Commit f75c9bb7 authored by Robert Ricci's avatar Robert Ricci

Finish lecture notes for Lecture 16

parent 7133799e
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\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,
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\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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\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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\2 Fat-tailed: usually in reference to normal
\2 Long-tailed: 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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\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{examples?}
\2 \emph{Examples?}
\1 Pareto
\2 Produces IID inter-arrival times
\2 Discrete equivalent is Zipf
\2 XXX: TODO
\1 Self-similarity
\2 XXX: TODO
\1 For next time: Read papers
\2 Power law: few account for the largest portion - eg. ``the 99%''
\2 Self-similar: 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 heavy-tailed 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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