Improved Bounds for Speed Scaling in Devices Obeying the Cube-Root Rule

Abstract

. (2012). Improved bounds for speed scaling in devices obeying the cube-root rule. Theory of Computing, 8(9), 209-229. DOI: 10.4086/toc.2012.v008a009 General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.• Users may download and print one copy of any publication from the public portal for the purpose of private study or research.• You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal ? Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Abstract: Speed scaling is a power management technology that involves dynamically changing the speed of a processor. This technology gives rise to dual-objective scheduling problems, where the operating system both wants to conserve energy and optimize some Quality of Service (QoS) measure of the resulting schedule. In the most investigated speed scaling problem in the literature, the QoS constraint is deadline feasibility, and the objective is to minimize the energy used. The standard assumption is that the processor power is of the form s α where s is the processor speed, and α > 1 is some constant; α ≈ 3 for CMOS based processors. In this paper we introduce and analyze a natural class of speed scaling algorithms that we call qOA. The algorithm qOA sets the speed of the processor to be q times the speed that the optimal offline algorithm would run the jobs in the current state. When α = 3, we show that qOA is 6.7-competitive, improving upon the previous best guarantee of 27 achieved by the algorithm Optimal Available (OA). We also give almost matching upper and lower bounds for qOA for general α. Finally, we give the first non-trivial lower bound, namely e α−1 /α, on the competitive ratio of a general deterministic online algorithm for this problem.

Speed Scaling for Weighted Flow Time

“…Constant competitive online algorithms are given in [16,5,3,4]. In particular, the online algorithm Optimal Available (OA), proposed in [16], was shown to be O(1)-competitive in [5] using a potential function analysis.…”

Optimality, fairness, and robustness in speed scaling designs

“…The analytic study of the speed scaling problem began with Yao et al [34] in 1995. Since [34], three main performance objectives balancing energy and delay have been considered: (i) minimize the total energy used in order to meet job deadlines, e.g., [6,25] (ii) minimize the average response time given an energy/power budget, e.g., [11,35], and (iii) minimize a linear combination of expected response time and energy usage per job [1,5]. In this work we focus on the third objective.…”

Multiprocessor speed scaling for jobs with arbitrary sizes and deadlines

“…A popular technology to reduce energy usage is dynamic speed scaling (see e.g., [1,2,3,6]) where the processor can vary its speed dynamically. The power consumption is modelled by s α when the processor runs at speed s, where α is typically 3 [4].…”

“…They gave a simple online algorithm AVR which is 2 α α α -competitive and they also proposed an online algorithm OA which was later shown by Bansal et al to be α α -competitive [3]. Algorithms with better competitive ratios were later proposed in [3,2].…”