The purpose of models is not to fit the data but to sharpen the questions. My original 1993 paper introduced the USL under the name “regression analysis term papers serial” model because, at that time, I viewed it as an extension of the serial fraction concept contained in Amdahl’s law.
The idea of applying it as a statistical regression model and extending it to three parameters came much later. The original derivation of the Universal Scalability Law, or USL, was presented at the 1993 CMG conference . 6 and 14 of my first book . A more complete derivation with example applications is presented in Chaps.
Computer system scalability must be quantified. If you can’t quantify it, you can’t guarantee it. The universal law of computational scaling provides that quantification. Every queueing facility in a performance model requires a service time as an input parameter.
Without the appropriate queues in the model, system performance metrics like throughtput and response time, cannot be predicted. The USL leapfrogs this entire problem by NOT requiring ANY low-level service time measurements as inputs. Each of these contributions can be combined into an equation that represents a scalability model, viz. The reasoning behind this modification can be found in my blog post . The applied load might be induced either by N virtual users e. The three coefficients, α, β, γ, in eqn. In this case, the number of users acts as the independent variable while the processor configuration remains fixed over the range of user-load measurements.
NOTE: The objective of using eqn. NOT to produce a curve that passes through every data point. That’s called curve fitting and that’s what graphics artists do with splines. As von Neumann said, “Give me 4 parameters and I’ll fit an elephant.
Give me 5 and I’ll make its trunk wiggle! Notice that the γ parameter plays no role in eqn. That’s because it locates the position of the maximum in the USL curve on the x-axis, whereas γ scales the y-axis values. The corresponding maximum throughput Xmax is found by substituting Nmax into eqn. 0, which means that Nmax occurs at infinity. See Chapter 6 Software Scalability in the GCAP book. The USL is equivalent to the synchronous queueing bound on throughput for a linear load-dependent machine repairman model of a multiprocessor.
The proof can be found in . Both Amdahl’s law and the USL belong to a class of mathematical functions called Rational Functions. Moreover, these theorems have also been confirmed experimentally using event-driven simulations . In other words, the whole USL approach to quantifying scalability rests on a fundamentally sound physical footing. Modeling disk arrays, SANs, and multicore processors. Accounts for such effects as memory thrashing, and cache-miss latencies. It cannot foretell the onset of broken measurements or intrinsic pathologies.