[Paper Review] Energy-Efficient Scheduling for Homogeneous Multiprocessor Systems

Mason Thammawichai, Eric C. Kerrigan|arXiv (Cornell University)|Oct 19, 2015

Distributed and Parallel Computing Systems3 citations

TL;DR

This paper proposes novel optimization-based scheduling algorithms for homogeneous multiprocessor systems that minimize energy consumption using dynamic voltage and frequency scaling (DVFS). By formulating the problem as a linear program (LP) for discrete speed levels and a nonlinear program (NLP) for continuous speeds, the method achieves energy optimality and feasibility in a single step, outperforming existing approaches with up to 80% energy savings compared to non-DVFS schemes and 70% compared to constant-frequency methods for constrained deadline tasksets.

ABSTRACT

We present a number of novel algorithms, based on mathematical optimization formulations, in order to solve a homogeneous multiprocessor scheduling problem, while minimizing the total energy consumption. In particular, for a system with a discrete speed set, we propose solving a tractable linear program. Our formulations are based on a fluid model and a global scheduling scheme, i.e. tasks are allowed to migrate between processors. The new methods are compared with three global energy/feasibility optimal workload allocation formulations. Simulation results illustrate that our methods achieve both feasibility and energy optimality and outperform existing methods for constrained deadline tasksets. Specifically, the results provided by our algorithm can achieve up to an 80% saving compared to an algorithm without a frequency scaling scheme and up to 70% saving compared to a constant frequency scaling scheme for some simulated tasksets. Another benefit is that our algorithms can solve the scheduling problem in one step instead of using a recursive scheme. Moreover, our formulations can solve a more general class of scheduling problems, i.e. any periodic real-time taskset with arbitrary deadline. Lastly, our algorithms can be applied to both online and offline scheduling schemes.

Motivation & Objective

• To address the growing energy consumption in real-time embedded systems such as sensor networks, satellites, and multi-robot systems.
• To develop a scheduling framework that minimizes total energy consumption in homogeneous multiprocessor systems under real-time constraints.
• To enable both online and offline scheduling with time-varying speed profiles for improved energy efficiency.
• To overcome limitations of recursive or heuristic-based methods by formulating a single-step, globally optimal solution.
• To extend existing feasibility-optimal algorithms to support arbitrary deadlines and dynamic voltage/frequency scaling (DVFS).

Proposed method

• Formulates the scheduling problem using a fluid model and global scheduling, allowing task migration between processors to improve energy and feasibility optimality.
• Develops a mixed-integer nonlinear program (MINLP) for discrete speed levels, a nonlinear program (NLP) for continuous speeds, and a tractable linear program (LP) for discrete speed sets.
• Incorporates task density and taskset density metrics to model workload and feasibility constraints, with speed-dependent execution times.
• Uses a time-varying speed profile that adapts dynamically based on workload and deadline requirements to minimize energy.
• Employs ZIMPL for modeling and SCIP for solving the optimization problems, enabling efficient computation with off-the-shelf solvers.
• Integrates DVFS into the scheduling formulation by modeling power as a function of frequency and voltage, enabling dynamic scaling.

Experimental results

Research questions

• RQ1 Can a single-step optimization-based scheduling algorithm achieve both energy and feasibility optimality in homogeneous multiprocessor systems?
• RQ2 How does time-varying speed scaling compare to constant-speed or non-DVFS schemes in terms of energy savings for constrained deadline tasksets?
• RQ3 Can the proposed formulations handle arbitrary deadline tasksets more effectively than existing global scheduling algorithms?
• RQ4 What is the trade-off between computational complexity and energy optimality in MINLP, NLP, and LP formulations for multiprocessor scheduling?
• RQ5 Can the proposed method be applied to both online and offline scheduling scenarios with minimal runtime overhead?

Key findings

• The LP formulation achieves energy optimality and feasibility with minimal computational cost, making it suitable for real-time deployment with discrete speed levels.
• The proposed algorithms achieve up to 80% energy savings compared to a non-DVFS baseline and up to 70% compared to a constant-frequency scheme for certain tasksets.
• Simulation results show that time-varying speed profiles significantly outperform constant-speed profiles, especially as taskset density increases.
• The MINLP and NLP formulations are energy and feasibility optimal, but require up to an hour to solve in some cases, while the LP is solved in milliseconds.
• The method outperforms existing algorithms such as GP-SVFS, GP-Discrete, and GP-NoDVFS in energy efficiency for constrained deadline tasksets.
• The energy savings are nonlinear and depend on the underlying power model, with cubic models (e.g., Xscale) showing different scaling behavior than quadratic models (e.g., PowerPC 405LP).