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Robert Ricci
Evaluating Networked Systems
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f75c9bb7
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f75c9bb7
authored
Mar 25, 2014
by
Robert Ricci
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Finish lecture notes for Lecture 16
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lectures/lecture16/lecturenotes.tex
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f75c9bb7
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@@ 21,8 +21,9 @@
\begin{outline}
\1
From last time
\2
How is the
\2
Thanks to Junguk and Makito for the scripts!
\2
Quick status: client, server, network conditions, client request
sizes, analysis
\1
Today: Talking about different prob distributions
\2
You many run into the need to generate data in these distributions,
...
...
@@ 64,6 +65,19 @@
\2
Mean:
$
\frac
{
pr
}{
1

p
}$
\2
\emph
{
What might you model with it?
}
\1
Poisson
\2
``The probability of a given number of events occurring in a fixed
interval of time and/or space if these events occur with a known
average rate and independently of the time since the last event''
\2
Produces a number of arrivals in a given time
\2
Particularly good if the sources are independent
\2
Parameter is mean (
$
\lambda
$
)
\2
Very often used for arrivals: eg. arrival of packets at a queue or
requests at a server
\2
Can be used over particular intervals of time; eg. daytime, to keep
the iid assumption
\2
\emph
{
Examples?
}
\1
Continuous distributions
\1
Uniform: All possibilities equally likely
...
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@@ 73,7 +87,7 @@
\2
Usually generated, not measured
\1
Exponential
\2
XXX More
\2
Models length of time between arrivals (compare to Poisson)
\2
Parameter
$
\lambda
$
 inverse of mean
\3
Sometimes called rate, eg. time between arrivals
\2
Memoryless: eg. time between arrivals
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...
@@ 87,7 +101,6 @@
\2
Fattailed: usually in reference to normal
\2
Longtailed: usually in reference to exponential
\2
Means ``unlikely'' things are actually more common than one might expect
\2
80/20 rule
\2
Long tail means ``light'' somewhere else
\1
Normal
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@@ 98,16 +111,30 @@
\2
Logarithms turn multiplication into addition:
$
\log
xy
=
\log
x
+
\log
y
$
\2
So, lognormal is like normal, but for products of idd variables
\2
Useful for things that accumulate by multiplication, for example errors
\2
\emph
{
e
xamples?
}
\2
\emph
{
E
xamples?
}
\1
Pareto
\2
Produces IID interarrival times
\2
Discrete equivalent is Zipf
\2
XXX: TODO
\1
Selfsimilarity
\2
XXX: TODO
\1
For next time: Read papers
\2
Power law: few account for the largest portion  eg. ``the 99
%''
\2
Selfsimilar: the same at different scales (think fractal)
\2
``Bursty on many or all time scales''
\2
Values correlated with future incidents
\2
Compare to other distributions
\ldots
eg Poisson
\2
Can be constructed with heavytailed ON/OFF sources
\2
Has either no mean or infinite variance
\1
Weibull
\2
Good for monitoring mean time to failure
\2
Parameters are scal (
$
\lambda
$
) and shape (
$
k
$
)
\2
``A value of k < 1 indicates that the failure rate decreases over time''
\2
``A value of k = 1 indicates that the failure rate is constant over time.''
\2
``A value of k > 1 indicates that the failure rate increases with time.''
\1
For next time:
\2
Read papers for Analysis 3
\2
Posted one reading for next Thursday
\2
Lab due a week from today
\end{outline}
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