CS536 Homework 1due Wednesday, September 21st (class time)September 8, 2011Submit your homework electronically in a text or PDF file. Upload yoursolution to Blackboard by 12:30pm on Friday, September 21st. Late submissionwill not be accepted, nor will collaboration.Collaboration on the homeworks is allowed, provided that the homeworkexplicitly state who collaboration was done with, and that the homework iswritten up completely independently. Questions about this homework shouldbe directed to the TAs or the Professor, not to fellow classmates.Answers should be justified and work shown. Answers with no justificationwill not receive credit.Problem 1 (20 pts)End-to-End Argument. Given that email does not provide an end-to-endreliability service, when needed it must be provided by either the email clientapplication, or the users of those applications. Devise a hypothetical protocolthat can provide reliable email transmission between sender and receiver, usingonly email as a communication medium. What guarantees can your protocolprovide about reliability and performance?Problem 2 (10 pts)Suppose users share a 9Mbps link. Also suppose each user transmits continu-ously at 1.5Mbps when transmitting, but each user transmits only 25% of thetime.a. When circuit switching is used, how many users can be supported?b. For the remainder of this problem, suppose packet switching is used. Whywill there be essentially no queueing delay before the link if six or fewerusers transmit at the same time? Why will there be a queueing delay ifseven users transmit at the same time?c. Suppose there are 10 users. Find the probability that at any given time,exactly n users are transmitting simultaneously. (Hint: Use the binomialdistribution.)1d. Find the probability that there are 7 or more users transmitting simulta-neously.Problem 3 (10 pts)Consider two hosts A and B, connected by a single link of rate R bps. Supposethat the two hosts are separated by m meters, and suppose the propagationspeed along the link is s meters/sec. Host A is to send a packet of size L bitsto hose B.a. Express the propagation delay, dprop, in terms of m and s.b. Determine the transmission time of the packet, dtrans, in terms of L andR.c. Ignoring processing and queueing delays, obtain an expression for the end-to-end delay.d. Suppose host A begins to transmit the packet at time t = 0. At timet = dtrans, where is the last bit of the packet?e. Suppose dpropis less than dtrans. At time t = dtrans, where is the first bitof the packet?f. Suppose dpropis greater than dtrans. At time t = dtrans, where is the firstbit of the packet?g. Suppose s = 2.5 × 108, L = 300 bits, and R = 56 kbps. Find the distancem so that dpropequals dtrans.Problem 4 (10 pts)Suppose two hosts, A and B, are separated by 15,000 kilometers and are con-nected by a direct link of R = 1 Mbps. Suppose the propagation speed over thelink is 2.5 × 108meters/sec.a. Calculate the bandwidth-delay product, R × dprop.b. Consider sending a file of 600,000 bits from host A to host B. Supposethe file is sent continuously as one large message. What is the maximumnumber of bits that will be in the link at any given time?c. Provide an interpretation of bandwidth-delay product.d. What is the width (in meters) of a bit in the link? Is it longer than afootball field (a football field is 100 yards)?e. Derive a general expression for the width of a bit in terms of the propa-gation speed s, the transmission rate R, and the length of a link m.2Problem 5 (20 pts)Akamai. DNS is a major component of how Akamai works. In what ways doesAkamai’s implementation of DNS differ from the traditional implementation?Problem 6 (10 pts)Consider a short, 10-meter link, over which a sender can transmit at a rate of 120bits/sec in both directions. Suppose that packets containing only control (e.gACK or handshaking) are 240 bits long. Assume that N parallel connectionseach get 1/N of the link bandwidth. Now consider the HTTP protocol, andsuppose that each downloaded object is 120 Kbits long, and that the initialdownloaded object contains 15 referenced objects from the same sender. Wouldparallel downloads via parallel instances of non-persistent HTTP make sense inthis case? Now consider persistent HTTP. Do you expect significant gains overthe non-persistent case? Justify and explain your answer.Problem 7 (10 pts)Give two examples of why the address given in an “RCPT TO:” SMTP com-mand would differ from the “To:” field in the email body.Problem 8 (10 pts)Consider distributing a file of F bits to N peers using a P2P architecture.Assume a fluid model. For simplicity assume that dminis very large, so thatpeer download bandwidth is never a bottleneck.a. Suppose that us≤ (us+ u1+ . . . + uN)/N. Specify a distribution schemethat has a distribution time of F/us.b. Suppose that us≥ (us+ u1+ . . . + uN)/N. Specify a distribution schemethat has a distribution time of NF/(us+ u1+ . . . + uN).c. Conclude that the minimum distribution time is in general given bymax{F/us, NF/(us+ u1+ . . . +