W , only one packet is lost (at the very end of the period). Show that the loss rate is equal to L = loss rate = 1 3 8 W 2 + 3 4 W . 5. (10 points) In the lecture note on TCP future (TCP over “long, fat pipes”, slide #34), we noted that, in order to achieve a throughput of 10Gbps, TCP could only tolerate a segment (packet) loss probability of 2 × 10 − 10 (or equivalently, one loss event for every 5,000,000,000 packets). Show the derivation for the values of 2 × 10 − 10 (1-out-of-5,000,000,000) when the RTT (round trip time) is 100ms and MSS (packet or segment size) is 1500 bytes. If TCP needed to support a 100 Gbps connection, what would be the tolerable loss rate? 6. (20 points, 10 points each) Consider TCP fairness scenario as shown in the lecture note, slide #26 in Transport chapter, which illustrates the convergence of TCP’s AIMD algorithm. There are two connections through the same bottleneck link of capacity R to the same server, as depicted in the figure in slide #25. Suppose that instead of a multiplicative decrease, TCP decreases the window size by a constant amount as follows: (a) Both connections decrease their window size by − 1 instead of multiplicative decrease. Would the resulting AIAD algorithm converge to an equal share? What are the long-term throughput of these two connections? Justify your answer by showing how the throughput of two connections (users) evolve over time, assuming that they start from the point ‘A’ in Figure 2 with short explanation on the plot you draw. (b) Now, connection 1 decreases its window size by − 3 while connection 2 decreases only by − 1. All other parts remain the same as above. Would this version of AIAD algorithm (but two connections behave differently) converge to an equal share? What are the long-term throughput of these two connections? Justify your answer by showing how the throughput of two connections (users) evolve over time, assuming that they start from the point ‘A’ in Figure 2 with short explanation on the plot you draw. 7. (15 points; taken from the past exam) Consider the same TCP fairness scenario as in the previous problem. There are two connections through the same bottleneck link of capacity R to the same server, as depicted in the figure in slide #25. Connection 1 follows the original AIMD algorithm as you learned in the class. Suppose that connection 2 (or user 2) is smart enough to modify his/her own TCP congestion control algorithm and performs the following: upon ACK, the window size increases by one as usual. Upon congestion, i.e., 3 duplicate acknowledgements, it maintains the same window 2