(b) Repeat (a) but this time choose one city in France and another city inGermany.(c) Pick a city in the United States, and perform traceroutes to two hosts, eachin a different city in China. How many links are common in the twotraceroutes? Do the two traceroutes diverge before reaching China?P20. Consider the throughput example corresponding to Figure 1.20(b). Nowsuppose that there are M client-server pairs rather than 10. Denote Rs, Rc, andR for the rates of the server links, client links, and network link. Assume allother links have abundant capacity and that there is no other traffic in thenetwork besides the traffic generated by the M client-server pairs. Derive ageneral expression for throughput in terms of Rs, Rc, R, and M.P21. Consider Figure 1.19(b). Now suppose that there are M paths between theserver and the client. No two paths share any link. Path k (k = 1, . . ., M ) con-sists of N links with transmission rates Rk1, Rk2, . . ., RkN. If the server can onlyuse one path to send data to the client, what is the maximum throughput thatthe server can achieve? If the server can use all M paths to send data, what isthe maximum throughput that the server can achieve?P22. Consider Figure 1.19(b). Suppose that each link between the server and theclient has a packet loss probability p, and the packet loss probabilities forthese links are independent. What is the probability that a packet (sent by theserver) is successfully received by the receiver? If a packet is lost in the pathfrom the server to the client, then the server will re-transmit the packet. Onaverage, how many times will the server re-transmit the packet in order forthe client to successfully receive the packet?P23. Consider Figure 1.19(a). Assume that we know the bottleneck link along thepath from the server to the client is the first link with rate Rsbits/sec. Supposewe send a pair of packets back to back from the server to the client, and thereis no other traffic on this path. Assume each packet of size L bits, and bothlinks have the same propagation delay dprop.a. What is the packet inter-arrival time at the destination? That is, how muchtime elapses from when the last bit of the first packet arrives until the lastbit of the second packet arrives?b. Now assume that the second link is the bottleneck link (i.e., Rc< Rs). Is itpossible that the second packet queues at the input queue of the secondlink? Explain. Now suppose that the server sends the second packet T sec-onds after sending the first packet. How large must T be to ensure noqueuing before the second link? Explain.P24. Suppose you would like to urgently deliver 40 terabytes data from Boston toLos Angeles. You have available a 100 Mbps dedicated link for data transfer.Would you prefer to transmit the data via this link or instead use FedEx over-night delivery? Explain. PROBLEMS 75the protocol stack. Is there an equivalent notion of header information thatis added to passengers and baggage as they move down the airline protocolstack?P31. In modern packet-switched networks, including the Internet, the source hostsegments long, application-layer messages (for example, an image or a musicfile) into smaller packets and sends the packets into the network. The receiverthen reassembles the packets back into the original message. We refer to thisprocess as message segmentation. Figure 1.27 illustrates the end-to-endtransport of a message with and without message segmentation. Consider amessage that is 8 · 106bits long that is to be sent from source to destination inFigure 1.27. Suppose each link in the figure is 2 Mbps. Ignore propagation,queuing, and processing delays.a. Consider sending the message from source to destination without messagesegmentation. How long does it take to move the message from the sourcehost to the first packet switch? Keeping in mind that each switch usesstore-and-forward packet switching, what is the total time to move themessage from source host to destination host?b. Now suppose that the message is segmented into 800 packets, with eachpacket being 10,000 bits long. How long does it take to move the firstpacket from source host to the first switch? When the first packet is beingsent from the first switch to the second switch, the second packet is beingsent from the source host to the first switch. At what time will the secondpacket be fully received at the first switch?c. How long does it take to move the file from source host to destination hostwhen message segmentation is used? Compare this result with youranswer in part (a) and comment.PROBLEMS 77Sourcea. Packet switch Packet switch DestinationMessageSourceb. Packet switchPacketPacket switch DestinationFigure 1.27  End-to-end message transport: (a) without messagesegmentation; (b) with message segmentationd. In addition to reducing delay, what are reasons to use message segmentation?e. Discuss the drawbacks of message segmentation.P32. Experiment with the Message Segmentation applet at the book’s Web site. Dothe delays in the applet correspond to the delays in the previous problem?How do link propagation delays affect the overall end-to-end delay for packetswitching (with message segmentation) and for message switching?P33. Consider sending a large file of F bits from Host A to Host B. There are threelinks (and two switches) between A and B, and the links are uncongested (that is, no queuing delays). Host A segments the file into segments of S bits each andadds 80 bits of header to each segment, forming packets of L = 80 + S bits. Eachlink has a transmission rate of R bps. Find the value of S that minimizes thedelay of moving the file from Host A to Host B. Disregard propagation delay.P34. Skype offers a service that allows you to make a phone call from a PC to anordinary phone. This means that the voice call must pass through both the Internet and through a telephone network. Discuss how this might be done.Wireshark Lab“Tell me and I forget. Show me and I remember. Involve me and I understand.”Chinese proverbOne’s understanding of network protocols can often be greatly deepened by seeingthem in action and by playing around with them—observing the sequence of mes-sages exchanged between two protocol entities, delving into the details of protocoloperation, causing protocols to perform certain actions, and observing these actionsand their consequences. This can be done in simulated scenarios or in a real networkenvironment such as the Internet. The Java applets at the