The article revisits scalability laws to refine system throughput modeling practices. Amdahl's Law, Gustafson's Law, and the Universal Scalability Law are critically analyzed: considering their individual merits and limitations in capturing the essence of system scalability. With theoretical insights and empirical data, this research provides practical guidelines for selecting the most suitable scalability model to ensure accurate and effective modeling of system throughput in diverse computing environments.
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So, what are the scalability laws? Unfortunately, in terms of combining computational
power, 1 + 1 does not equal 2. It could be some sort of cost-effective for batch work, but this
combination was not effective for OLTP (Online transaction processing) and other real-time
computations.[
Gene Amdahl made an early attempt to quantify the speedup factor – a number that
shows how much additional performance a system will get by adding more computational
units to that system to battle the increasing load.[
Neil Gunther proposed a slightly different approach to scalability quantification. His model not only uses the serial penalty but also introduces a coherence or crosstalk penalty which results in delays for data to become consistent during the execution for multiprocessor environments. Gunther’s Law later became known as the Universal Scalability Law. It can be described as follows: →∞ lim ( ) =
1 1 − (2) (3) where N – number of computational units, - fraction between 0 and 1 represents a serial penalty in the workload, - a fraction between 0 and 1, represents a coherence penalty in the workload. maximum throughput increase.
In application throughput modeling N can represent the number of active users for
If =0, then equation (3) simplifies to the well-known Amdahl’s Law[
In terms of capacity planning, [7] USL has a sufficient number of parameters for predicting the effects of concurrency, contention, and coherency delay, but it can’t be super precise because the scalability of any particular system should be considered in light of many factors simultaneously.
Another approach was proposed by Dr. John Gustafson to overcome the pessimistic results of Amdahl’s Law speedup dependence from a serial delay as described in (2). Instead of fixing the parallelizable part of the workload, it fixes the running time.[8] In other words, it answers the following question: How much of the execution time would this problem have taken if it ran on a serial processor instead of a multicore or multiprocessor system?[9] Gustafson’s observations show more generally that the serial fraction of the workload does not theoretically limit parallel speed enhancement. Algebraically it can be described as follows: ( ) = − ( − 1), (4) (5) where S – scaled speedup over N number of computational units, - a fraction between 0 and 1 representing the serial part of the workload.
Later, [10] J. Gustafson summarized his work: “The model is not a contradiction of Amdahl's law as some have stated, but an observation that Amdahl's assumptions don't match the way people use parallel processors. People scale their problems to match the power available, in contrast to Amdahl's assumption that the problem is always the same no matter how capable the computer.”
Figure 4 shows how parallel processing can reduce the execution time.
Even after Gustafson’s Law provided a more optimistic perspective on parallel computing compared to Amdahl’s Law it omits the complexities of modern software design and can poorly predict scaled speedup for algorithms with nonlinear runtimes.[11]
After careful analysis of the three proposed laws in this article, the authors advise using the Universal Scalability Law for scalability predictions of real-world systems. Because neither Amdahl’s Law nor Gustafson-Barsis Law takes into account the coherence penalty that is almost inevitable in today’s multicore and multiprocessor world and, at the same time, the most significant part of the USL equation that will kick diminishing returns early on for throughput scaling that can lead to overall performance degradation.
To achieve better results in throughput modeling using USL, try to use measurement data for throughput and concurrency obtained from stable workloads. USL works best for constant workloads with no variability. Still, the authors admit that obtaining such measurements can sometimes be unrealistic because of the significant complexities in the design and function of real-world applications.
All three models can model the capacity of the system throughput. Amdahl’s Law provides a straightforward way to estimate the maximum achievable throughput by considering the proportion of the workload that can be parallelized but completely ignores parallel crosstalk which is inevitable in modern applications.
Gustafson’s Law recognizes the potential for adjusting the problem size to fully utilize additional resources, which can lead to higher system throughput in parallel environments, but also ignores the parallel crosstalk, which can result in more theoretical throughput values.
Universal Scalability Law accounts for saturation effects that may occur as system resources are increased, providing insights into the maximum achievable throughput and the diminishing returns of adding more resources, more practical than the first two but has a cost of additional complexity and more experienced researchers when determining coefficients for an actual system.
In summary, each law has its strengths and weaknesses, and the choice of model depends on the specific characteristics of the system being analyzed and the level of detail required in the analysis. [7] B. Shwartz, E. Fortune Forecasting MySQL Scalability with Universal Scalability Law URL:https://www.percona.com/sites/default/files/white-paper-forecastingmysql-scalability.pdf [8] J. Gustafson Gustafson’s Law, (2011) ResearchGate.net. doi: 10.1007/978-0-38709766-4_78 [9] J. Gustafson Reevaluating Amdahl’s Law (1988).
URL:http://www.johngustafson.net/pubs/pub13/amdahl.pdf [10] J. Gustafson Gustafson’s Law. URL: http://www.johngustafson.net/glaw.html [11] L. Snyder Type Architectures, shared memory, and the corollary of modest potential (1986) doi: 10.1146/annurev.cs.01.060186.001445