Minimizing Task Preemptions and Migrations in Multiprocessor Optimal Real-Time Schedules

We present a jointly optimal selection and scheduling scheme for the lossy transmission of frames governed by a dependency relation and a delay constraint over a link with limited capacity. A main application for this is scalable video streaming. Our objective is to select a subset of frames and decide their transmission schedule such that the overall video quality at the receiver is maximized. The problem is solved for two of the most common classes of dependency structures for video encoding, which include as a special case the popular hierarchical dyadic structure. We formally characterize the structural properties of an optimal transmission schedule in terms of frame dependency. It is shown that regardless of the subset of frames selected for transmission, any optimal schedule has an equivalent canonical form that is a subsequence of a unique universal sequence containing all frames. The canonical form can be computed efficiently through the construction of a dependency tree. This leads to separable but jointly optimal frame selection and scheduling algorithms that have quadratic computational complexity in the number of frames. Simulation with video traces demonstrates that the optimal scheme can substantially outperform existing suboptimal alternatives.

Two-stage heuristic procedure for scheduling job shops

The maximum matching algorithm for bipartite graphs can be used to provide optimal scheduling for crossbar based interconnection networks. Unfortunately, maximum matching requires O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) time for an N times N communication system, which has limited its application to real-time network scheduling. In this paper, we show how maximum matching can be reformulated in terms of Boolean operations rather than the more traditional formulations. By taking advantage of the inherent parallelism available in custom hardware design, we introduce three maximum matching implementations in hardware and show how we can trade design complexity for performance. Specifically, we examine a pure logic scheduler with three dimensions of parallelism, a matrix scheduler with two dimensions of parallelism and a vector scheduler with one dimension of parallelism. These designs reduce the algorithmic time complexity down to O(1), O(K), and O(KN), respectively, where K is the number of optimization steps. While an optimal scheduling algorithm requires K=2N-1 steps, our simulation results show that the scheduler can achieve 99% of the optimal schedule when K=9. We examine hardware and time complexity of these architectures for crossbar sizes of up to N=1024. Using FPGA synthesis results, we show that a greedy schedule for various sized crossbars, ranging from 8 times 8 to 256 times 256, can be optimized in less than 20 ns per optimization step. For crossbars reaching 1024 times 1024 the scheduling can be completed in approximately 10 s with current technology and could reach under 90 ns with future technologies

The maximum matching algorithm for bipartite graphs can be used to provide optimal scheduling for crossbar based interconnection networks. Unfortunately, maximum matching requires O(N3) time for an N x N communication system, which has limited its application to real-time network scheduling. In this paper, we show how maximum matching can be reformulated in terms of Boolean operations rather than the more traditional formulations. By taking advantage of the inherent parallelism available in custom hardware design, we introduce three Maximum Matching implementations in hardware and show how we can trade design complexity for performance. Specifically, we examine a Pure Logic Scheduler with three dimensions of parallelism, a Matrix Scheduler with two dimensions of parallelism and a Vector Scheduler with one dimension of parallelism. These designs reduce the algorithmic time complexity down to O(1), O(K), and O(KN), respectively, where K is the number of optimization steps. While an optimal scheduling algorithm requires K = 2N -- 1 steps, our simulation results show that the scheduler can achieve 99% of the optimal schedule when K = 9. We examine hardware and time complexity of these architectures for crossbar sizes of up to N = 1024. Using FPGA synthesis results, we show that a greedy schedule for various sized crossbars, ranging from 8 x 8 to 256 x 256, can be optimized in less than 20 ns per optimization step. For crossbars reaching 1024 x 1024 the scheduling can be completed in approximately 10 μs with current technology and could reach under 90 ns with future technologies.

SummaryModern power systems are being shifted its attention towards distributed generations (DGs). DGs have allured more concern as an auspicious opportunity with considerable economic profits. To minimize the power generation costs of DGs, day‐to‐day operation scheduling is essential. The role of this study is to offer an optimal operation schedule for DG with several energy sources including renewable energy sources (RES), considering economic facets. In order to achieve the cost minimization along with optimal scheduling, an objection function has been formulated and solved using the optimization algorithms. This study aims to present the applications of differential evolution (DE) algorithm and its variants such as opposition‐based differential evolution (ODE), self‐adaptive differential evolution (SaDE), improved differential evolution (IDE), and cultivated differential evolution (CuDE) for scheduling DG optimally. A scheme for optimal scheduling of thermal, wind power, and solar PV generators has been evaluated. The simulations have been carried out on IEEE 14 bus system, IEEE 30 bus system, IEEE 57 bus system, and Tamil Nadu Generation and Distribution Corporation Limited (TANGEDCO), as a real part of 62 bus Indian utility system (IUS). The novelty of this study lies in simulating a real‐time system for solving optimal scheduling problem, in that way helping decision makers to choose the optimal operation points. The results indicate that the SaDE outperformed other DE variants by giving the best fitness value and convergence rate.

The use of real-time scheduling methods to coordinate a set of power loads is being explored in the field of Cyber-Physical Energy Systems, with the goal of optimizing the aggregated peak load of power used by many electric loads. Real-time scheduling has attractive features in this domain. Thanks to its inherent resource optimization, which limits the number of concurrent tasks that are running at the same time, real-time scheduling provides direct benefits to peak load optimization. This paper shows the combined use of a two-dimensional bin-packing method and an optimal multi-processor real-time scheduling algorithm to coordinate the activation of electric loads. The result is an effective global scheduling approach where the activation of loads is organized into a pattern that takes into account the timing constraints of the loads and the actual combination of active loads. The validation is done by scheduling a set of thermal loads (heaters) in a building, with accurately modeled temperature dynamics. The proposed method is shown to achieve a significant peak load reduction, up to around 70%, w.r.t. the traditional thermostat controller.

Scheduling tasks is an essential requirement in most real-time and embedded systems, but leads to unwanted central processing unit (CPU) overheads. The authors present a real-time schedulability algorithm for preemptable, asynchronous and periodic reconfigurable task systems with arbitrary relative deadlines, scheduled on a uniprocessor by an optimal scheduling algorithm based on the earliest deadline first (EDF) principles and on the dynamic reconfiguration. A reconfiguration scenario is assumed to be a dynamic automatic operation allowing addition, removal or update of operating system’s (OS) functional asynchronous tasks. When such a scenario is applied to save the system at the occurrence of hardware-software faults, or to improve its performance, some real-time properties can be violated. The authors propose an intelligent agent-based architecture where a software agent is used to satisfy the user requirements and to respect time constraints. The agent dynamically provides precious technical solutions for users when these constraints are not verified, by removing tasks according to predefined heuristic, or by modifying the worst case execution times (WCETs), periods, and deadlines of tasks in order to meet deadlines and to minimize their response time. They implement the agent to support these services which are applied to a Blackberry Bold 9700 and to a Volvo system and present and discuss the results of experiments.

An aggregate scheduling problem for a flexible manufacturing system which consists of a machining and an assembly subsystem is presented. The aggregate schedule developed is used as an input to a real-time scheduling problem discussed previously by the author (Proc. 2nd ORSA/TIMS Conf. on Flexible Manuf. Syst: Oper. Res. Methods and Appl., Elsevier NY, 1986, pp.521-32). Although features of the flexible manufacturing environment are not explicit at the aggregate scheduling level, they are incorporated at the real-time scheduling level. The single-product and N-product scheduling problems are considered. To solve the problems two optimal scheduling algorithms are developed. Each algorithm is illustrated with a numerical example. The results are also applicable to the single-batch and N-batch scheduling problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In multitasking real-time systems, the choice of scheduling algorithm is an important factor to ensure that response time requirements are met while maximising limited system resources. Two popular scheduling algorithms include fixed priority (FP) and earliest deadline first (EDF). While they have been studied in great detail before, they have not been compared when taking into account cache related pre-emption delays (CRPD). Memory and cache are split into a number of blocks containing instructions and data. During a pre-emption, cache blocks from the pre-empting task can evict those of the pre-empted task. When the pre-empted task is resumed, if it then has to re-load the evicted blocks, CRPD are introduced which then affect the schedulability of the task. In this paper we compare FP and EDF scheduling algorithms in the presence of CRPD using the state-of-the-art CRPD analysis. We find that when CRPD is accounted for, the performance gains offered by EDF over FP, while still notable, are diminished. Furthermore, we find that under scenarios that cause relatively high CRPD, task layout optimisation techniques can be applied to allow FP to schedule tasksets at a similar processor utilisation to EDF. Thus making the choice of the task layout in memory as important as the choice of scheduling algorithm. This is very relevant for industry, as it is much cheaper and simpler to adjust the task layout through the linker than it is to switch the scheduling algorithm.

In this paper, we derive bounds on performance guarantees of online algorithms for real-time preemptive scheduling of jobs with deadlines on K machines when jobs are characterized in terms of their minimum stretch factor α (or, equivalently, their maximum execution rate r =1 /α). We consider two well known preemptive models that are of interest from practical applications: the hard real-time scheduling model in which a job must be completed if it was admitted for execution by the online scheduler, and the firm real-time scheduling model in which the scheduler is allowed not to complete a job even if it was admitted for execution by the online scheduler. In both models, the objective is to maximize the sum of execution times of the jobs that were executed to completion, preemption is allowed, and the online scheduler must immediately decide, whenever a job arrives, whether to admit it for execution or reject it. We measure the competitive ratio of any online algorithm as the ratio of the value of the objective function obtained by this algorithm to that of the best possible offline algorithm. We show that no online algorithm can have a competitive ratio greater than 1 − (1/α )+ e for hard real-time scheduling with K ≥ 1 machines and greater than 1 − (3/(4� α� )) + e for firm real-time scheduling on a single machine, where e> 0 may be arbitrarily small, even if the algorithm is allowed to know the value of α in advance. On the other hand, we exhibit a simple online scheduler that achieves a competitive ratio of at least 1 − (1/α) in either of these models with K machines. The performance guarantee of our simple scheduler shows that it is in fact an optimal scheduler for hard real-time scheduling with K machines. We also describe an alternative scheduler for firm real-time scheduling on a single machine in which the competitive ratio does not go to zero as α approaches 1. Both of our schedulers do not know the value of α in advance.

Task Scheduling is one of the key elements in any distributed-memory machine (DMM), and an efficient algorithm can help reduce the interprocessor communication time. As optimal scheduling of tasks to DMMs is a strong NP-hard problem, many heuristic algorithms have been introduced in the literature. This paper presents a Task Duplication based Scheduling (TDS) algorithm which can schedule directed acyclic graphs (DAGs) with a complexity of O(|V|/sup 2/), where |V| is the number of tasks in the DAG. This algorithm generates an optimal schedule for a class of DAGs which satisfy a simple cost relationship. The performance of the algorithm has been observed by its application to some practical DAGs, and by comparing it with other existing scheduling schemes in terms of the schedule length and algorithm complexity.

An optimal scheduling algorithm for minimizing the computing period of cyclic synchronous tasks on multiprocessors

Timed Petri nets (TPNs) have been widely used for modeling discrete-event systems of diverse manufacturing and service industries. In this article, we introduce a reachability tree-based optimization algorithm to optimize cyclic schedules of TPNs. In particular, we focus on a special class of cyclic schedules that are referred to as one-cyclic schedules, i.e., the algorithm efficiently finds the optimal one-cyclic transition firing schedule of a TPN. The proposed scheduling method can be robustly applied and extended to a number of different scheduling models since the methodology is not bounded to a specific domain. To enhance the computational performance, we establish a set of transition ordering constraints that can reduce the tree size during the search procedure. We evaluate the computational efficiency of the suggested algorithm by examining robotized manufacturing systems where one-cyclic schedules are popularly being used. It is numerically shown that the proposed algorithm is computationally more efficient than the previously studied Petri net-based optimization methods. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Resource scheduling is one of the most important managerial issues in diverse industrial systems. An optimal scheduling method for a certain industrial system is often locally developed by utilizing domain-specific operational properties. Although such domain-dependent knowledge can contribute to enhancing the computational efficiency of an optimization method, such an approach has a weak point that the method might not be applicable to scheduling problems of different industrial fields. Our motivation is to develop an algorithm for optimizing steady-state schedules that can be robustly applied for various types of discrete-event systems. The algorithm is developed on the basis of the Petri net modeling framework as it is widely being used for describing cyclic behaviors of diverse manufacturing systems, service systems, and social systems. It is experimentally shown that the proposed algorithm is computationally efficient compared with the existing cyclic scheduling methods.

This chapter deals with Reconfigurable Uniprocessor embedded Real-Time Systems to be classically implemented by different OS tasks that we suppose independent, asynchronous, and periodic in order to meet functional and temporal properties described in user requirements. The authors define a schedulability algorithm for preemptable, asynchronous, and periodic reconfigurable task systems with arbitrary relative deadlines, scheduled on a uniprocessor by an optimal scheduling algorithm based on the EDF principles and on the dynamic reconfiguration. Two forms of automatic reconfigurations are assumed to be applied at run-time: Addition-Remove of tasks and just modifications of their temporal parameters: WCET and/or Periods. Nevertheless, when such a scenario is applied to save the system at the occurrence of hardware-software faults, or to improve its performance, some real-time properties can be violated. The authors define a new semantic of the reconfiguration where a crucial criterion to consider is the automatic improvement of the system’s feasibility at run-time by using an Intelligent Agent that automatically checks the system’s feasibility after any reconfiguration scenario to verify if all tasks meet the required deadlines. Indeed, if a reconfiguration scenario is applied at run-time, then the Intelligent Agent dynamically provides otherwise precious technical solutions for users to remove some tasks according to predefined heuristic (based on soft or hard task), or by modifying the Worst Case Execution Times (WCETs), periods, and/or deadlines of tasks that violate corresponding constraints by new ones, in order to meet deadlines and to minimize their response time. To handle all possible reconfiguration solutions, they propose an agent-based architecture that applies automatic reconfigurations in order to re-obtain the system’s feasibility and to satisfy user requirements. Therefore, the authors developed the tool RT-Reconfiguration to support these contributions that they apply to a Blackberry Bold 9700 and to a Volvo system as running example systems and we apply the Real-Time Simulator Cheddar to check the whole system behavior and to evaluate the performance of the algorithm (detailed descriptions are available at the Website: http://beru.univ-brest.fr/~singhoff/cheddar). The authors present simulations of this architecture where they evaluate the agent that they implemented. In addition, the authors present and discuss the results of experiments that compare the accuracy and the performance of their algorithm with others.

This article presents the first optimal algorithm for trace scheduling. The trace is a global scheduling region used by compilers to exploit instruction-level parallelism across basic block boundaries. Several heuristic techniques have been proposed for trace scheduling, but the precision of these techniques has not been studied relative to optimality. This article describes a technique for finding provably optimal trace schedules, where optimality is defined in terms of a weighted sum of schedule lengths across all code paths in a trace. The optimal algorithm uses branch-and-bound enumeration to efficiently explore the entire solution space. Experimental evaluation of the algorithm shows that, with a time limit of 1 s per problem, 91% of the hard trace scheduling problems in the SPEC CPU 2006 Integer Benchmarks are solved optimally. For 58% of these hard problems, the optimal schedule is improved compared to that produced by a heuristic scheduler with a geometric mean improvement of 3.2% in weighted schedule length and 18% in compensation code size.