Hotsos 2013: Superlinear Scalability

As readers of this blog know, the Universal Scalability Law (USL) is a framework for quantifying performance measurements and extrapolating load-test data. Applied as a statistical regression model, the two USL contention (α) and coherency (β) parameters numerically indicate the degree of sublinear scalability in the data, i.e., how much linear scaling you're losing due to sharing and consistency overheads. Some examples of USL scalability analysis applied to databases, include:

• VoltDB
• Postgres
• My USL analysis of the Postgres data

More recently, it was brought to my attention that the USL fails when it comes to modeling superlinear performance (e.g., see this Comments section). Superlinear scalability means you get more throughput than the available capacity would be expected to support. It's even discussed on the Wikipedia (so it must be true, right?). Nice stuff, if you can get it. But it also smacks of an effect like perpetual motion.

Every so often, you see a news report about someone discovering (again) how to beat the law of conservation of energy. They will swear up and down that it works and it will be accompanied by a contraption that proves it works. Seeing is believing, after all. The hard part is not whether to believe their claim, it's debugging their contraption to find the mistake that has led them to the wrong conclusion.

Similarly with superlinearity. Some data are just plain spurious. In other cases, however, certain superlinear measurements do appear to be correct, in that they are repeatable and not easily explained away. In that case, it was assumed that the USL needed to be corrected to accommodate superlinearity by introducing a third modeling parameter. This is bad news for many reasons, but primarily because it would weaken the universality of the universal scalability law.

To my great surprise, however, I eventually discovered that the USL can accommodate superlinear data without any modification to the equation. As an unexpected benefit, the USL also warns you that you're modeling an unphysical effect: like a perpetual-motion detector. A corollary of this new analysis is the existence of a payback penalty for incurring superlinear scalability. You can think of this as a mathematical statement of the old adage: If it looks too good to be true, it probably is.

I'll demonstrate this remarkable result with examples in my Hotsos presentation.