Finish lecture notes for Lecture 16

lectures/lecture16/lecturenotes.tex

@@ -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
@@ -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
@@ -87,7 +101,6 @@
     \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
@@ -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{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}