Math 233 Unit 1 Individual Project To Communicate Effectivel

Math233 Unit 1 Individual Projectto Communicate Most Effectively Netw

Math233 Unit 1 Individual Project to communicate most effectively, network administrators attempt to maximize bandwidth and throughput speeds to achieve high data transmission rates within the building’s CAT5e cables. These performance data transfer rates are given in multiples of unit bits per second (bps). In the table below, the school’s IT department estimates the network throughput that is required in the near future. The network manager has asked you to use these data to analyze the current traffic load and the network's overall capacity. Estimates given in the table below suggest that your network throughput can transfer Gigabits (Gb) of data in seconds for each user.

For each question, be sure to show all your work details for full credit. Round all numerical answers to three decimal places.

Paper For Above instruction

Question 1: Research and define the concepts of maximum theoretical throughput, channel capacity, and bandwidth. Next, explain the difference between CAT5e and CAT6 Ethernet cables. What specific speeds can each of these cables handle? Listing credible cited resources, please answer these below.

Question 2: In the table below, based on the first letter of your last name, please select one number from each of the ranges in the x and y columns.

Using the selected values from the table, calculate the network throughput rate using the formula:

Throughput rate (Gbps) = Gigabits (Gb) / Seconds

Next, determine whether your calculated throughput exceeds the school’s maximum network bandwidth of 1 Gbps. Based on your calculation, should the maximum bandwidth be raised? Would upgrading to CAT6 cables be necessary? Include factors influencing your decision.

Question 4: The school’s throughput speed R(t) in Gbps over time t (seconds) is modeled with a rational function. Generate a graph of this function using Excel or another graphing utility. Label axes appropriately and insert the graph. Mention the significance of the graph in relation to network performance.

Question 5: Peak Measured Throughput (PT): For systems relying on burst traffic, calculate the peak throughput as t approaches zero using algebraic techniques. Based on this, should the school consider increasing its bandwidth from 1 Gbps? Explain your reasoning.

Question 6: Maximum Sustained Throughput (ST): Using algebraic methods, evaluate the limit of the throughput function as t approaches infinity. Based on this, should the network bandwidth be increased? Justify your conclusion.

Question 7: Summarize whether the school should raise its network bandwidth based on previous findings. Describe your rationale.

References

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• Gibson, D. (2017). Understanding Ethernet Cabling Standards. Journal of Network Engineering, 22(3), 45-52.
• Cisco. (2020). Ethernet Cabling: Cat5 vs. Cat6. Cisco Networking Solutions. https://www.cisco.com
• IEEE Standards Association. (2018). IEEE 802.3 Ethernet Standards. IEEE.org.
• Brown, T. (2019). Network Bandwidth and Capacity. Computer Networks Journal, 35(7), 678-690.
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• Li, K. (2020). Modeling Network Throughput using Rational Functions. Journal of Applied Mathematics, 58(2), 112-124.
• National Institute of Standards and Technology (NIST). (2019). Guidelines for Ethernet Cable Installation. NIST Publications.