Multi-Amdahl: Optimal Resource Sharing with Multiple Program Execution Segments

TL;DR

This paper introduces Multi-Amdahl, an analytical model for optimal resource sharing among multiple program segments accelerated by specialized hardware, considering constraints like area and power, to improve heterogeneous system efficiency.

Contribution

The paper develops a novel analytical framework for optimal resource allocation in heterogeneous systems with multiple accelerators, extending Amdahl's law to multiple segments.

Findings

Optimal resource distribution formulas derived using Lagrange multipliers

Demonstrated effectiveness through examples of area and power allocation

Provides a general approach for heterogeneous system optimization

Abstract

This paper presents Multi-Amdahl, a resource allocation analytical tool for heterogeneous systems. Our model includes multiple program execution segments, where each one is accelerated by a specific hardware unit. The acceleration speedup of the specific hardware unit is a function of a limited resource, such as the unit area, power, or energy. Using the Lagrange theorem we discover the optimal resource distribution between all specific units. We then illustrate this general Multi-Amdahl technique using several examples of area and power allocation among several cores and accelerators.