Editing Scalability (section)

==Performance tuning versus hardware scalability==
It is often advised to focus system design on hardware scalability rather than on capacity. It is typically cheaper to add a new node to a system in order to achieve improved performance than to partake in [[performance tuning]] to improve the capacity that each node can handle. But this approach can have diminishing returns (as discussed in [[performance engineering]]). For example: suppose 70% of a program can be sped up if parallelized and run on multiple CPUs instead of one. If <math>\alpha</math> is the fraction of a calculation that is sequential, and <math>1-\alpha</math> is the fraction that can be parallelized, the maximum [[speedup]] that can be achieved by using P processors is given according to [[Amdahl's Law]]:

: <math>\frac 1 {\alpha+\frac{1-\alpha} P}.</math>

Substituting the value for this example, using 4 processors gives

: <math>\frac 1 {0.3+\frac{1-0.3} 4} = 2.105.</math>

Doubling the computing power to 8 processors gives

: <math>\frac 1 {0.3+\frac{1-0.3} 8} = 2.581.</math>

Doubling the processing power has only sped up the process by roughly one-fifth. If the whole problem was parallelizable, the speed would also double. Therefore, throwing in more hardware is not necessarily the optimal approach.