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computer networking

Data Communications and Networking 5th edition Behrouz A. Forouzan - Solutions

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 Rsbits/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
Consider Figure 1. 1 (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
Visit the Queuing and Loss applet at the companion Web site. What is the maximum emission rate and the minimum transmission rate? With those rates, what is the traffic intensity? Run the applet with these rates and deter mine how long it takes for packet loss to occur. Then repeat the experiment a
Consider Figure 1.19(b). Now suppose that there are M paths between the server and the client. Nu two paths share any link. Path k (k = 1,...,M) consists of N links with transmission rates Rk1, Rk2, .. . , RkN. 1f the server can only use one path to send data to the client, what is the maximum
(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 in the two traceroutes? Is the transatlantic link the same?(b) Repeat (a) but this time choose one city in France and
Consider sending a packet from a source host to a destination host over a fixed route. List the delay components in the end-to-end delay. Which of these delays are constant and which are variable?
Some content providers have created their own networks. Describe Google’s network. What motivates content providers to create these networks?
Why will two ISPs at the same level of the hierarchy often peer with each other? How does an TXP earn money?
(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
What are some of the physical media that Ethernet can run over?
List the available residential access technologies in your city. For each type of access, provide the advertised downstream rate, upstream rate, and monthly price.
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
List six access technologies. Classify each one as home access, enterprise access, or wide-area wireless access.
Why are standards important for protocols?
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-to-back over the N links.
The word protocol is often used to describe diplomatic relations. How does Wikipedia describe diplomatic protocol?
What is the difference between a host and an end system? List several different types of end systems. Is a Web server an end system?
Assume we need to create codewords that can automatically correct a one-bit error. What should the number of redundant bits (r) be, given the number of bits in the dataword (k)? Remember that the codeword needs to be n = k + r bits, called C(n, k). After finding the relationship, find the number of
How does a single-bit error differ from a burst error?
What is the maximum effect of a 2-ms burst of noise on data transmitted at the following rates?a. 1500 bpsb. 12 kbpsc. 100 kbpsd. 100 Mbps
What is the definition of a linear block code?
Assume that the probability that a bit in a data unit is corrupted during transmission is p. Find the probability that x number of bits are corrupted in an n-bit data unit for each of the following cases.a. n = 8, x = 1, p = 0.2b. n = 16, x = 3, p = 0.3c. n = 32, x = 10, p = 0.4
In a block code, a dataword is 20 bits and the corresponding codeword is 25 bits. What are the values of k, r, and n according to the definitions in the text? How many redundant bits are added to each dataword?
Exclusive-OR (XOR) is one of the most used operations in the calculation of codewords. Apply the exclusive-OR operation on the following pairs of patterns. Interpret the results.a. (10001) ⊕ (10001)b. (11100) ⊕ (00000)c. (10011) ⊕ (11111)
In a codeword, we add two redundant bits to each 8-bit data word. Find the number ofa. valid codewords.b. invalid codewords
In Table 10.1, the sender sends dataword 10. A 3-bit burst error corrupts the codeword. Can the receiver detect the error? Defend your answer.Table 10.1 Dataword Codeword Dataword Codeword 101 110 000 00 10 11 01 011
What is the minimum Hamming distance?
If we want to be able to detect two-bit errors, what should be the minimum Hamming distance?
Prove that the code represented by the following codewords is not linear. You need to find only one case that violates the linearity.{(00000), (01011), (10111), (11111)}
A category of error detecting (and correcting) code, called the Hamming code, is a code in which dmin = 3. This code can detect up to two errors (or correct one single error). In this code, the values of n, k, and r are related as: n = 2r − 1 and k = n − r. Find the number of bits in the
What is the Hamming distance for each of the following codewords?a. d (10000, 00000)b. d (10101, 10000)c. d (00000, 11111)d. d (00000, 00000)
In CRC, if the dataword is 5 bits and the codeword is 8 bits, how many 0s need to be added to the dataword to make the dividend? What is the size of the remainder? What is the size of the divisor?
Although it can be formally proved that the code in Table 10.3 is both linear and cyclic, use only two tests to partially prove the fact:Table 10.3a. Test the cyclic property on codeword 0101100.b. Test the linear property on codewords 0010110 and 1111111. Dataword Codeword Codeword Dataword 0000
In CRC, which of the following generators (divisors) guarantees the detection of a single bit error?a. 101b. 100c. 1
Referring to the CRC-8 in Table 5.4, answer the following questions:a. Does it detect a single error? Defend your answer.b. Does it detect a burst error of size 6? Defend your answer.c. What is the probability of detecting a burst error of size 9?d. What is the probability of detecting a burst
In CRC, which of the following generators (divisors) guarantees the detection of an odd number of errors?a. 10111b. 101101c. 111
Assuming even parity, find the parity bit for each of the following data units.a. 1001011b. 0001100c. 1000000d. 1110111
In CRC, we have chosen the generator 1100101. What is the probability of detecting a burst error of lengtha. 5?b. 7?c. 10?
A simple parity-check bit, which is normally added at the end of the word (changing a 7-bit ASCII character to a byte), cannot detect even numbers of errors. For example, two, four, six, or eight errors cannot be detected in this way. A better solution is to organize the characters in a table and
Assume we are sending data items of 16-bit length. If two data items are swapped during transmission, can the traditional checksum detect this error? Explain.
Given the dataword 101001111 and the divisor 10111, show the generation of the CRC codeword at the sender site (using binary division).
Can the value of a traditional checksum be all 0s (in binary)? Defend your answer.
Apply the following operations on the corresponding polynomials:a. (x3 + x2 + x + 1) + (x4 + x2 + x + 1)b. (x3 + x2 + x + 1) − (x4 + x2 + x + 1)c. (x3 + x2) × (x4 + x2 + x + 1)d. (x3 + x2 + x + 1) / (x2 + 1)
Show how the Fletcher algorithm (Figure 10.18) attaches weights to the data items when calculating the checksum.Figure 10.18 Notes Start L: Left 8-bit checksum R: Right 8-bit checksum R=L= 0 D;: Next 8-bit data item More data? [yes] L = (L+ R) mod 256 R = (R + Dj) mod 256 [no] 16-bit Checksum = L x
Answer the following questions:a. What is the polynomial representation of 101110?b. What is the result of shifting 101110 three bits to the left?c. Repeat part b using polynomials.d. What is the result of shifting 101110 four bits to the right?e. Repeat part d using polynomials.
Show how the Adler algorithm (Figure 10.19) attaches weights to the data items when calculating the checksum.Figure 10.19 Start Notes L: Left 16-bit checksum R: Right 16-bit checksum D;: Next 16-bit data item R=1 L=0 More data? [yes] R = (R + D;) mod 65,521 L= (L+ R) mod 65,521 [no] R Checksum = L
Which of the following CRC generators guarantee the detection of a single bit error?a. x3 + x + 1b. x4 + x2c. 1d. x2 + 1
Referring to the CRC-8 polynomial in Table 10.7, answer the following questions:a. Does it detect a single error? Defend your answer.b. Does it detect a burst error of size 6? Defend your answer.c. What is the probability of detecting a burst error of size 9?d. What is the probability of detecting
Referring to the CRC-32 polynomial in Table 10.4, answer the following questions:Table 10.4a. Does it detect a single error? Defend your answer.b. Does it detect a burst error of size 16? Defend your answer.c. What is the probability of detecting a burst error of size 33?d. What is the probability
Manually simulate the Adler algorithm (Figure 10.19) to calculate the checksum of the following words: (FBFF)16and (EFAA)16. Also show that the result is a weighted checksum.Figure 10.19 Start Notes L: Left 16-bit checksum R: Right 16-bit checksum D;: Next 16-bit data item R=1 L=0 More data? [yes]
One of the examples of a weighted checksum is the ISBN-10 code we see printed on the back cover of some books. In ISBN-10, there are 9 decimal digits that define the country, the publisher, and the book. The tenth (rightmost) digit is a checksum digit. The code, D1D2D3D4D5D6D7D8D9C, satisfies the
An ISBN-13 code, a new version of ISBN-10, is another example of a weighted checksum with 13 digits, in which there are 12 decimal digits defining the book and the last digit is the checksum digit. The code, D1D2D3D4D5D6D7D8D9D10D11D12C, satisfies the following.In other words, the weights are 1 and
Assume we want to send a dataword of two bits using FEC based on the Hamming distance. Show how the following list of datawords/codewords can automatically correct up to a one-bit error in transmission.00 → 00000 01→ 01011 10 → 10101 11 → 11110
Using the ideas in the previous two problems, we can create a general formula for correcting any number of errors (m) in a codeword of size (n). Develop such a formula. Use the combination of n objects taking x objects at a time.
In Figure 10.22, assume we have 100 packets. We have created two sets of packets with high and low resolutions. Each high-resolution packet carries on average 700 bits. Each low-resolution packet carries on average 400 bits. How many extra bits are we sending in this scheme for the sake of FEC?
Alice and Bob are experimenting with CSMA using a W2Walsh table (see Figure 12.29). Alice uses the code [+1, +1] and Bob uses the code [+1, ˆ’1]. Assume that they simultaneously send a hexadecimal digit to each other. Alice sends (6)16and Bob sends (B)16. Show how they can detect what the
What is the purpose of NAV in CSMA/CA?
There is no acknowledgment mechanism in CSMA/CD, but we need this mechanism in CSMA/CA. Explain the reason.
We have a pure ALOHA network with a data rate of 10 Mbps. What is the maximum number of 1000-bit frames that can be successfully sent by this network?
In a wireless LAN, station A is assigned IFS = 5 milliseconds and station B is assigned IFS = 7 milliseconds. Which station has a higher priority? Explain.
Although the throughput calculation of a CSMA/CD is really involved, we can calculate the maximum throughput of a slotted CSMA/CD with the specification we described in the previous problem. We found that the average number of contention slots a station needs to wait is k = e slots. With this
Assume we have a slotted CSMA/CD network. Each station in this network uses a contention period, in which the station contends for access to the shared channel before being able to send a frame. We assume that the contention period is made of contention slots. At the beginning of each slot, the
Assume the propagation delay in a broadcast network is 12 μs and the frame transmission time is 8 μs.a. How long does it take for the first bit to reach the destination?b. How long does it take for the last bit to reach the destination after the first bit has arrived?c. How long is the network
The random variable R (Figure 12.13) is designed to give stations different delays when a collision has occurred. To alleviate the collision, we expect that different stations generate different values of R. To show the point, find the probability that the value of R is the same for two stations
Assume the propagation delay in a broadcast network is 5 μs and the frame transmission time is 10 μs.a. How long does it take for the first bit to reach the destination?b. How long does it take for the last bit to reach the destination after the first bit has arrived?c. How long is the network
In a bus 1-persistence CSMA/CD with Tp = 50 μs and Tfr = 120 μs, there are two stations, A and B. Both stations start sending frames to each other at the same time. Since the frames collide, each station tries to retransmit. Station A comes out with R = 0 and station B with R = 1. Ignore any
Explain why collision is an issue in random access protocols but not in channelization protocols.
To understand why we need to have a minimum frame size Tfr = 2 × Tp in a CDMA/CD network, assume we have a bus network with only two stations, A and B, in which Tfr = 40 μs and Tp = 25 μs. Station A starts sending a frame at time t = 0.0 μs and station B starts sending a frame at t = 23.0 μs.
Explain why collision is an issue in random access protocols but not in controlled access protocols.
There are only two stations, A and B, in a bus 1-persistence CSMA/CD network with Tp= 25.6 Î¼s and Tfr= 51.2 Î¼s. Station A has a frame to send to station B. The frame is unsuccessful two times and succeeds on the third try. Draw a time line diagram for this problem.
Assume the propagation delay in a broadcast network is 6 μs and the frame transmission time is 4 μs. Can the collision be detected no matter where it occurs?
Assume that there are only two stations, A and B, in a bus CSMA/CD network. The distance between the two stations is 2000 m and the propagation speed is 2 × 108 m/s. If station A starts transmitting at time t1:a. Does the protocol allow station B to start transmitting at time t1 + 8 μs? If the
Assume the propagation delay in a broadcast network is 3 μs and the frame transmission time is 5 μs. Can the collision be detected no matter where it occurs?
In a bus CSMA/CD network with a data rate of 10 Mbps, a collision occurs 20 μs after the first bit of the frame leaves the sending station. What should the length of the frame be so that the sender can detect the collision?
Assume the propagation delay in a broadcast network is 5 μs and the frame transmission time is 10 μs.a. How long does it take for the first bit to reach the destination?b. How long does it take for the last bit to reach the destination after the first bit has arrived?c. How long is the network
We have defined the parameter a as the number of frames that can fit the medium between two stations, or a = (Tp)/(Tfr). Another way to define this parameter is a = Lb/Fb, in which Lb is the bit length of the medium and Fb is the frame length of the medium. Show that the two definitions are
Based on Figure 12.15, how do we interpret success in an Aloha network?Figure 12.15 Station has a frame to send K= 0 Legend K: Number of attempts Tg: Backoff time IFS: Interframe Space RTS: Request to send CTS: Clear to send Channel free? [false] [true] Carrier sense Wait IFS Choose a random number
Another useful parameter in a LAN is the bit length of the medium (Lb), which defines the number of bits that the medium can hold at any time. Find the bit length of a LAN if the data rate is 100 Mbps and the medium length in meters (Lm) for a communication between two stations is 200 m. Assume the
One of the useful parameters in a LAN is the number of bits that can fit in one meter of the medium (nb/m). Find the value of nb/m if the data rate is 100 Mbps and the medium propagation speed is 2 × 108 m/s.
Based on Figure 12.3, how do we interpret success in an Aloha network?Figure 12.3 Station has Legend a frame to send K : Number of attempts Tp: Maximum propagation time Tr: Average transmission time TR: (Backoff time): R × T,or R × Tfr R : (Random number): 0 to 2K – 1 K = 0 Send the Wait TB
A slotted Aloha network is working with maximum throughput.a. What is the probability that a slot is empty?b. How many slots, n, on average, should pass before getting an empty slot?
To understand the uses of K in Figure 12.15, find the probability that a station can send immediately in each of the following cases:Figure 12.15a. After two failures.b. After five failures. Station has a frame to send K= 0 Legend K: Number of attempts Tg: Backoff time IFS: Interframe Space RTS:
There are only three active stations in a slotted Aloha network: A, B, and C. Each station generates a frame in a time slot with the corresponding probabilities pA = 0.2, pB = 0.3, and pC = 0.4 respectively.a. What is the probability that any station can send a frame in the first slot?b. What is
To understand the uses of K in Figure 12.13, find the probability that a station can send immediately in each of the following cases:Figure 12.13a. After one failure.b. After four failures. Station has a frame to send K = 0 Legend Tip: Frame average transmission time K : Number of attempts R :
There are only three active stations in a slotted Aloha network: A, B, and C. Each station generates a frame in a time slot with the corresponding probabilities pA = 0.2, pB = 0.3, and pC = 0.4 respectively.a. What is the throughput of each station?b. What is the throughput of the network?
To understand the uses of K in Figure 12.3, find the probability that a station can send immediately in each of the following cases:Figure 12.3a. After one failure.b. After three failures. Station has Legend a frame to send K : Number of attempts Tp: Maximum propagation time Tr: Average
In the previous problem, we found the throughputs of a pure and a slotted Aloha network as S = Np (1−p)2(N−1) and S = Np (1−p)(N−1) respectively. In this problem we want to find the maximum throughput with respect to p.a. Find the value of p that maximizes the throughput of a pure Aloha
In a slotted Aloha network with G = 1/2, how is the throughput affected in each of the following cases?a. G is increased to 1.b. G is decreased to 1/4.
In the previous problem, we found the probability of success for a station to send a frame successfully during the vulnerable time. The throughput of a network with a limited number of stations is the probability that any station (out of N stations) can send a frame successfully. In other words,
In a pure Aloha network with G = 1/2, how is the throughput affected in each of the following cases?a. G is increased to 1.b. G is decreased to 1/4.
A multiple access network with a large number of stations can be analyzed using the Poisson distribution. When there is a limited number of stations in a network, we need to use another approach for this analysis. In a network with N stations, we assume that each station has a frame to send during
Stations in an slotted Aloha network send frames of size 1000 bits at the rate of 1 Mbps. What is the vulnerable time for this network?
In the previous problem, we showed that the throughput is S = Ge−2G for a pure Aloha network and S = Ge−G for a slotted Aloha network. In this problem, we want to find the value of G in each network that makes the throughput maximum and find the value of the maximum throughput. This can be done
Stations in a pure Aloha network send frames of size 1000 bits at the rate of 1 Mbps. What is the vulnerable time for this network?
In the previous problem, we found that the probability of a station (in a G-station network) successfully sending a frame in a vulnerable time is P = e−2G for a pure Aloha and P = e−G for a slotted Aloha network. In this problem, we want to find the throughput of these networks, which is the
Which of the following is a channelization protocol?a. ALOHAb. Token-passingc. CDMA
In the previous problem, we used the Poisson distribution to find the probability of generating x number of frames, in a certain period of time, in a pure or slotted Aloha network as p[x] = (e−λ × λx)/(x!). In this problem, we want to find the probability that a frame in such a network reaches
Which of the following is a controlled-access protocol?a. Token-passingb. Pollingc. FDMA
To formulate the performance of a multiple-access network, we need a mathematical model. When the number of stations in a network is very large, the Poisson distribution, p[x] = (e−λ × λx)/(x!), is used. In this formula, p[x] is the probability of generating x number of frames in a period of
Which of the following is a random-access protocol?a. CSMA/CDb. Pollingc. TDMA

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