We first consider online speed scaling algorithms to minimize the energy used subject to the constraint that every job finishes by its deadline. We assume that the power required to run at speed ¡ is ¢¤ £. We provide a tight bound on the competitive ratio of the previously pro-posed Optimal Available algorithm. This improves the best known competitive ratio by a factor � � of. We then introduce a new online algorithm, and show that this algorithm’s competitive ratio is at � £ �� � £ �¨����¥�¥����� � most. This competitive ratio is significantly better and is � ������� approximately for large �. Our result is essentially tight for large �. In particular, as � approaches infinity, we show that any algorithm must have competitive ratio �� � (up to lower order terms). We then turn to the problem of dynamic speed scaling to minimize the maximum temperature that the device ever reaches, again subject to the constraint that all jobs finish by their deadlines. We assume that the device cools according to Fourier’s law. We show how to solve this problem in polynomial time, within any error bound, using the Ellipsoid algorithm. 1.

We consider the speed scaling problem of minimizing the average response time of a collection of dynamically released jobs subject to a constraint A on energy used. We propose an algorithmic approach in which an energy optimal schedule is computed for a huge A, and then the energy optimal schedule is maintained as A decreases. We show that this approach yields an efficient algorithm for equi-work jobs. We note that the energy optimal schedule has the surprising feature that the job speeds are not monotone functions of the available energy. We then explain why this algorithmic approach is problematic for arbitrary work jobs. Finally, we explain how to use the algorithm for equi-work jobs to obtain an algorithm for arbitrary work jobs that is O(1)-approximate with respect to average response time, given an additional factor of (1 + ffl)energy.

We study scheduling problems in battery-operated computing devices, aiming at schedules with low total energy consumption. While most of the previous work has focused on finding feasible schedules in deadline-based settings, in this article we are interested in schedules that guarantee good response times. More specifically, our goal is to schedule a sequence of jobs on a variable-speed processor so as to minimize the total cost consisting of the energy consumption and the total flow time of all jobs. We first show that when the amount of work, for any job, may take an arbitrary value, then no online algorithm can achieve a constant competitive ratio. Therefore, most of the article is concerned with unit-size jobs. We devise a deterministic constant competitive online algorithm and show that

In this paper, we present a measurement study of the energy consumption characteristics of three widespread mobile networking technologies: 3G, GSM, and WiFi. We find that 3G and GSM incur a high tail energy overhead because of lingering in high power states after completing a transfer. Based on these measurements, we develop a model for the energy consumed by network activity for each technology. Using this model, we develop TailEnder, a protocol that reduces energy consumption of common mobile applications. For applications that can tolerate a small delay such as e-mail, TailEnder schedules transfers so as to minimize the cumulative energy consumed while meeting user-specified deadlines. We show that the TailEnder scheduling algorithm is within a factor 2 × of the optimal and show that any online algorithm can at best be within a factor 1.62 × of the optimal. For applications like web search that can benefit from prefetching, TailEnder aggressively prefetches several times more data and improves user-specified response times while consuming less energy. We evaluate the benefits of TailEnder for three different case study applications—email, news feeds, and web search—based on real user logs and show significant reduction in energy consumption in each case. Experiments conducted on the mobile phone show that TailEnder can download 60 % more news feed updates and download search results for more than 50 % of web queries, compared to using the default policy.

Interconnects have been shown to be a dominant source of energy consumption in modern day System-on-Chip (SoC) designs. With a large (and growing) number of electronic systems being designed with battery considerations in mind, minimizing the energy consumed in on-chip interconnects becomes crucial. Further, the use of nanometer technologies is making it increasingly important to consider reliability issues during the design of SoC communication architectures. Continued supply voltage scaling has led to decreased noise margins, making interconnects more susceptible to noise sources such as crosstalk, power supply noise, radiation induced defects, etc. The resulting transient faults cause the interconnect to behave as an unreliable transport medium for data signals. Therefore, fault tolerant communication mechanisms, such as Automatic Repeat Request (ARQ), Forward Error Correction (FEC), etc., which have been widely used in the networking community, are likely to percolate to the SoC domain.

Abstract. We study online scheduling to minimize flow time plus energy usage in the dynamic speed scaling model. We devise new speed scaling functions that depend on the number of active jobs, replacing the existing speed scaling functions in the literature that depend on the remaining work of active jobs. The new speed functions are more stable and also more efficient. They can support better job selection strategies to improve the competitive ratios of existing algorithms [5,8], and, more importantly, to remove the requirement of extra speed. These functions further distinguish themselves from others as they can readily be used in the non-clairvoyant model (where the size of a job is only known when the job finishes). As a first step, we study the scheduling of batched jobs (i.e., jobs with the same release time) in the non-clairvoyant model and present the first competitive algorithm for minimizing flow time plus energy (as well as for weighted flow time plus energy); the performance is close to optimal. 1

Abstract. This paper extends the study of online algorithms for energy-efficient deadline scheduling to the overloaded setting. Specifically, we consider a processor that can vary its speed between 0 and a maximum speed T to minimize its energy usage (of which the rate is roughly a cubic function of the speed). As the speed is upper bounded, the system may be overloaded with jobs and no scheduling algorithms can meet the deadlines of all jobs. An optimal schedule is expected to maximize the throughput, and furthermore, its energy usage should be the smallest among all schedules that achieve the maximum throughput. In designing a scheduling algorithm, one has to face the dilemma of selecting more jobs and being conservative in energy usage. Even if we ignore energy usage, the best possible online algorithm is 4-competitive on throughput [12]. On the other hand, existing work on energy-efficient scheduling focuses on minimizing the energy to complete all jobs on a processor with unbounded speed, giving several O(1)-competitive algorithms with respect to the energy usage [2,20]. This paper presents the first online algorithm for the more realistic setting where processor speed is bounded and the system may be overloaded; the algorithm is O(1)-competitive on both throughput and energy usage. If the maximum speed of the online scheduler is relaxed slightly to (1+ǫ)T for some ǫ> 0, we can improve the competitive ratio on throughput to arbitrarily close to one, while maintaining O(1)-competitive on energy usage. 1

In this paper we investigate algorithmic instruments leading to low power consumption in computing devices. While previous work on energy-efficient algorithms has mostly focused on single processor environments, in this paper we investigate multi-processor settings. We study the basic problem of scheduling a set of jobs, each specified by a release time, a deadline and a processing volume, on variable speed processors so as to minimize the total energy consumption. We first settle the complexity of speed scaling with unit size jobs. More specifically, we devise a polynomial time algorithm for agreeable deadlines and prove NP-hardness results for arbitrary release dates and deadlines. For the latter setting we also develop a polynomial time algorithm achieving a constant factor approximation guarantee that is independent of the number of processors. Additionally, we study speed scaling of jobs with arbitrary processing requirements and, again, develop constant factor approximation algorithms. We finally transform our offline algorithms into constant competitive online strategies.

Abstract. We study the problem of non-preemptive scheduling to minimize energy consumption for devices that allow dynamic voltage scaling. Specifically, consider a device that can process jobs in a non-preemptive manner. The input consists of (i) the set R of available speeds of the device, (ii) a set J of jobs, and (iii) a precedence constraint Π among J. Each job j in J, defined by its arrival time aj, deadline dj, and amount of computation cj, is supposed to be processed by the device at a speed in R. Under the assumption that a higher speed means higher energy consumption, the power-saving scheduling problem is to compute a feasible schedule with speed assignment for the jobs in J such that the required energy consumption is minimized. This paper focuses on the setting of weakly dynamic voltage scaling, i.e., speed change is not allowed in the middle of processing a job. To demonstrate that this restriction on many portable power-aware devices introduces hardness to the power-saving scheduling problem, we prove that the problem is NP-hard even if aj = aj ′ and dj = dj ′ hold for all j, j ′ ∈ J and |R | = 2. If |R | < ∞, we also give fully polynomial-time approximation schemes for two cases of the general NP-hard problem: (a) all jobs share a common arrival time, and (b) Π = ∅ and for any j, j ′ ∈ J, aj ≤ aj ′ implies dj ≤ dj ′. To the best of our knowledge, there is no previously known approximation algorithm for any special case of the NP-hard problem. 1

Procrastination scheduling has gained importance for energy efficiency due to the rapid increase in the leakage power consumption. Under procrastination scheduling, task executions are delayed to extend processor shutdown intervals, thereby reducing the idle energy consumption. We propose algorithms to compute the maximum procrastination intervals for tasks scheduled by either the fixed priority or the dual priority scheduling policy. We show that dual priority scheduling always guarantees longer shutdown intervals than fixed priority scheduling. We further combine procrastination scheduling with dynamic voltage scaling to minimize the total static and dynamic energy consumption of the system. Our simulation experiments show that the proposed algorithms can extend the sleep intervals up to 5 times while meeting the timing requirements. The results show up to 18% energy gains over dynamic voltage scaling.