Deadline scheduling and power management for speed bounded processors

Energy consumption has become an important issue in the study of processor scheduling. Energy reduction can be achieved by allowing a processor to vary the speed dynamically (dynamic speed scaling) [2–4, 7, 10] or to enter a sleep state [1, 5, 8]. In the past, these two mechanisms are often studied separately. It is indeed natural to consider an integrated model in which a processor, when awake, can run at any speed s > 0, using power P (s) = sα + σ, where α is typically 3 [6] and σ > 0 is a constant.1 To have zero energy usage, the processor can enter the sleep state, but wake-up requires ω > 0 energy. Irani et al. [9] are the first to consider this integrated model; they studied deadline scheduling in the infinite speed model (processor speed can be scaled arbitrarily large). The aim is to minimize the energy for completing all jobs by their deadlines. In this paper, we extend this study to the more realistic bounded speed model [7] where a processor has a maximum speed T . With bounded speed, the system may be overloaded and cannot meet all job deadlines. The objective is to maximize the throughput (total size of jobs completed by their deadlines) while using the minimum amount of energy. Adding a sleep state complicates the nature of speed scaling. To save energy in this model, a scheduler has to be proactive, sometimes forcing the processor to work faster (instead of slower) and to sleep more. In the infinite speed model, it is “safe” to let the processor to oversleep, and rely on extra speed to catch up with the deadlines. Yet this is no longer obvious for a speed bounded processor. In this paper, we present an online algorithm SOA that can exploit speed scaling and a sleep state more effectively. SOA can be considered as the sleep-aware version of the speed scaling algorithms OA [10] and OAT [7]. • In the infinite speed model, SOA (coupled with EDF) completes all jobs and is (αα + 2)competitive for energy, improving the ratio of Irani et al. [9] (which is 2α−1αα +2α−1 +2). • The major contribution of SOA is on the bounded speed model. SOA, capped at the maximum speed T , can support the job selection strategy Slow-D (proposed in [2]) to obtain an algorithm that is 4-competitive for throughput and (αα +α24α +2)-competitive for energy (note that the throughput ratio is optimal). ∗Department of Mathematical Informatics, University of Tokyo, Japan. [email protected] †Department of Computer Science, University of Hong Kong, Hong Kong. {twlam, lklee}@cs.hku.hk T.W. Lam is partly supported by HKU Grant 7176104. ‡Department of Computer Science, University of Liverpool, UK. {isaacto, pwong}@liverpool.ac.uk I.K.K. To and P.W.H. Wong are partly supported by EPSRC Grant EP/E028276/1. s is the dynamic power which is due to dynamic switching loss and increases with the processor speed; the static power σ is dissipated due to leakage current and is independent of processor speed.