Speed-scaling with no Preemptions

We revisit the non-preemptive speed-scaling problem, in which a set of jobs have to be executed on a single or a set of parallel speed-scalable processor(s) between their release dates and deadlines so that the energy consumption to be minimized. We adopt the speed-scaling mechanism first introduced in [Yao et al., FOCS 1995] according to which the power dissipated is a convex function of the processor's speed. Intuitively, the higher is the speed of a processor, the higher is the energy consumption. For the single-processor case, we improve the best known approximation algorithm by providing a $(1+\epsilon)^{\alpha}\tilde{B}_{\alpha}$-approximation algorithm, where $\tilde{B}_{\alpha}$ is a generalization of the Bell number. For the multiprocessor case, we present an approximation algorithm of ratio $\tilde{B}_{\alpha}((1+\epsilon)(1+\frac{w_{\max}}{w_{\min}}))^{\alpha}$ improving the best known result by a factor of $(\frac{5}{2})^{\alpha-1}(\frac{w_{\max}}{w_{\min}})^{\alpha}$. Notice that our result holds for the fully heterogeneous environment while the previous known result holds only in the more restricted case of parallel processors with identical power functions

Feedback and time are essential for the optimal control of computing systems

The performance, reliability, cost, size and energy usage of computing systems can be improved by one or more orders of magnitude by the systematic use of modern control and optimization methods. Computing systems rely on the use of feedback algorithms to schedule tasks, data and resources, but the models that are used to design these algorithms are validated using open-loop metrics. By using closed-loop metrics instead, such as the gap metric developed in the control community, it should be possible to develop improved scheduling algorithms and computing systems that have not been over-engineered. Furthermore, scheduling problems are most naturally formulated as constraint satisfaction or mathematical optimization problems, but these are seldom implemented using state of the art numerical methods, nor do they explicitly take into account the fact that the scheduling problem itself takes time to solve. This paper makes the case that recent results in real-time model predictive control, where optimization problems are solved in order to control a process that evolves in time, are likely to form the basis of scheduling algorithms of the future. We therefore outline some of the research problems and opportunities that could arise by explicitly considering feedback and time when designing optimal scheduling algorithms for computing systems

A Multi-objective Perspective for Operator Scheduling using Fine-grained DVS Architecture

The stringent power budget of fine grained power managed digital integrated circuits have driven chip designers to optimize power at the cost of area and delay, which were the traditional cost criteria for circuit optimization. The emerging scenario motivates us to revisit the classical operator scheduling problem under the availability of DVFS enabled functional units that can trade-off cycles with power. We study the design space defined due to this trade-off and present a branch-and-bound(B/B) algorithm to explore this state space and report the pareto-optimal front with respect to area and power. The scheduling also aims at maximum resource sharing and is able to attain sufficient area and power gains for complex benchmarks when timing constraints are relaxed by sufficient amount. Experimental results show that the algorithm that operates without any user constraint(area/power) is able to solve the problem for most available benchmarks, and the use of power budget or area budget constraints leads to significant performance gain.Comment: 18 pages, 6 figures, International journal of VLSI design & Communication Systems (VLSICS

MORA: an Energy-Aware Slack Reclamation Scheme for Scheduling Sporadic Real-Time Tasks upon Multiprocessor Platforms

In this paper, we address the global and preemptive energy-aware scheduling problem of sporadic constrained-deadline tasks on DVFS-identical multiprocessor platforms. We propose an online slack reclamation scheme which profits from the discrepancy between the worst- and actual-case execution time of the tasks by slowing down the speed of the processors in order to save energy. Our algorithm called MORA takes into account the application-specific consumption profile of the tasks. We demonstrate that MORA does not jeopardize the system schedulability and we show by performing simulations that it can save up to 32% of energy (in average) compared to execution without using any energy-aware algorithm.Comment: 11 page