We are using Amdahl's Law and Gustafson's Law to calculate overall speedup and scaled speedup. Given a10% serial section of a program, calculate both speedups for a 64-processor machine.

Answered: We are using Amdahl's Law and…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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We are using Amdahl's Law and Gustafson's Law to calculate overall speedup and scaled speedup. Given a
10% serial section of a program, calculate both speedups for a 64-processor machine.

Expert Solution

Step 1

Amdahl's Law states that the maximum theoretical speedup of a program is limited by the fraction of the program that must be executed serially. The formula for speedup is given by:

Speedup = 1 / ( (1 - p) + (p/n) )

where p is the fraction of the program that must be executed serially, and n is the number of processors.

For a 10% serial section of a program, p = 0.10.

Speedup = 1 / ( (1 - 0.10) + (0.10/64) ) = 1 / (0.9 + 0.0015625) = 1 / 0.9015625 = 1.107972

So, the maximum theoretical speedup for a 64-processor machine according to Amdahl's Law is 1.11.

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