Optimization

Amdahl's Law is used extensively in our chosen task distribution architecture to predict the theoretical maximum speedup for a task when only part of the task can be parallelized. The speedup of a program using multiple processors in parallel computing is limited by the time needed for the sequential fraction of the program. Below is a detailed breakdown of the sequence diagram that integrates Amdahl’s Law into Cerebrum’s operating methodology:

Logic Flow of Amdahs Law Integration

Evaluate Current Methods

• Cerebrum to Amdahl's Law: Cerebrum Cloud initiates a review of current computational processes to identify potential areas for applying Amdahl’s Law.

Application of Amdahl's Law

• Loop (Applying speedup calculations): Cerebrum Cloud repeatedly applies Amdahl's Law to calculate the possible speedup by parallelizing different parts of operations. The formula used is:

$$S = \frac{1}{(1-P) + \frac{P}{N}}$$

Where 𝑆 is the speedup, 𝑃 is the proportion of the program that can be parallelized, and N is the number of processors.

Integrate Improvements

• Cerebrum to System: From the calculation done, Cerebrum integrates improvements in system architecture or the processing pipeline to exploit parallel computing based on insight gained through Amdahl's Law.

Confirm Integration Success

• Cerebrum to Amdahl's Law (Confirmation): Cerebrum Cloud would then send a confirmation back to the theoretical framework of Amdahl's Law, thus completing the loop of integration.

Performance Improvement Monitoring

• Amdahl's Law to Cerebrum (Asynchronous Monitoring): As this is an ongoing process, monitoring is effected to ensure that the theoretical increase in speed is practically manifested.