# Step-by-Step Excellence: Solutions for 'Computer Networking 7th Edition' Chapter 1

Welcome to an in-depth exploration of Chapter 1 from 'Computer Networking: A Top-Down Approach,' 7th edition. In this comprehensive package, you'll find a treasure trove of 34 thought-provoking questions that delve into the core concepts of computer networking. These questions are meticulously designed to test your understanding of the fundamental principles covered in Chapter 1. From network protocols to the structure of the Internet, these inquiries will challenge your knowledge and critical thinking skills. Whether you're a student looking to reinforce your grasp of the subject or a professional seeking to refresh your networking expertise, these questions serve as an excellent tool to expand your understanding of computer networking's foundational concepts. Dive in and test your knowledge as you embark on a journey of learning and discovery in the world of computer networking.

list of the 34 questions with its answers:

P1. Design and describe an application-level protocol to be used between an automatic teller

machine and a bank’s centralized computer. Your protocol should allow a user’s card and

password to be verified, the account balance (which is maintained at the centralized computer)

to be queried, and an account withdrawal to be made (that is, money disbursed to the user).

Your protocol entities should be able to handle the all-too-common case in which there is not

enough money in the account to cover the withdrawal. Specify your protocol by listing the

messages exchanged and the action taken by the automatic teller machine or the bank’s

centralized computer on transmission and receipt of messages. Sketch the operation of your

protocol for the case of a simple withdrawal with no errors, using a diagram similar to that in

Figure 1.2 . Explicitly state the assumptions made by your protocol about the underlying end-toend

transport service.

P2. Equation 1.1 gives a formula for the end-to-end delay of sending one packet of length L

over N links of transmission rate R. Generalize this formula for sending P such packets back-toback

over the N links.

See the AnswerP3. Consider an application that transmits data at a steady rate (for example, the sender

generates an N-bit unit of data every k time units, where k is small and fixed). Also, when such

an application starts, it will continue running for a relatively long period of time. Answer the

following questions, briefly justifying your answer:

a. Would a packet-switched network or a circuit-switched network be more appropriate for

this application? Why?

b. Suppose that a packet-switched network is used and the only traffic in this network

comes from such applications as described above. Furthermore, assume that the sum of

the application data rates is less than the capacities of each and every link. Is some form

of congestion control needed? Why?

P4. Consider the circuit-switched network in Figure 1.13 . Recall that there are 4 circuits on

each link. Label the four switches A, B, C, and D, going in the clockwise direction.

a. What is the maximum number of simultaneous connections that can be in progress at

any one time in this network?

b. Suppose that all connections are between switches A and C. What is the maximum

number of simultaneous connections that can be in progress?

c. Suppose we want to make four connections between switches A and C, and another four

connections between switches B and D. Can we route these calls through the four links

to accommodate all eight connections?

P5. Review the car-caravan analogy in Section 1.4 . Assume a propagation speed of 100

km/hour.

a. Suppose the caravan travels 150 km, beginning in front of one tollbooth, passing through

a second tollbooth, and finishing just after a third tollbooth. What is the end-to-end delay?

b. Repeat (a), now assuming that there are eight cars in the caravan instead of ten.

P6. This elementary problem begins to explore propagation delay and transmission delay, two

central concepts in data networking. Consider two hosts, A and B, connected by a single link of

rate R bps. Suppose that the two hosts are separated by m meters, and suppose the

propagation speed along the link is s meters/sec. Host A is to send a packet of size L bits to

Host B.

Exploring propagation delay and transmission delay

a. Express the propagation delay, d , in terms of m and s.

b. Determine the transmission time of the packet, d , in terms of L and R.

c. Ignoring processing and queuing delays, obtain an expression for the end-to-end delay.

d. Suppose Host A begins to transmit the packet at time . At time d , where is the

last bit of the packet?

e. Suppose d is greater than d . At time , where is the first bit of the packet?

f. Suppose d is less than d . At time , where is the first bit of the packet?

g. Suppose , , and Find the distance m so that d equals

P7. In this problem, we consider sending real-time voice from Host A to Host B over a packetswitched

network (VoIP). Host A converts analog voice to a digital 64 kbps bit stream on the fly.

Host A then groups the bits into 56-byte packets. There is one link between Hosts A and B; its

transmission rate is 2 Mbps and its propagation delay is 10 msec. As soon as Host A gathers a

packet, it sends it to Host B. As soon as Host B receives an entire packet, it converts the

packet’s bits to an analog signal. How much time elapses from the time a bit is created (from the

original analog signal at Host A) until the bit is decoded (as part of the analog signal at Host B)?

P8. Suppose users share a 3 Mbps link. Also suppose each user requires 150 kbps when

transmitting, but each user transmits only 10 percent of the time. (See the discussion of packet

switching versus circuit switching in Section 1.3 .)

a. When circuit switching is used, how many users can be supported?

b. For the remainder of this problem, suppose packet switching is used. Find the probability

that a given user is transmitting.

c. Suppose there are 120 users. Find the probability that at any given time, exactly n users

are transmitting simultaneously. (Hint: Use the binomial distribution.)

d. Find the probability that there are 21 or more users transmitting simultaneously.

P9. Consider the discussion in Section 1.3 of packet switching versus circuit switching in which

an example is provided with a 1 Mbps link. Users are generating data at a rate of 100 kbps when

busy, but are busy generating data only with probability . Suppose that the 1 Mbps link is

prop

trans

t=0 t= trans

prop trans t=dtrans

prop trans t=dtrans

s=2.5⋅108 L=120 bits R=56 kbps. prop

trans

p=0.1

replaced by a 1 Gbps link.

a. What is N, the maximum number of users that can be supported simultaneously under

circuit switching?

b. Now consider packet switching and a user population of M users. Give a formula (in

terms of p, M, N) for the probability that more than N users are sending data.

P10. Consider a packet of length L that begins at end system A and travels over three links to a

destination end system. These three links are connected by two packet switches. Let d, s , and

R denote the length, propagation speed, and the transmission rate of link i, for . The

packet switch delays each packet by d . Assuming no queuing delays, in terms of d, s , R,

, and L, what is the total end-to-end delay for the packet? Suppose now the packet is

1,500 bytes, the propagation speed on all three links is the transmission rates of all

three links are 2 Mbps, the packet switch processing delay is 3 msec, the length of the first link is

5,000 km, the length of the second link is 4,000 km, and the length of the last link is 1,000 km.

For these values, what is the end-to-end delay?

P11. In the above problem, suppose and . Further suppose the packet

switch does not store-and-forward packets but instead immediately transmits each bit it receives

before waiting for the entire packet to arrive. What is the end-to-end delay?

P12. A packet switch receives a packet and determines the outbound link to which the packet

should be forwarded. When the packet arrives, one other packet is halfway done being

transmitted on this outbound link and four other packets are waiting to be transmitted. Packets

are transmitted in order of arrival. Suppose all packets are 1,500 bytes and the link rate is 2

Mbps. What is the queuing delay for the packet? More generally, what is the queuing delay when

all packets have length L, the transmission rate is R, x bits of the currently-being-transmitted

packet have been transmitted, and n packets are already in the queue?

P13.

a. Suppose N packets arrive simultaneously to a link at which no packets are currently

being transmitted or queued. Each packet is of length L and the link has transmission

rate R. What is the average queuing delay for the N packets?

b. Now suppose that N such packets arrive to the link every LN/R seconds. What is the

average queuing delay of a packet?

P14. Consider the queuing delay in a router buffer. Let I denote traffic intensity; that is, .

Suppose that the queuing delay takes the form for .

a. Provide a formula for the total delay, that is, the queuing delay plus the transmission

delay.

b. Plot the total delay as a function of L /R.

P15. Let a denote the rate of packets arriving at a link in packets/sec, and let μ denote the link’s

transmission rate in packets/sec. Based on the formula for the total delay (i.e., the queuing delay

i i

i i=1,2,3

proc i i i

(i=1,2,3)

2.5⋅108m/s,

R1=R2=R3=R dproc=0

I=La/R

IL/R(1−I) I<1

plus the transmission delay) derived in the previous problem, derive a formula for the total delay

in terms of a and μ.

P16. Consider a router buffer preceding an outbound link. In this problem, you will use Little’s

formula, a famous formula from queuing theory. Let N denote the average number of packets in

the buffer plus the packet being transmitted. Let a denote the rate of packets arriving at the link.

Let d denote the average total delay (i.e., the queuing delay plus the transmission delay)

experienced by a packet. Little’s formula is . Suppose that on average, the buffer contains

10 packets, and the average packet queuing delay is 10 msec. The link’s transmission rate is

100 packets/sec. Using Little’s formula, what is the average packet arrival rate, assuming there

is no packet loss?

P17.

a. Generalize Equation 1.2 in Section 1.4.3 for heterogeneous processing rates,

transmission rates, and propagation delays.

b. Repeat (a), but now also suppose that there is an average queuing delay of d at each

node.

P18. Perform a Traceroute between source and destination on the same continent at three

different hours of the day.

Using Traceroute to discover network paths and measure network delay

a. Find the average and standard deviation of the round-trip delays at each of the three

hours.

b. Find the number of routers in the path at each of the three hours. Did the paths change

during any of the hours?

c. Try to identify the number of ISP networks that the Traceroute packets pass through from

source to destination. Routers with similar names and/or similar IP addresses should be

considered as part of the same ISP. In your experiments, do the largest delays occur at

the peering interfaces between adjacent ISPs?

d. Repeat the above for a source and destination on different continents. Compare the

intra-continent and inter-continent results.

P19.

a. Visit the site www.traceroute.org and perform traceroutes from two different cities in

France to the same destination host in the United States. How many links are the same

N=a⋅d

queue

in the two traceroutes? Is the transatlantic link the same?

b. Repeat (a) but this time choose one city in France and another city in Germany.

c. Pick a city in the United States, and perform traceroutes to two hosts, each in a different

city in China. How many links are common in the two traceroutes? Do the two

traceroutes diverge before reaching China?

P20. Consider the throughput example corresponding to Figure 1.20(b) . Now suppose that

there are M client-server pairs rather than 10. Denote R , R , and R for the rates of the server

links, client links, and network link. Assume all other links have abundant capacity and that there

is no other traffic in the network besides the traffic generated by the M client-server pairs. Derive

a general expression for throughput in terms of R , R , R, and M.

P21. Consider Figure 1.19(b) . Now suppose that there are M paths between the server and the

client. No two paths share any link. Path consists of N links with transmission rates

. If the server can only use one path to send data to the client, what is the

maximum throughput that the server can achieve? If the server can use all M paths to send data,

what is the maximum throughput that the server can achieve?

P22. Consider Figure 1.19(b) . Suppose that each link between the server and the client has a

packet loss probability p, and the packet loss probabilities for these links are independent. What

is the probability that a packet (sent by the server) is successfully received by the receiver? If a

packet is lost in the path from the server to the client, then the server will re-transmit the packet.

On average, how many times will the server re-transmit the packet in order for the client to

successfully receive the packet?

P23. Consider Figure 1.19(a) . Assume that we know the bottleneck link along the path from the

server to the client is the first link with rate R bits/sec. Suppose we send a pair of packets back

to back from the server to the client, and there is no other traffic on this path. Assume each

packet of size L bits, and both links have the same propagation delay d .

a. What is the packet inter-arrival time at the destination? That is, how much time elapses

from when the last bit of the first packet arrives until the last bit of the second packet

arrives?

b. Now assume that the second link is the bottleneck link (i.e., ). Is it possible that

the second packet queues at the input queue of the second link? Explain. Now suppose

that the server sends the second packet T seconds after sending the first packet. How

large must T be to ensure no queuing before the second link? Explain.

P24. Suppose you would like to urgently deliver 40 terabytes data from Boston to Los 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.

P25. Suppose two hosts, A and B, are separated by 20,000 kilometers and are connected by a

direct link of Mbps. Suppose the propagation speed over the link is meters/sec.

a. Calculate the bandwidth-delay product, .

s c

s c

k(k=1,…,M)

R1k,R2k,…,RNk

s

prop

Rc<Rs

R=2 2.5⋅108

R⋅dprop

b. Consider sending a file of 800,000 bits from Host A to Host B. Suppose the file is sent

continuously as one large message. What is the maximum number of bits that will be in

the link at any given time?

c. Provide an interpretation of the bandwidth-delay product.

d. What is the width (in meters) of a bit in the link? Is it longer than a football

field?

e. Derive a general expression for the width of a bit in terms of the propagation speed s, the

transmission rate R, and the length of the link m.

P26. Referring to problem P25, suppose we can modify R. For what value of R is the width of a

bit as long as the length of the link?

P27. Consider problem P25 but now with a link of Gbps.

a. Calculate the bandwidth-delay product, .

b. Consider sending a file of 800,000 bits from Host A to Host B. Suppose the file is sent

continuously as one big message. What is the maximum number of bits that will be in the

link at any given time?

c. What is the width (in meters) of a bit in the link?

P28. Refer again to problem P25.

a. How long does it take to send the file, assuming it is sent continuously?

b. Suppose now the file is broken up into 20 packets with each packet containing 40,000

bits. Suppose that each packet is acknowledged by the receiver and the transmission

time of an acknowledgment packet is negligible. Finally, assume that the sender cannot

send a packet until the preceding one is acknowledged. How long does it take to send

the file?

c. Compare the results from (a) and (b).

P29. Suppose there is a 10 Mbps microwave link between a geostationary satellite and its base

station on Earth. Every minute the satellite takes a digital photo and sends it to the base station.

Assume a propagation speed of meters/sec.

a. What is the propagation delay of the link?

b. What is the bandwidth-delay product, ?

c. Let x denote the size of the photo. What is the minimum value of x for the microwave link

to be continuously transmitting?

P30. Consider the airline travel analogy in our discussion of layering in Section 1.5 , and the

addition of headers to protocol data units as they flow down the protocol stack. Is there an

equivalent notion of header information that is added to passengers and baggage as they move

down the airline protocol stack?

P31. In modern packet-switched networks, including the Internet, the source host segments

long, application-layer messages (for example, an image or a music file) into smaller packets

R=1

R⋅dprop

2.4⋅108

R⋅dprop

and sends the packets into the network. The receiver then reassembles the packets back into

the original message. We refer to this process as message segmentation. Figure 1.27 illustrates

the end-to-end transport of a message with and without message segmentation. Consider a

message that is bits long that is to be sent from source to destination in Figure 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 message

segmentation. How long does it take to move the message from the source host to the

first packet switch? Keeping in mind that each switch uses store-and-forward packet

switching, what is the total time to move the message from source host to destination

host?

b. Now suppose that the message is segmented into 800 packets, with each packet being

10,000 bits long. How long does it take to move the first packet from source host to the

first switch? When the first packet is being sent from the first switch to the second switch,

the second packet is being sent from the source host to the first switch. At what time will

the second packet be fully received at the first switch?

c. How long does it take to move the file from source host to destination host when

message segmentation is used? Compare this result with your answer in part (a) and

comment.

GO TO THE ANSWERFigure 1.27 End-to-end message transport: (a) without message segmentation;

(b) with message segmentation

d. 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. Do the 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 packet switching (with message segmentation) and for

message switching?

P33. Consider sending a large file of F bits from Host A to Host B. There are three links (and two

switches) between A and B, and the links are uncongested (that is, no queuing delays). Host A

P34. Skype offers a service that allows you to make a phone call from a PC to an ordinary

phone. This means that the voice call must pass through both the Internet and through a

telephone network. Discuss how this might be done.