Non-preemptive Scheduling in a Smart Grid Model and its Implications on Machine Minimization

We study a scheduling problem arising in demand response management in smart grid. Consumers send in power requests with a flexible feasible time interval during which their requests can be served. The grid controller, upon receiving power requests, schedules each request within the specified interval. The electricity cost is measured by a convex function of the load in each timeslot. The objective is to schedule all requests with the minimum total electricity cost. Previous work has studied cases where jobs have unit power requirement and unit duration. We extend the study to arbitrary power requirement and duration, which has been shown to be NP-hard. We give the first online algorithm for the general problem, and prove that the problem is fixed parameter tractable. We also show that the online algorithm is asymptotically optimal when the objective is to minimize the peak load. In addition, we observe that the classical non-preemptive machine minimization problem is a special case of the smart grid problem with min-peak objective, and show that we can solve the non-preemptive machine minimization problem asymptotically optimally

Algorithmic And Mathematical Programming Approaches To Scheduling Problems With Energy-Based Objectives

This dissertation studies scheduling as a means to address the increasing concerns related to energy consumption and electricity cost in manufacturing enterprises. Two classes of problems are considered in this dissertation: (i) minimizing the makespan in a permutation flow shop with peak power consumption constraints (the PFSPP problem for short) and (ii) minimizing the total electricity cost on a single machine under time-of-use tariffs (the SMSEC problem for short). We incorporate the technology of dynamic speed scaling and the variable pricing of electricity into these scheduling problems to improve energy efficiency in manufacturing.The challenge in the PFSPP problem is to keep track of which jobs are running concurrently at any time so that the peak power consumption can be properly taken into account. The challenge in the SMSEC problem is to keep track of the electricity prices at which the jobs are processed so that the total electricity cost can be properly computed. For the PFSPP problem, we consider both mathematical programming and combinatorial approaches. For the case of discrete speeds and unlimited intermediate storage, we propose two mixed integer programs and test their computational performance on instances arising from the manufacturing of cast iron plates. We also examine the PFSPP problem with two machines and zero intermediate storage, and investigate the structural properties of optimal schedules in this setting. For the SMSEC problem, we consider both uniform-speed and speed-scalable machine environments. For the uniform-speed case, we prove that this problem is strongly NP-hard, and in fact inapproximable within a constant factor, unless P = NP. In addition, we propose an exact polynomial-time algorithm for this problem when all the jobs have the same work volume and the electricity prices follow a so-called pyramidal structure. For the speed-scalable case, in which jobs can be processed at an arbitrary speed with a trade-off between speed and energy consumption, we show that this problem is strongly NP-hard and that there is no polynomial time approximation scheme for this problem. We also present different approximation algorithms for this case and test the computational performance of these approximation algorithms on randomly generated instances

Optimal Nonpreemptive Scheduling in a Smart Grid Model

We study a scheduling problem arising in demand response management in smart grid. Consumers send in power requests with a flexible feasible time interval during which their requests can be served. The grid controller, upon receiving power requests, schedules each request within the specified interval. The electricity cost is measured by a convex function of the load in each timeslot. The objective is to schedule all requests with the minimum total electricity cost. Previous work has studied cases where jobs have unit power requirement and unit duration. We extend the study to arbitrary power requirement and duration, which has been shown to be NP-hard. We give the first online algorithm for the general problem, and prove that the worst case competitive ratio is asymptotically optimal. We also prove that the problem is fixed parameter tractable. Due to space limit, the missing proofs are presented in the full paper

Achieving an optimal trade-off between revenue and energy peak within a smart grid environment

We consider an energy provider whose goal is to simultaneously set revenue-maximizing prices and meet a peak load constraint. In our bilevel setting, the provider acts as a leader (upper level) that takes into account a smart grid (lower level) that minimizes the sum of users' disutilities. The latter bases its decisions on the hourly prices set by the leader, as well as the schedule preferences set by the users for each task. Considering both the monopolistic and competitive situations, we illustrate numerically the validity of the approach, which achieves an 'optimal' trade-off between three objectives: revenue, user cost, and peak demand

k2U: A General Framework from k-Point Effective Schedulability Analysis to Utilization-Based Tests

To deal with a large variety of workloads in different application domains in real-time embedded systems, a number of expressive task models have been developed. For each individual task model, researchers tend to develop different types of techniques for deriving schedulability tests with different computation complexity and performance. In this paper, we present a general schedulability analysis framework, namely the k2U framework, that can be potentially applied to analyze a large set of real-time task models under any fixed-priority scheduling algorithm, on both uniprocessor and multiprocessor scheduling. The key to k2U is a k-point effective schedulability test, which can be viewed as a "blackbox" interface. For any task model, if a corresponding k-point effective schedulability test can be constructed, then a sufficient utilization-based test can be automatically derived. We show the generality of k2U by applying it to different task models, which results in new and improved tests compared to the state-of-the-art. Analogously, a similar concept by testing only k points with a different formulation has been studied by us in another framework, called k2Q, which provides quadratic bounds or utilization bounds based on a different formulation of schedulability test. With the quadratic and hyperbolic forms, k2Q and k2U frameworks can be used to provide many quantitive features to be measured, like the total utilization bounds, speed-up factors, etc., not only for uniprocessor scheduling but also for multiprocessor scheduling. These frameworks can be viewed as a "blackbox" interface for schedulability tests and response-time analysis

Exact and Heuristic Algorithms for Energy-Efficient Scheduling

The combined increase of energy demand and environmental pollution at a global scale is entailing a rethinking of the production models in sustainable terms. As a consequence, energy suppliers are starting to adopt strategies that flatten demand peaks in power plants by means of pricing policies that stimulate a change in the consumption practices of customers. A representative example is the Time-of-Use (TOU)-based tariffs policy, which encourages electricity usage at off-peak hours by means of low prices, while penalizing peak hours with higher prices. To avoid a sharp increment of the energy supply costs, manufacturing industry must carefully reschedule the production process, by shifting it towards less expensive periods. The TOU-based tariffs policy induces an implicit partitioning of the time horizon of the production into a set of time slots, each associated with a non-negative cost that becomes a part of the optimization objective. This thesis focuses on a representative bi-objective energy-efficient job scheduling problem on parallel identical machines under TOU-based tariffs by delving into the description of its inherent properties, mathematical formulations, and solution approaches. Specifically, the thesis starts by reviewing the flourishing literature on the subject, and providing a useful framework for theoreticians and practitioners. Subsequently, it describes the considered problem and investigates its theoretical properties. In the same chapter, it presents a first mathematical model for the problem, as well as a possible reformulation that exploits the structure of the solution space so as to achieve a considerable increase in compactness. Afterwards, the thesis introduces a sophisticated heuristic scheme to tackle the inherent hardness of the problem, and an exact algorithm that exploits the mathematical models. Then, it shows the computational efficiency of the presented solution approaches on a wide test benchmark. Finally, it presents a perspective on future research directions for the class of energy-efficient scheduling problems under TOU-based tariffs as a whole

Optimal Algorithms for Scheduling under Time-of-Use Tariffs

We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling objectives of minimizing the makespan and the sum of (weighted) completion times. It is not difficult to derive a polynomial-time algorithm for preemptive scheduling to minimize the makespan on unrelated machines. The problem of minimizing the total (weighted) completion time is considerably harder, even on a single machine. We present a polynomial-time algorithm that computes for any given sequence of jobs an optimal schedule, i.e., the optimal set of time-slots to be used for scheduling jobs according to the given sequence. This result is based on dynamic programming using a subtle analysis of the structure of optimal solutions and a potential function argument. With this algorithm, we solve the unweighted problem optimally in polynomial time. For the more general problem, in which jobs may have individual weights, we develop a polynomial-time approximation scheme (PTAS) based on a dual scheduling approach introduced for scheduling on a machine of varying speed. As the weighted problem is strongly NP-hard, our PTAS is the best possible approximation we can hope for.Comment: 17 pages; A preliminary version of this paper with a subset of results appeared in the Proceedings of MFCS 201

GPU의 실시간 보장 및 더 나은 스케줄링 가능성을 위한 슬라이스 수 탐색

학위논문(석사) -- 서울대학교대학원 : 공과대학 컴퓨터공학부, 2021.8. 이창건.This paper proposes a conditionally optimal slice counts searching algorithm to improve GPU's real-time guarantee and better schedulability. Despite the growing importance of GPUs due to the recent advances in deep learning, there is still a lack of technology to utilize them in real-time. This paper assumes a GPU as a uniprocessor and uses non-preemptive EDF to schedule GPU kernels. Additionally, solving the schedulability degradation problem caused by non-preemptive uniprocessor assumption through searching the slice count of each kernel that makes the GPU task set to be schedulable.본 논문은 GPU의 실시간성 보장 및 더 나은 스케줄링 가능성을 위한 조건부 최적 슬라이스 카운트 탐색 알고리즘을 제안한다. 근래 딥러닝의 발전으로 인해 GPU의 중요성이 커지고 있음에도 불구하고, GPU를 실시간으로 활용하기 위한 기술들은 아직 부족한 실정이다. 본 논문은 GPU를 단일 프로세서로 가정하고 비선점형 EDF를 GPU 커널의 스케줄링에 사용한다. 또한 GPU task set을 스케줄링 가능하게 만드는 슬라이스 카운트 탐색 기법을 통해 비선점형 단일 프로세서로의 가정으로 인한 스케줄링 가능성 저하 문제를 해결한다.1 Introduction 1 2 RelatedWorks 3 3 Real-Time Gaurantee of GPUs through Non-Preemptive Uniprocessor Assumption 5 4 Problem Description 9 5 Slice Counts Search 11 5.1 Blocking point, blocking tolerance, and blocking candidates 13 5.2 Searching slice counts for a task set 14 5.3 Stop conditions 18 5.4 Optimality of the slice counts search 18 5.5 Applying slice counts search in Real System 20 6 Experiment Results 21 6.1 Simulation Experiment 21 6.2 Implementation Results 23 7 Conclusion 25 References 26석

Smart Grid-aware scheduling in data centres

© 2016 In several countries the expansion and establishment of renewable energies result in widely scattered and often weather-dependent energy production, decoupled from energy demand. Large, fossil-fuelled power plants are gradually replaced by many small power stations that transform wind, solar and water power into electrical power. This leads to changes in the historically evolved power grid that favours top-down energy distribution from a backbone of large power plants to widespread consumers. Now, with the increase of energy production in lower layers of the grid, there is also a bottom-up flow of the grid infrastructure compromising its stability. In order to locally adapt the energy demand to the production, some countries have started to establish Smart Grids to incentivise customers to consume energy when it is generated. This paper investigates how data centres can benefit from variable energy prices in Smart Grids. In view of their low average utilisation, data centre providers can schedule the workload dependent on the energy price. We consider a scenario for a data centre in Paderborn, Germany, hosting a large share of interruptible and migratable computing jobs. We suggest and compare two scheduling strategies for minimising energy costs. The first one merely uses current values from the Smart Meter to place the jobs, while the other one also estimates the future energy price in the grid based on weather forecasts. In spite of the complexity of the prediction problem and the inaccuracy of the weather data, both strategies perform well and have a strong positive effect on the utilisation of renewable energy and on the reduction of energy costs. This work improves and extends the paper of the same title published on the SustainIT conference (Mäsker et al., 2015). While that paper puts more emphasis on the utilisation of green energy, the new algorithms find a better balance between energy costs and turnaround time. We slightly alter the scenario using a more realistic multi-queue batch system and improve the scheduling algorithms which can be tuned to prioritise turnaround time or green energy utilisation