Speed scaling to manage temperature

We consider speed scaling algorithms to minimize device temperature subject to the constraint that every task finishes by its deadline. We assume that the device cools according to Fouriers law. We show that the optimal offline algorithm proposed in [18] for minimizing total energy (that we call YDS) is an O(1)-approximation with respect to temperature. Tangentially, we observe that the energy optimality of YDS is an elegant consequence of the well known KKT optimality conditions. Two online algorithms, AVR and Optimal Available, were proposed in [18] in the context of energy management. It was shown that these algorithms were O(1)-competitive with respect to energy in [18] and [2]. Here we show these algorithms are not O(1)-competitive with respect to temperature. This demonstratively illustrates the observation from practice that power management techniques that are effective for managing energy may not be effective for managing temperature. We show that the most intuitive temperature management algorithm, running at such a speed so that the temperature is constant, is surprisingly not O(1)-competitive with respect to temperature. In contrast, we show that the online algorithm BKP, proposed in [2], is O(1)-competitive with respect to temperature. This is the first O(1)-competitiveness analysis with respect to temperature for an online algorithm

Scheduling for speed bounded processors

Abstract. We consider online scheduling algorithms in the dynamic speed scaling model, where a processor can scale its speed between 0 and some maximum speed T. The processor uses energy at rate s α when run at speed s, where α> 1 is a constant. Most modern processors use dynamic speed scaling to manage their energy usage. This leads to the problem of designing execution strategies that are both energy efficient, and yet have almost optimum performance. We consider two problems in this model and give essentially optimum possible algorithms for them. In the first problem, jobs with arbitrary sizes and deadlines arrive online and the goal is to maximize the throughput, i.e. the total size of jobs completed successfully. We give an algorithm that is 4-competitive for throughput and O(1)-competitive for the energy used. This improves upon the 14 throughput competitive algorithm of Chan et al. [10]. Our throughput guarantee is optimal as any online algorithm must be at least 4-competitive even if the energy concern is ignored [7]. In the second problem, we consider optimizing the trade-off between the total flow time incurred and the energy consumed by the jobs. We give a 4-competitive algorithm to minimize total flow time plus energy for unweighted unit size jobs, and a (2 + o(1))α / ln α-competitive algorithm to minimize fractional weighted flow time plus energy. Prior to our work, these guarantees were known only when the processor speed was unbounded (T = ∞) [4].