The Geometry of Latency

... AKA hyperbolae.

Here's a mnemonic tabulation based on dishes and bowls:

Hopefully this makes amends for the more complicated explanation I wrote for CMG back in 2009 entitled: "Mind Your Knees and Queues: Responding to Hyperbole with Hyperbolæ", which I'm pretty sure almost nobody understood.

WTF is Modeling, Anyway?

A conversation with performance and capacity management veteran Boris Zibitsker, on his BEZnext channel, about how to save multiple millions of dollars with a one-line performance model (at 21:50 minutes into the video) that has less than 5% error. I wish my PDQ models were that good. :/

The strength of the model turns out to be its explanatory power, rather than prediction, per se. However, with the correct explanation of the performance problem in hand (which also proved that all other guesses were wrong), this model correctly predicted a 300% reduction in application response time for essentially no cost. Modeling doesn't get much better than this.

Footnotes

1. According to Computer World in 1999, a 32-node IBM SP2 cost $2 million to lease over 3 years. This SP2 cluster was about 6 times bigger.
2. Because of my vain attempt to suppress details (in the interests of video length), Boris gets confused about the kind of files that are causing the performance problem (near 26:30 minutes). They're not regular data files and they're not executable files. The executable is already running but sometimes waits—for a long time. The question is, waits for what? They are, in fact, special font files that are requested by the X-windows application (the client, in X parlance). These remote files may also get cached, so it's complicated. In my GCAP class, I have more time to go into this level of detail. Despite all these potential complications, my 'log model' accurately predicts the mean application launch time.
3. Log_2 assumes a binary tree organization of font files whereas, Log_10 assumes a denary tree.
4. Question for the astute viewer. Since these geophysics applications were all developed in-house, how come the developers never saw the performance problems before they ever got into production? Here's a hint.
5. Some ppl have asked why there's no video of me. This was the first time Boris had recorded video of a Skype session and he pushed the wrong button (or something). It's prolly better this way. :P

Bandwidth vs. Latency — The World is Curved

Despite what you may have read in the press lately, neither our world nor the world of performance is flat. This is especially true of the performance metrics commonly known as bandwidth (or throughput) and latency. The performance relationship between these two metrics is curved or nonlinear. In general, this nonlinearity is a consequence of these two metrics being inversely related to each another: increase system throughput to decrease the latency of each request, and vice versa. A common misconception persists, however, that bandwidth and latency are independent performance metrics. I'm going to call that view the Flat-Earth view. Where does that view come from?

Window on the World

In part, it depends on your window to the world. When we look out a window, the Earth looks flat.

Occasionally, we are reminded that the Earth is actually curved. That's something most of us accept and expect, even if we're not aware of it all of the time.

Bandwidth and Latency are Related Like Overclocked Chocolates

Prior to the appearance of special relativity theory (SRT) in 1905, physicists were under the impression that space and time are completely independent aspects of reality described by Newton's equations of motion. Einstein's great insight, that led to SRT, was that space and time are intimately related through the properties of light.

Space and time are related

Instead of objects simply being located at some arbitrary position x at some arbitrary time t, everything moves on a world-line given by the space-time pair (x, ct), where c is the universal speed of light. Notice that x has the engineering dimensions of length and so does the new variable ct: a speed multiplied by time. In Einstein's picture, everything is a length; there is no separate time metric. Time is now part of what has become known as space-time—because nobody came up with a better word.

Plotting PDQ Output with R

One the nice things about PDQ-R (coming in release 5.0) is the ability to plot PDQ output directly in R. Here's a PDQ-R script, together with the corresponding graphical output, that I knocked up to show the effect on the throughput curve of adding more queueing delay stages (K), with everything else held constant.