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MATH233 Unit 1 Individual Project
NAME (Required):
To communicate most effectively, network administrators attempt to maximize
bandwidth and throughput speeds to achieve high data transmission rates within the
buildingโs CAT5e cables. These performance data transfer rates are given in multiples of
unit bits per second (bps). In the table below, the schoolโs 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 ๐ฆ
Gigabits (Gb) of data in ๐ฅ 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.
1. Research and define the concepts of maximum theoretical throughput, channel
capacity, and bandwidth. Next, explain the similarities and differences between
CAT5e and CAT6 Ethernet cables. What specific speeds can each of these cables
handle? Listing credible cited resources, please answer these below.
2. In the table below, based on the first letter of your last name (mine starts with a
โNโ), please select one number from each of the ranges in the x and y columns.
Table A: Estimates of bit-transmissions and times
๐ฅ
๐ฆ
Seconds
2 to 3.99
4 to 7.99
8 to 15.99
16 to 31.99
32 to 63.99
64 to 79.99
Gigabits (Gb)
2 to 3.99
4 to 7.99
8 to 15.99
16 to 31.99
32 to 63.99
64 to 79.99
First Letter of Your
Last Name
AโD
EโH
IโL
MโP
QโT
UโZ
Given that the throughput is the tableโs Gigabits per seconds (Gbps), calculate and
record this transfer rate for your chosen values with the formula:
๐๐ก๐ซ๐จ๐ฎ๐ ๐ก๐ฉ๐ฎ๐ญ =
๐ ๐๐ข๐ ๐๐๐ข๐ญ๐ฌ
๐ ๐๐๐๐จ๐ง๐๐ฌ
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3. Your schoolโs CAT5e network has a maximum bandwidth of 1 Gbps. Does your answer
from above exceed that or not? Based strictly on your value, do you think the maximum
bandwidth should be raised? If you think the network needs to be upgraded, will the network
infrastructure need to be upgraded to support CAT6 cables? How did you arrive at this
conclusion? Include the factors that influenced your decision.
NOTE: The questions below do not specifically use the calculations in questions #2.
4. It has been found that the schoolโs network throughput speed R(t) in Gbps, with respect to
time in seconds, is best modeled with the rational function:
๐๐๐ + ๐
๐น(๐) = ๐
๐ + ๐๐
Generate a graph of this function using Excel or another graphing utility. (There are
free downloadable programs like Graph 4.4.2 or Mathematics 4.0; or, there are also
online utilities such as this site and many others.) Insert the graph into the Word
document containing your answers and work details. Be sure to label and number the
axes appropriately.
5. Peak Measured Throughput (PT): Peak or instantaneous throughputs (PT)
measure values useful for systems that rely on bursts of data in a CAT5e cable.
Unlike continuous streaming, information travels in short bursts. For example,
during in-class demonstrations, a computer labโs user experiences high traffic usage
spikes on a very high-bandwidth that is transmitted over a relatively short period of
time. Activity is important during these in-use peak times. Peak rates are measured
limits taken with respect to throughput as time approaches zero. So for the above
function, use algebraic techniques and limit theorems to show the work details for
calculating the following limit:
๐๐ = ๐ฅ๐ข๐ฆ+ ๐น(๐) = ๐ฅ๐ข๐ฆ+
๐โ๐
๐โ๐
๐๐๐ + ๐
๐๐ + ๐๐
Based strictly on this result, do you think your school should raise its current
networkโs bandwidth of 1 Gbps? How did you arrive at this conclusion?
6.
Maximum Sustained Throughput (ST): One of the most accurate indicators of
system performance for high duty cycle networks is the maximum sustained
throughput (ST) averaged over a long period of time. This value measures the
network capacity fully utilized over its entire existence. Essentially, high volumes of
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continuously streamed transmissions max out the amounts of data being transferred
in because the network is busy processing current data and unable to efficiently enter
the cable. This builds up the delivery time causing latency instabilities. In this case,
sustained rates are measured limits taken with respect to throughput as time
increases towards infinity. So for the above function, use algebraic techniques and
limit theorems to show the work details for calculating the following limit:
๐๐๐ + ๐
๐โโ ๐๐ + ๐๐
๐๐ = ๐ฅ๐ข๐ฆ ๐(๐ญ) = ๐ฅ๐ข๐ฆ
๐ญโโ
Based strictly on this result, do you think your school should raise its current
networkโs bandwidth of 1 Gbps? How did you arrive at this conclusion?
References
Desmos. (n.d.). Retrieved from https://www.desmos.com/
Graph 4.4.2. (n.d.). Retrieved from the Graph Web site: http://www.padowan.dk/
Mathematics 4.0. (n.d.). Retrieved from the Microsoft Web site: http://microsoftmathematics.en.uptodown.com/
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