An evolutionary approach to multiprocessor scheduling of dependent tasks

The scheduling of application tasks is a problem that occurs in all multiprocessor systems. This problem has been shown to be NP-hard if the tasks are not independent but are interrelated by mutual exclusion and precedence constraints.

This paper presents an approach for pre-runtime scheduling of periodic tasks on multiple processors for a real-time system that must meet hard deadlines. The tasks can be related to each other by mutual exclusion and precedence forming an acyclic graph. The proposed scheduler is based on genetic algorithms, which relieves the user from knowing how to construct a solution. Consequently, the paper focuses on the problem encoding, i.e., the representation of the problem by genes and chromosomes, and the derivation of an appropriate fitness function. The main benefit of the approach is that it is scalable to any number of processors and can easily be extended to incorporate further requirements.     

Performance of local search heuristics on scheduling a class of pipelined multiprocessor tasks

This paper presents the evaluation of the solution quality of heuristic algorithms developed for scheduling multiprocessor tasks for a class of multiprocessor architectures designed to exploit temporal and spatial parallelism simultaneously. More specifically, we deal with multi-level or partitionable architectures where MIMD parallelism and multiprogramming support are the two main characteristics of the system. We investigate scheduling a number of pipelined multiprocessor tasks with arbitrary processing times and arbitrary processor requirements in this system. The scheduling problem consists of two interrelated sub-problems, which are finding a sequence of pipelined multiprocessor tasks on a processor and finding a proper mapping of tasks to the processors that are already being sequenced. For the solution of the second problem, various techniques are available. However, the problem remains of generating a feasible sequence for the pipelined operations. We employed three well-known local search heuristic algorithms that are known to be robust methods applicable to various optimization problems. These are Simulated Annealing, Tabu Search, and Genetic Algorithms. We then conduct computational experiments and evaluate the reduction achieved in completion time by each heuristic. We have also compared the results with well-known simple list-based heuristics.     

An optimal boundary fair scheduling algorithm for multiprocessor real-time systems

With the emergence of multicore processors, the research on multiprocessor real-time scheduling has caught more researchers’ attention recently. Although the topic has been studied for decades, it is still an evolving research field with many open problems. In this work, focusing on periodic real-time tasks with quantum-based computation requirements and implicit deadlines, we propose a novel optimal scheduling algorithm, namely boundary fair (Bfair), which can achieve full system utilization as the well-known Pfair scheduling algorithms. However, different from Pfair algorithms that make scheduling decisions and enforce proportional progress (i.e., fairness) for all tasks at each and every time unit, Bfair makes scheduling decisions and enforces fairness to tasks only at tasks’ period boundaries (i.e., deadlines of periodic tasks). The correctness of the Bfair algorithm to meet the deadlines of all tasks’ instances is formally proved and its performance is evaluated through extensive simulations. The results show that, compared to that of Pfair algorithms, Bfair can significantly reduce the number of scheduling points (by up to 94%) and the overhead of Bfair at each scheduling point is comparable to that of the most efficient Pfair algorithm (i.e., PD²). Moreover, by aggregating the time allocation of tasks for the time interval between consecutive period boundaries, the resulting Bfair schedule can dramatically reduce the number of required context switches and task migrations (as much as 82% and 85%, respectively) when compared to those of Pfair schedules, which in turn reduces the run-time overhead of the system.     

Utility accrual real-time scheduling for multiprocessor embedded systems

We present the first Utility Accrual (or UA) real-time scheduling algorithm for multiprocessors, called the global Multiprocessor Utility Accrual scheduling algorithm (or gMUA). The algorithm considers an application model where real-time activities are subject to time/utility function time constraints, variable execution time demands, and resource overloads where the total activity utilization demand exceeds the total capacity of all processors. We consider the scheduling objective of (1) probabilistically satisfying lower bounds on each activity’s maximum utility, and (2) maximizing the system-wide, total accrued utility. We establish several properties of gMUA including optimal total utility (for a special case), conditions under which individual activity utility lower bounds are satisfied, a lower bound on system-wide total accrued utility, and bounded sensitivity for assurances to variations in execution time demand estimates. Finally, our simulation experiments validate our analytical results and confirm the algorithm’s effectiveness.     

Power-aware scheduling algorithms for sporadic tasks in real-time systems

In this paper, we consider the canonical sporadic task model with the system-wide energy management problem. Our solution uses a generalized power model, in which the static power and the dynamic power are considered. We present a static solution to schedule the sporadic task set, assuming worst-case execution time for each sporadic tasks release, and propose a dynamic solution to reclaim the slacks left by the earlier completion of tasks than their worst-case estimations. The experimental results show that the proposed static algorithm can reduce the energy consumption by 20.63%–89.70% over the EDF* algorithm and the dynamic algorithm consumes 2.06%–24.89% less energy than that of the existing DVS algorithm.     

Minimizing migrations in fair multiprocessor scheduling of persistent tasks

Suppose that we are given n persistent tasks (jobs) that need to be executed in an equitable way on m processors (machines). Each machine is capable of performing one unit of work in each integral time unit and each job may be executed on at most one machine at a time. The schedule needs to specify which job is to be executed on each machine in each time window. The goal is to find a schedule that minimizes job migrations between machines while guaranteeing a fair schedule. We measure the fairness by the drift d defined as the maximum difference between the execution times accumulated by any two jobs. As jobs are persistent we measure the quality of the schedule by the ratio of the number of migrations to time windows. We show a tradeoff between the drift and the number of migrations. Let n = qm + r with 0 < r < m (the problem is trivial for n ≤ m and for r = 0). For any d ≥ 1, we show a schedule that achieves a migration ratio less than r(m − r)/(n(q(d − 1)) + ∊ > 0; namely, it asymptotically requires r(m − r) job migrations every n(q(d − 1) + 1) time windows. We show how to implement the schedule efficiently. We prove that our algorithm is almost optimal by proving a lower bound of r(m − r)/(nqd) on the migration ratio. We also give a more complicated schedule that matches the lower bound for a special case when 2q ≤ d and m = 2r. Our algorithms can be extended to the dynamic case in which jobs enter and leave the system over time.     

Power-aware fixed priority scheduling for sporadic tasks in hard real-time systems

In this paper, we consider the generalized power model in which the focus is the dynamic power and the static power, and we study the problem of the canonical sporadic task scheduling based on the rate-monotonic (RM) scheme. Moreover, we combine with the dynamic voltage scaling (DVS) and dynamic power management (DPM). We present a static low power sporadic tasks scheduling algorithm (SSTLPSA), assuming that each task presents its worst-case work-load to the processor at every instance. In addition, a more energy efficient approach called a dynamic low power sporadic tasks scheduling algorithm (DSTLPSA) is proposed, based on reclaiming the dynamic slack and adjusting the speed of other tasks on-the-fly in order to reduce energy consumption while still meeting the deadlines. The experimental results show that the SSTLPSA algorithm consumes 26.55–38.67% less energy than that of the RM algorithm and the DSTLPSA algorithm reduces the energy consumption up to 18.38–30.51% over the existing DVS algorithm.     

Schedulability issues for EDZL scheduling on real-time multiprocessor systems

EDZL (Earliest Deadline first until Zero Laxity) is an efficient and practical scheduling algorithm on multiprocessor systems. It has a comparable number of context switch to EDF (Earliest Deadline First) and its schedulable utilization seems to be higher than that of EDF. Previously, there was a conjecture that the utilization bound of EDZL is 3m/4=0.75m for m processors. In this paper, we disprove this conjecture and show that the utilization bound of EDZL is no greater than m(1−1/e)≈0.6321m, where e≈2.718 is the Euler's number.     

A new algorithm for scheduling periodic, real-time tasks

We consider the problem of preemptively scheduling a set of periodic, real-time tasks on a multiprocessor computer system. We give a new scheduling algorithm, the so-called Slack-Time Algorithm, and show that it is more effective than the known Deadline Algorithm. We also give an (exponential-time) algorithm to decide if a task system is schedulable by the Slack-Time or the Deadline Algorithm. The same algorithm can also be used to decide if a task system is schedulable by any given fixed-priority scheduling algorithm. This resolves an open question posed by Leung and Whitehead. Finally, it is shown that the problem of deciding if a task system is schedulable by the Slack-Time, the Deadline, or any given fixed-priority scheduling algorithm is co-NP-hard for each fixedm.     

An improved Hybrid Quantum-Inspired Genetic Algorithm (HQIGA) for scheduling of real-time task in multiprocessor system

This article concerns an efficient real-time task scheduling assisted by Hybrid Quantum-Inspired Genetic Algorithm (HQIGA) in multiprocessor environment. Relying on concepts and the principles of quantum mechanics, HQIGA explores the computing power of quantum computation. To drive schedule toward better convergence, HQIGA operates using rotation gate for exploration of variable chromosomes described by qubits in Hilbert hyperspace. A fitness function associated with popularly known heuristic earliest deadline first (EDF) is employed and random key distribution is adopted to convert the qubits chromosomes to valid schedule solutions. In addition to this, permutation based trimming technique is applied to diversify the population which yields good quality schedules. To establish the effectiveness of the suggested HQIGA, it demonstrates using various number of real-time tasks and processors along with arbitrary processing time. Simulation result shows that HQIGA outperforms the classical genetic algorithm (CGA) and Hybrid Particle Swarm Optimization (HPSO) in terms of fitness values obtained using less number of generations and also it improves the scheduling time significantly. HQIGA is also tested separately with the heuristic Shortest Computation Time First (SCTF) technique to show the superiority of EDF over SCTF.     

Transient solution of multiprocessor systems with state-dependent arrivals

In this paper, the transient solution is obtained for a multiprocessor system with multiple Poisson streams of task and exponential execution times. Each task requires exactly one processor for its execution and the scheduling policy is FCFS. The scheduler schedules a newly arriving task into any one of the idle processors, and the task is rejected if there is no idle processor. For this model, the exact time-dependent solution of system size probabilities at various streams, their means, variances and correlations are obtained using the properties of tridiagonal determinants.     

LBBA: An efficient online benefit-aware multiprocessor scheduling for QoS via online choice of approximation algorithms

Maximizing the benefit gained by soft real-time jobs in many applications and embedded systems is highly needed to provide an acceptable QoS (Quality of Service). This paper considers a benefit model for on-line preemptive multiprocessor scheduling. The goal is to maximize the total benefit gained by the jobs that meet their deadlines. This method prioritizes the jobs using their benefit density functions and schedules them in a real-time basis. We propose an online choice of two approximation algorithms in order to partition the jobs among identical processors at the time of their arrival without using any statistics. Our analysis and experiments show that we are able to maximize the gained benefit and decrease the computational complexity (compared to existing algorithms) while minimizing makespan (response time, also referred to as cost), with fewer missed deadlines and more balanced usage of processors. Our solution is applicable to a wide variety of soft real-time applications and embedded systems such as, but not limited to multimedia applications, medical monitoring systems or those with higher utilization such as bursty hosting servers.¹     

Deadline-based scheduling of periodic task systems on multiprocessors

We consider the problem of scheduling periodic task systems on multiprocessors and present a deadline-based scheduling algorithm for solving this problem. We show that our algorithm successfully schedules on m processors any periodic task system with utilization at most m²/(2m−1).     

实时系统中弹性调度策略

弹性调度面向负载可变的实时系统,通过动态调整任务属性以满足系统的灵活性要求,是一种高效的任务调度策略。针对弹性调度研究中的成果及问题,概述了弹性调度的研究背景,从任务模型、调度模型以及调度算法三个方面对弹性调度的国内外研究进展进行综述,探讨当前研究中存在的问题,并对弹性调度未来研究工作进行分析和展望。     

Supervisory control for fault-tolerant scheduling of real-time multiprocessor systems with aperiodic tasks

Supervisory control theory is a well-established theoretical framework for feedback control of discrete event systems whose behaviours are described by automata and formal languages. In this article, we propose a formal constructive method for optimal fault-tolerant scheduling of real-time multiprocessor systems based on supervisory control theory. In particular, we consider a fault-tolerant and schedulable language which is an achievable set of event sequences meeting given deadlines of accepted aperiodic tasks in the presence of processor faults. Such a language eventually provides information on whether a scheduler (i.e., supervisor) should accept or reject a newly arrived aperiodic task. Moreover, we present a systematic way of computing a largest fault-tolerant and schedulable language which is optimal in that it contains all achievable deadline-meeting sequences.     

Improved bounds for hybrid flow shop scheduling with multiprocessor tasks

In this paper, we investigate the problem of minimizing makespan in a multistage hybrid flow-shop scheduling with multiprocessor tasks. To generate high-quality approximate solutions to this challenging NP-hard problem, we propose a discrepancy search heuristic that is based on the new concept of adjacent discrepancies. Moreover, we describe a new lower bound based on the concept of dual feasible functions. The proposed lower and upper bounds are assessed through computational experiments conducted on 300 benchmark instances with up to 100 jobs and 8 stages. For these instances, we provide evidence that the proposed bounds consistently outperform the best existing ones. In particular, the proposed heuristic successfully improved the best known solution of 75 benchmark instances.     

Energy-aware task migration for multiprocessor real-time systems

A task migration method is proposed for energy savings in multiprocessor real-time systems. The method is based on the portioned scheduling technique which classifies each task as a fixed task or a migratable task. The basic task migration problem with specific parameters is formulated as a linear programming problem to minimize average power. Then, the method is extended to more general case with a complete migration algorithm. Moreover, a scheduling algorithm is proposed for migratable tasks. Simulation results on two processor models demonstrated significant energy savings over existing methods.     

A comparison of multiprocessor task scheduling algorithms with communication costs

Both parallel and distributed network environment systems play a vital role in the improvement of high performance computing. Of primary concern when analyzing these systems is multiprocessor task scheduling. Therefore, this paper addresses the challenge of multiprocessor task scheduling parallel programs, represented as directed acyclic task graph (DAG), for execution on multiprocessors with communication costs. Moreover, we investigate an alternative paradigm, where genetic algorithms (GAs) have recently received much attention, which is a class of robust stochastic search algorithms for various combinatorial optimization problems. We design the new encoding mechanism with a multi-functional chromosome that uses the priority representation—the so-called priority-based multi-chromosome (PMC). PMC can efficiently represent a task schedule and assign tasks to processors. The proposed priority-based GA has show effective performance in various parallel environments for scheduling methods.     

Nonpreemptive scheduling of periodic tasks in uni- and multiprocessor systems

In this paper we study the problem of scheduling a set of periodic tasks nonpreemptively in hard-real-time systems, where it is critical for all requests of the tasks to be processed in time. A taskT is characterized by itsarrival time A, itsperiod P, and itsexecution time C. Starting fromA, a new request ofT arrives in everyP units of time, requestingC units of processing time, and itsdeadline coincides with the arrival of the next request ofT. All requests must be processed nonpreemptively to meet their corresponding deadlines. We show that the problem of testing the feasibility of a given task set {T ¹,T ²,,T ⁿ} satisfyingP ₁₊₁=k_i p_i, wherek _i; is an integer 1 for 1i n–1, on a single processor is NP-hard in the strong sense, even if all tasks have the same arrival time. For task sets satisfyingP ⁱ⁺¹=K Pⁱ, whereK is an integer 2 for 1 i n–1 and all tasks have the same arrival time, we present linear-time (in the number of requests) optimal scheduling algorithms as well as linear-time (in the number of tasks, i.e.,n) algorithms for testing feasibility in both uniprocessor and multiprocessor systems. We also extend our results to more general task sets.