In computer system the performance is utmost important factor when it comes to the question of computer program whether it is simple program or an operating system itself. The basic question which need to be answered is, when only part of the system is improved then what is the impact of it on overall computer performance? .This is all about Amdahl's law.
The basic problem statement is if we improve some of part of the computer system then how it can impact on overall performanrce on the system.
Amdahl's law is more relevant in parallel computing when number of parallel process
Amdahl stated the simple mathematics if P part of the program is improved its performance by speed S then run time is P/S whereas (1-P) is the runtime of rest of the program which speed is 1x .
Total run time = (1-P)/1 + P/S
Performance is inversely proportion to runtime = 1/(1-P) + P/S
Similarly if Ps are defined as part of program and P1 improves 1x and P2 2x and and P3 3x also P1+P2+P3 = 1 (1 program divided into three parts each has own speed up ratio) then overall performance improved is
1/ (P1/1 + P2/2 + P3/3) lets take P1 is 50% and P2 is 20% P3 is 30% then overall improvement is
1/0.7 = 1.43 (approx)
Similarly , In case of parallel programming if the P is portion of program that can be made parallel by N processor then overall performance is 1/(1-P) + P/N
The basic problem statement is if we improve some of part of the computer system then how it can impact on overall performanrce on the system.
Amdahl's law is more relevant in parallel computing when number of parallel process
Amdahl stated the simple mathematics if P part of the program is improved its performance by speed S then run time is P/S whereas (1-P) is the runtime of rest of the program which speed is 1x .
Total run time = (1-P)/1 + P/S
Performance is inversely proportion to runtime = 1/(1-P) + P/S
Similarly if Ps are defined as part of program and P1 improves 1x and P2 2x and and P3 3x also P1+P2+P3 = 1 (1 program divided into three parts each has own speed up ratio) then overall performance improved is
1/ (P1/1 + P2/2 + P3/3) lets take P1 is 50% and P2 is 20% P3 is 30% then overall improvement is
1/0.7 = 1.43 (approx)
Similarly , In case of parallel programming if the P is portion of program that can be made parallel by N processor then overall performance is 1/(1-P) + P/N
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