Non-preemptive Scheduling Research Articles

NPSCS: Non-Preemptive Stochastic Coflow Scheduling With Time-Indexed LP Relaxation

Coflows model a scheduling setting that is commonly found in a variety of applications in distributed and cloud computing. A stochastic coflow task contains a set of parallel flows with randomly distributed sizes. Further, many applications require non-preemptive scheduling of coflow tasks. This article gives an approximation algorithm on the weighted expected completion time for non-preemptive stochastic coflow scheduling. The proposed approach uses a time-indexed linear program relaxation, and uses its solution to come up with a feasible schedule. This algorithm is shown to achieve an approximation ratio of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(2\log {m}{+}1)(1{+}\sqrt {m {\Delta }})(1{+}m\sqrt {{\Delta }}){(1{+}{\Delta })}$ </tex-math></inline-formula> for zero-release times, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2(2\log {m}{+}1)(1{+}\sqrt {m{\Delta }})(1{+}m\sqrt {{\Delta }})(1{+}{\Delta })$ </tex-math></inline-formula> for general release times, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Delta }$ </tex-math></inline-formula> represents the upper bound of squared coefficient of variation of processing times, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> is the number of servers.

Novel Offline Software-in-the-Loop Simulation Technique for Modular Single-Phase Flyback Current Source Grid-Tie Inverter System

This paper proposes a novel approach in the offline Software-in-the-Loop (SIL) simulation technique to speed up the firmware development cycle of power electronics and enhance the firmware maintenance of commercial products. In the conventional SIL simulation process, Model-in-the-Loop (MIL) is always performed prior to the execution of SIL because it allows users to automatically generate C code for testing in the subsequent SIL. Furthermore, the target device can be programmed with the compiled files only if the simulation tools support specific models of control chips. In light of this, the goal to use SIL to validate firmware in early power electronics product development becomes more complex and limited due to the limited selection of simulation tools. In this paper, non-preemptive scheduling (NPS) and common firmware architecture (CFA) are explored to illustrate the integration of the application layer for implementing the proposed offline SIL. Users can directly use circuit simulation software that supports Dynamic-Link Library (DLL) to simultaneously develop source codes and verify the offline SIL process of the product. To further illustrate the practical application of the power electronics product in the microcontroller (MCU) mock model and the power stage circuit model, a single 300W power module composed of three single-phase quasi-resonant (QR) flyback current source converters connected in parallel and cascaded with an H-bridge unfolder is used as an example to execute offline SIL in the SIMULINK. Finally, a system-level experiment was conducted to validate the firmware of 16 power modules assembled in a 4.8 kW fuel cell (FC) grid-tie inverter system, which was modulated through the power management unit (PMU) and the monitoring graphical user interface (GUI).

Corrigendum to “A Bucket Indexed Formulation for Nonpreemptive Single Machine Scheduling Problems,” INFORMS Journal on Computing 28(1):14–30, 2016

Abstract. This note corrects an error in our paper “N. Boland, R. Clement, and H. Waterer. A bucket indexed formulation for nonpreemptive single machine scheduling problems. INFORMS Journal on Computing 28(1):14–30, 2016.”

Dynamic Priority Assignment for Aperiodic Tasks in Limited Preemptive Scheduling

Internet of Things (IoT) systems and other real-time systems are required to handle both periodic and aperiodic incoming tasks. In a situation in which periodic and aperiodic tasks are mixed into task scheduling using a fixed priority system, the schedulability of periodic tasks could be reduced due to interruptions by aperiodic tasks. This study analyzes the effects of aperiodic tasks on non-preemptive scheduling and limited preemptive scheduling methods, such as fixed preemption points, preemption threshold scheduling, and deferred preemptive scheduling, which have recently been proposed by complementarily combining fully preemptive and non-preemptive scheduling. This study then proposes an algorithm for assigning an appropriate priority to an aperiodic task by analyzing the worst-case response time of all tasks to enhance schedulability of both periodic and aperiodic tasks.

Three-machine open shop with a bottleneck machine revisited

The paper considers the three-machine open shop scheduling problem to minimize the makespan. In the model, each job consists of two operations, one of which is to be processed on the bottleneck machine, which is the same for all jobs. A new linear-time algorithm to find an optimal non-preemptive schedule is developed. The suggested algorithm considerably simplifies the only previously known method as it straightforwardly exploits the structure of the problem and its key components to yield an optimal solution.

Towards Fully Jitterless Applications: Periodic Scheduling in Multiprocessor MCSs Using a Table-Driven Approach

In mixed criticality systems (MCSs), the time-triggered scheduling approach focuses on a special case of safety-critical embedded applications which run in a time-triggered environment. Sometimes, for these types of MCSs, perfectly periodical (i.e., jitterless) scheduling for certain critical tasks is needed. In this paper, we propose FENP_MC (Fixed Execution Non-Preemptive Mixed Criticality), a real-time, table-driven, non-preemptive scheduling method specifically adapted to mixed criticality systems which guarantees jitterless execution in a mixed criticality time-triggered environment. We also provide a multiprocessor version, namely, P_FENP_MC (Partitioned Fixed Execution Non-Preemptive Mixed Criticality), using a partitioning heuristic. Feasibility tests are proposed for both uniprocessor and homogenous multiprocessor systems. An analysis of the algorithm performance is presented in terms of success ratio and scheduling jitter by comparing it against a time-triggered and an event-driven method in a non-preemptive context.

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 the best-possible in an asymptotically sense 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 achieve the best-possible competitive ratio in an asymptotically sense when solving the non-preemptive machine minimization problem.

Reliability Aware Energy Optimized Scheduling of Non-Preemptive Periodic Real-Time Tasks on Heterogeneous Multiprocessor System

Higher reliability and lower energy consumption are conflicting, yet among the most important design objectives for the real-time systems. Moreover, in the domain of real-time systems, non-preemptive scheduling is relatively unexplored with objectives such as reliability and energy. Thus we propose an active replication based framework to schedule a set of periodic real-time tasks in the non-preemptive heterogeneous environment such that the given reliability and timing constraints are satisfied whereas the energy consumption is minimized. First, we formulate the problem as a constraint optimization problem that provides an optimal solution; however, it does not scale well. Thus, we also propose heuristics which apply reservation of processors and reallocation of jobs, to compute suboptimal solution efficiently in terms of energy consumption as well as schedulability. Heuristics make use of the interplay of task-level reliability target, reliability of replicas, number of replicas, reliability of tasks, and energy consumption. We perform an experimental study on the test cases generated by extending UUnisort algorithm [1] and observe the effect of various simulation parameters on energy consumption and schedulability.

Speeding Up the Schedulability Analysis and Priority Assignment of Sporadic Tasks Under Uniprocessor FPNS

Fixed-priority non-preemptive scheduling (FPNS) is widely used in practice because of its simplicity and predictability. This article aims to enhance the efficiency of the schedulability analysis and priority assignment of sporadic tasks under uniprocessor FPNS. To speed-up the schedulability analysis, we first improve the state-of-the-art worst-case response time analysis for uniprocessor fixed-priority non-preemptive scheduling. In addition, we present two special conditions under which the worst-case response time of a task can be analyzed from its first job, which further improves the efficiency of the analysis. To accelerate the priority assignment, we present two priority-assignment algorithms based on the improved Audsley's algorithm: improved Audsley-based longest deadline first (IA-LDF) and improved Audsley-based longest worst-case execution time first (IA-LCF). The numerical experiments show that IA-LDF and IA-LCF can lead to 31.2% and 36% decrease in runtime compared to longest deadline first (LDF) and longest worst-case execution time first (LCF), respectively.

Improved Schedulability Test for Non-Preemptive Fixed-Priority Scheduling on Multiprocessors

Non-preemptive scheduling is essential to tasks that inherently disallow any preemption and useful for tasks that exhibit extremely large preemption/migration overhead; however, studies of non-preemptive scheduling have not matured for real-time tasks subject to timing constraints. In this letter, we propose an improved schedulability test for non-preemptive fixed-priority scheduling (NP-FP), which offers timing guarantees for a set of real-time tasks executed on a multiprocessor platform. To this end, we first carefully investigate the NP-FP properties, and present an observation why the existing technique is pessimistic in calculating interference from higher-priority tasks. We then develop a new technique that tightly upper bounds the amount of the interference, and show how to incorporate the technique into the existing schedulability test. Via simulations, we demonstrate that our proposed test improves schedulability performance of NP-FP up to 18%, compared with the state-of-the-art existing tests.

Online Multi-Resource Social Welfare Maximization for Non-Preemptive Jobs

Multi-resource allocation is ubiquitous in datacenters. Usually, the datacenter scheduler associates each user with a utility function and then allocates multiple resources so as to maximize the social welfare, which is the sum of the utilities of the users. We refer to this problem as the Social Welfare Maximization (SWM) problem. Meanwhile, given the dynamic nature of datacenters, the scheduler is supposed to support non-preemptive scheduling, where jobs of users that are being processed would not be interrupted by the reconfiguration of resources. Non-preemptive solutions to SWM incorporating pricing considerations include dynamic pricing and bidding/auctions. However, both strategies are quite complex. Meanwhile, traditional Lagrange solutions to SWM does not support non-preemptive job scheduling. In this paper, we propose Adaptive Dominant Resource Fairness (ADRF), that provides near-optimal social welfare where each user is assigned an α-fair utility function and when 1 <; α ≤ 2. Based on ADRF, we propose Cumulative ADRF (C-ADRF), an online algorithm that greedily assigns the idle resources to the current poorest user, making it quite simple to schedule jobs from users non-preemptively. Compared with the polynomial or exponential form of time complexities in other SWM solutions, C-ADRF requires only O(log N) work, where N is the number of users. Extensive simulations using Google and Facebook cluster-data traces show an impressive behavior of C-ADRF in providing social welfare, only 3% and 2% away from the optimal social welfare, respectively.

Scheduling MapReduce Jobs on Identical and Unrelated Processors

We consider non-preemptive scheduling of MapReduce jobs consisting of multiple map-reduce rounds so as to minimize their average weighted completion time on identical or unrelated processor environments. For identical processors, we present LP-based O(1)-approximation algorithms, while for unrelated processors the approximation ratio naturally depends on the maximum number of rounds of any job (which is a small constant in practice). For the single-round case, we substantially improve on previously best known approximation ratios, while also we introduce into our model the crucial cost of the data shuffle phase, i.e., the cost for the transmission of intermediate data from Map to Reduce tasks. Finally, we evaluate our algorithms via simulations in the general case of unrelated processors, comparing them with a lower bound on the optimal cost of the problem as well as with a fast algorithm which combines a simple online assignment of tasks to processors with a standard scheduling policy. As we observe, for random instances that capture data locality issues, our algorithm achieves an excellent average performance.

An Energy-Aware Multiobjective Optimization Framework to Minimize Total Tardiness and Energy Cost on a Single-Machine Nonpreemptive Scheduling

Energy-aware scheduling in a manufacturing environment with real-time energy pricing is a challenging problem. The purpose of this paper is to study a nonpreemptive scheduling problem on a single-machine to minimize the total tardiness and total energy cost under time-of-use electricity tariffs, which is a mixed-integer multi-objective mathematical programming model. To achieve these objectives, we develop several new holistic genetic algorithms. The proposed model is solved via several methods including weighted sum method and multiobjective genetic algorithms based on dominance rank (GA-1), weighted sum aggregation (GA-2), dominance ranking procedure and crowding distance comparison (GA-3), and heuristic approach (GA-H). This paper illustrates that operations management, which is typically observed as a significant technique that allows manufacturing to operate in challenging data enabled environment in an industrial internet of things ecosystem, can also carefully optimize a production process to improve energy cost in order to manage environmental challenges. Thus, the findings provide information on when to start each job. We provide detailed experimental results evaluating the performance of the proposed algorithms. In a case study, we illustrate how the results of the multiobjective model could be utilized in decision making using the technique for order preference by similarity to ideal solution method.

Polynomial Time Schedulability Test for Periodic Non-Preemptive 2-Task System

Non-preemptive scheduling of tasks is often preferred in safety-critical systems because of its simplicity in implementation. But, one of the major issues with non-preemptive scheduling is that no known polynomial time schedulability condition exists. The general problem of schedulability of a set of tasks on a single processor under such scheme is known to be NP-Hard [1]. People have attempted to propose different sufficient or necessary conditions for schedulability of a set of tasks under various constrained scenarios. In this work, we explore schedulability condition for 2-task systems when the tasks are scheduled non-preemptively and periodically using work conserving model of execution. We assume that the tasks are released at the same point of time initially. We show that the proposed condition for 2-task systems can be evaluated in polynomial time.

Feasibility Analysis of Non-Preemptive Periodic Systems from Infeasibility Perspective

Due to simple implementation, non-preemptive scheduling has the advantage over preemptive counterpart when it comes to deployment of real-time systems. Accordingly, many feasibility techniques have been established to answer schedulability of the task set for non-preemptive case. The time complexity of exact condition for non-preemptive under dynamic priority assignment is of pseud-polynomial nature. Recently, efforts are made to decrease the computation cost of existing exact solutions. However, the time complexity class remains the same. In such systems, feasibility is tested by starting with highest priority task and test continues in that order until the last task is analyzed in the set. Normally, higher priority tasks rarely miss the deadline and hence, when a system is determined infeasible, it is mainly because of the low priority tasks as these tasks are assigned low priorities and can claim CPU time only when there is no pending higher priority task in the queue. In this study, we propose a mechanism that reduces the computation cost of feasibility for non-preemptive earliest deadline first scheduling algorithm by testing the infeasibility of the system in reverse priority order. In worst case, the proposed technique is not inferior for a system with low utilization that scans a task set from feasibility perspectives. On the other hand, our test exhibits better performance when the system infeasibility is tested for the system demanding higher CPU utilization. Our experimental results show that the overall computation cost, especially for the larger task sets with higher CPU demands, is significantly reduced with the proposed solution by evaluating a system from infeasibility perspective.

Simultaneous Approximation Ratios for Parallel Machine Scheduling Problems

Motivated by the problem to approximate all feasible schedules by one schedule in a given scheduling environment, we introduce in this paper the concepts of strong simultaneous approximation ratio and weak simultaneous approximation ratio. Then we study the two variants under various scheduling environments, such as non-preemptive, preemptive or fractional scheduling on identical, related or unrelated machines.

Control-schedule co-design for fast stabilization in real time systems facing repeated reconfigurations

Efficient scheduling of tasks in cyber-physical systems or internet-of-things is a challenging prospect primarily due to their demands to meet critical performance goals in the face of stringent resource constraints. In addition, to enhance ease of implementation and more efficient usage of resources, these schedulers are many-a-times restricted to be non-preemptive, where jobs once started must be continuously executed until completion. In this work, we address the following resource allocation issue. Given, (i) a set of functionalities (tasks) whose performance qualities are directly proportional to the rates at which they receive service from a resource, and (ii) a discrete set of allowable alternative execution rates for each task, the objective is to determine a non-preemptive execution schedule for the tasks with appropriately chosen rates over time, such that the performance of the overall system combining all functionalities, is optimized. In this work, performance of the system is considered to be directly proportional to the time taken to re-stabilize all functionalities within stipulated thresholds, subsequent to reconfigurations in the desired outputs of a subset of these functionalities. We first propose branch and bound based techniques for determining optimal schedules under different restrictions on the adaptability of execution rates for the tasks. However, although optimal, branch and bound based solutions incur significant computational overheads, which often make them prohibitively expensive towards online application, especially for large task-set sizes. Hence, we further propose two fast and efficient heuristic strategies to quickly obtain near optimal schedules. Experimental results show that the proposed schemes are able to achieve significant performance gain, 30–55% in case of optimal strategy and 10–50% for heuristic methods compared to traditional fixed rate execution mode.

Processor Bounding for an Efficient Non-preemptive Task Scheduling Algorithm

The scheduling problem, which is the core of all approaches related to real-time systems, has received proper attention from the research community. However, while preemptive scheduling has benefited from most of the results to date, the more difficult case of non-preemptive scheduling is still lacking similar achievements. This paper is approaching non-preemptive scheduling from two different angles. First, the number of processors that would allow a feasible schedule for a given task set is analyzed, yielding both lower and upper limits which can be determined in polynomial time. Second, a hybrid scheduling algorithm, combining two widely known techniques, namely EDF and LLF, is proposed and tested. A common feature of both objectives is the transition from a single-instance task to a periodic task. The relationships between these two cases are investigated, resulting in a better understanding of periodic behavior.

Discrete and continuous-time formulations for dealing with break periods: Preemptive and non-preemptive scheduling

This paper presents new mixed-integer linear programming (MILP) approaches for handling preemption both in discrete and continuous-time scheduling formulations. Preemption refers to the capability of interrupting the execution of a task when encountering a pre-defined break period, assuming that the task continues immediately after the end of such time window. We rely on Generalized Disjunctive Programming to derive the constraints for the continuous-time formulations and on a compact convex hull reformulation to make them computationally efficient. We investigate both the general precedence and multiple time grids representation concepts. Generalization of the discrete-time formulation is simpler, involving a change in the model parameters. Validation and comparison of the mathematical formulations is done through the solution of sixteen benchmark problems, involving instances with one to four sets of breaks. The results show that the general precedence formulation is computationally more effective for flexible flowshops, being outperformed by the discrete-time approach when considering common rather than machine-dependent breaks. For single stage plants with parallel units, the continuous multiple time grid formulation prevails.

Energy and time constrained scheduling for optimized quality of service

Minimizing the total completion time has practical application in providing the best quality of service. We consider energy and time constrained task scheduling for minimized total completion time and minimized total energy consumption. We show that there is a polynomial time algorithm to find a nonpreemptive schedule with the minimum total completion time for a given total energy consumption constraint. Similarly, there is a polynomial time algorithm to find a nonpreemptive schedule with the minimum total energy consumption for a given total completion time constraint.