You are employed as a network engineer and have been asked to analyze a communication network to determine the current data rates and ensure that the links aren't at risk of "reaching capacity." In the following figure of the network, the sender is transmitting data at a total rate of 100+50= 150 megabits per second (Mbps). The data is transmitted from the sender to the receiver over a network of five different routers. These routers are labeled A, B, C, D, and E. The connections and data rates between the routers are labeled as x1, x2, X3, x4, and x5. B (()) Sender 100 50 A X₂ ° ()), X3 X₂ X₁ E (()). X5 X5 X₂ •D ((cp)), X₂ 120 Receiver Directions In this project, you will analyze the communication network and solve for the unknown data rates using a variety of techniques. The system can be modeled mathematically as a system of linear equations by writing an equation for each node/router in the network. Each of these equations can be written by noting that the sum of inputs must equal the sum of outputs. To complete the project, work on the problems described below. As you complete each part, show your work and carefully describe how you arrive at your final answer. The methods and conclusions need to be clear when sharing your results with management. Any MATLAB code or MATLAB terminal outputs you generate should be provided in your submitted document to support your answers and work. 1. Develop a system of linear equations for the network by writing an equation for each router (A, B, C, D, and E). Make sure to write your final answer as Ax = b where A is the 5 x 5 coefficient matrix, x is the 5 x 1 vector of unknowns, and b is a 5 x 1 vector of constants. 2 Use MATLAB to construct the augmented matrix! A bland then perform row reduction using the rref() function Write out your reduced
You are employed as a network engineer and have been asked to analyze a communication network to determine the current data rates and ensure that the links aren't at risk of "reaching capacity." In the following figure of the network, the sender is transmitting data at a total rate of 100+50= 150 megabits per second (Mbps). The data is transmitted from the sender to the receiver over a network of five different routers. These routers are labeled A, B, C, D, and E. The connections and data rates between the routers are labeled as x1, x2, X3, x4, and x5. B (()) Sender 100 50 A X₂ ° ()), X3 X₂ X₁ E (()). X5 X5 X₂ •D ((cp)), X₂ 120 Receiver Directions In this project, you will analyze the communication network and solve for the unknown data rates using a variety of techniques. The system can be modeled mathematically as a system of linear equations by writing an equation for each node/router in the network. Each of these equations can be written by noting that the sum of inputs must equal the sum of outputs. To complete the project, work on the problems described below. As you complete each part, show your work and carefully describe how you arrive at your final answer. The methods and conclusions need to be clear when sharing your results with management. Any MATLAB code or MATLAB terminal outputs you generate should be provided in your submitted document to support your answers and work. 1. Develop a system of linear equations for the network by writing an equation for each router (A, B, C, D, and E). Make sure to write your final answer as Ax = b where A is the 5 x 5 coefficient matrix, x is the 5 x 1 vector of unknowns, and b is a 5 x 1 vector of constants. 2 Use MATLAB to construct the augmented matrix! A bland then perform row reduction using the rref() function Write out your reduced
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Question
![You are employed as a network engineer and have been asked to analyze a communication network to determine the current data rates and
ensure that the links aren't at risk of "reaching capacity." In the following figure of the network, the sender is transmitting data at a total rate of
100+50 = 150 megabits per second (Mbps). The data is transmitted from the sender to the receiver over a network of five different routers.
These routers are labeled A, B, C, D, and E. The connections and data rates between the routers are labeled as x1, x2, X3, x4, and x5.
B (())
Sender
100
50
A
X₂
c (()),
X3
X₂
X₁
E (()).
X5
X5
X₂
X₂
•D ((cp)), 120
Receiver
Directions
In this project, you will analyze the communication network and solve for the unknown data rates using a variety of techniques. The system
can be modeled mathematically as a system of linear equations by writing an equation for each node/router in the network. Each of these
equations can be written by noting that the sum of inputs must equal the sum of outputs.
To complete the project, work on the problems described below. As you complete each part, show your work and carefully describe how you
arrive at your final answer. The methods and conclusions need to be clear when sharing your results with management. Any MATLAB code or
MATLAB terminal outputs you generate should be provided in your submitted document to support your answers and work.
1. Develop a system of linear equations for the network by writing an equation for each router (A, B, C, D, and E). Make sure to write your
final answer as Ax = b where A is the 5 x 5 coefficient matrix, x is the 5 x 1 vector of unknowns, and b is a 5 × 1 vector of constants.
2. Use MATLAB to construct the augmented matrix [A b] and then perform row reduction using the rref() function. Write out your reduced
matrix and identify the free and basic variables of the system.
3. Use MATLAB to compute the LU decomposition of A, i.e., find A = LU. For this decomposition, find the transformed set of equations
Ly = b. Solve the system of equations Ly = b for the unknown vector y.
4. Use MATLAB to compute the inverse of using the inv() function.
5. Compute the solution to the original system of equations by transforming y into x, i.e., compute x = U-¹y.
6. Check your answer for 1 using Cramer's Rule.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1120ccc1-7cdf-42e0-b411-8eb1bbbfa3eb%2Fb56bea09-9890-4417-ade5-3e547e3536d0%2Fjmd3g6_processed.png&w=3840&q=75)
Transcribed Image Text:You are employed as a network engineer and have been asked to analyze a communication network to determine the current data rates and
ensure that the links aren't at risk of "reaching capacity." In the following figure of the network, the sender is transmitting data at a total rate of
100+50 = 150 megabits per second (Mbps). The data is transmitted from the sender to the receiver over a network of five different routers.
These routers are labeled A, B, C, D, and E. The connections and data rates between the routers are labeled as x1, x2, X3, x4, and x5.
B (())
Sender
100
50
A
X₂
c (()),
X3
X₂
X₁
E (()).
X5
X5
X₂
X₂
•D ((cp)), 120
Receiver
Directions
In this project, you will analyze the communication network and solve for the unknown data rates using a variety of techniques. The system
can be modeled mathematically as a system of linear equations by writing an equation for each node/router in the network. Each of these
equations can be written by noting that the sum of inputs must equal the sum of outputs.
To complete the project, work on the problems described below. As you complete each part, show your work and carefully describe how you
arrive at your final answer. The methods and conclusions need to be clear when sharing your results with management. Any MATLAB code or
MATLAB terminal outputs you generate should be provided in your submitted document to support your answers and work.
1. Develop a system of linear equations for the network by writing an equation for each router (A, B, C, D, and E). Make sure to write your
final answer as Ax = b where A is the 5 x 5 coefficient matrix, x is the 5 x 1 vector of unknowns, and b is a 5 × 1 vector of constants.
2. Use MATLAB to construct the augmented matrix [A b] and then perform row reduction using the rref() function. Write out your reduced
matrix and identify the free and basic variables of the system.
3. Use MATLAB to compute the LU decomposition of A, i.e., find A = LU. For this decomposition, find the transformed set of equations
Ly = b. Solve the system of equations Ly = b for the unknown vector y.
4. Use MATLAB to compute the inverse of using the inv() function.
5. Compute the solution to the original system of equations by transforming y into x, i.e., compute x = U-¹y.
6. Check your answer for 1 using Cramer's Rule.
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Follow-up Question
based on the diagram above: Router A is transmitting X2 Two times, and only transmitting X1 once. Would that make the equation for Router A : X1 + 2X2= 100? instead of 2X1 +X2 + 100?
Transcribed Image Text:Sender
100
50
A
с
((cp))
²
X₂
X₁
X₂
B (())
2
・D (()),
X
120
Receiver
Solution
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