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MATH 233 Unit 1 Individual Project

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MATH 233 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
y Gigabits (Gb) of data in x 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 difference 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, please select one
number from each of the ranges in the x and y columns.
Table A: Estimates of bit-transmissions and times
x y Seconds Gigabits (Gb) A–D 2 to 3.99 2 to 3.99 E–H 4 to 7.99 4 to 7.99 I–L 8 to 15.99 8 to 15.99 M–P 16 to 31.99 16 to 31.99 First Letter of Your
last Name Page 1 of 3 Q–T 32 to 63.99 32 to 63.99 U–Z 64 to 79.99 64 to 79.99 Given that the throughput is the table’s Gigabits per seconds (Gbps), calculate and
record this transfer rate for your chosen values with the formula:
Throughput= y Gigabits
x Seconds 3. Your school’s maximum network bandwidth is 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? 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. 4. According to your research, the school’s throughput speed R(t) in Gbps, with respect to time
in seconds, is best modeled with the rational function: R (t)= t 2+ t
2
t + 2t 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 lab’s 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 to find: Page 2 of 3 PT=lim R(t)
t→0 Based strictly on this result, do you think your school should raise its current
network’s 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 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 to find the following:
ST =lim R(t)
t→∞ Based strictly on this result, do you think your school should raise its current
network’s bandwidth of 1 Gbps? How did you arrive at this conclusion? 7. Based on all of your previous results, do you think your school should raise its current
network’s 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/ Page 3 of 3