How Much Wayback for CaP?

How much data do you need to retain for meaningful capacity planning and performance analysis purposes? Sounds like one of those "how long is a piece of string?" questions and I've never really thought about it in any formal way, but it occurred to me that 5 years is not an unreasonable archival period.

Mister Peabody and Sherman in front of the WABAC machine
My reasoning goes like this:

Subjugation to the Sigmas

No doubt you've heard about the tyranny of the 9s in reference to computer system availability. You're probably also familiar with the phrase six sigma, either in the context of manufacturing process quality control or the improvement of business processes. As we discovered in the recent Guerrilla Data Analysis Techniques class, the two concepts are related.

Nines	Percent	Downtime/Year	σ Level
4	99.99%	52.596 minutes	4σ
5	99.999%	5.2596 minutes	-
6	99.9999%	31.5576 seconds	5σ
7	99.99999%	3.15576 seconds	-
8	99.999999%	315.6 milliseconds	6σ

In this way, people like to talk about achieving "5 nines" availability or a "six sigma" quality level. These phrases are often bandied about without appreciating:

IBM Introduces the Cognitive Chip

Last week, in the GDAT class, we were discussing performance visualization tools as requiring a good impedance match between the digital computer under analysis and the cognitive computer of the analyst—AKA the brain.

GDAT 2011 in Review

As usual, the Guerrilla Data Analysis Techniques (GDAT) class was a total blast. Motivated students always guarantee that. It would really help our scheduling, however, if people didn't wait until the last nanosecond to register for the class. But given the crazy economic climate, I'm more than happy to do whatever it takes to make GDAT fly.

Guerrillas in the data mist [Photo: P. Newsom]

Some course highlights that you missed:

Q-Q Plots and Power Laws in Database Performance Data

I'm in the process of putting together some slides on how to apply Quantile-Quantile plots to performance data. Q-Q plots are a handy tool for visually inspecting how well your data matches a known probability distribution (prob dsn). If the match is good, the data should line up more or less diagonally in the Q-Q plot. A common usage is to verify normality, i.e. how well the data matches a Normal or Gaussian dsn. In fact, this usage is so common that R even has a separate function called qqnorm() for doing just that.

The Multiserver Numbers Game

In a previous post, I explained why \begin{equation} R_m \neq \dfrac{R_1}{m} \label{eqn:badest} \end{equation} and therefore doesn't work as an estimator of the mean residence time in an M/M/m multi-server queue. Although we expect the extra server capacity with m-servers to produce a shorter residence time ($R_m$), it is not m-times smaller than the residence time ($R_1$) for a single-server (i.e., $m = 1$) queue.

M/M/m multiserver queue

The problem is that eqn. \eqref{eqn:badest} grossly underestimates $R_m$, which is precisely the wrong direction for capacity planning scenarios. For that purpose, it's generally better to overestimate performance metrics. That's too bad because it would be a handy Guerrilla-style formula if it did work. You would be able do the calculation in your head and impress everyone on your team (not to mention performing it as a party trick).

Given that eqn. \eqref{eqn:badest} is a poor estimator, you might wonder if there's a better one, and if you'd been working for Thomas Edison he would have told you: "There's a better wsy. Find it!" Easy for him to say. But if you did decide to take up Edison's challenge, how would you even begin to search for such a thing?

Little's Lore

Guerrilla alumnus Paul P. has a penchant for sending me interesting things, and recently he sent me a piece on Little's law. Remarkably, it wasn't just another proof of L = λW, but a brief retrospective written by none other than John Little himself. I quote it here because it not only provides some unusual insight into how these things get done, but it is written in a charming and self-effacing style.