A non-preemptive scheduling algorithm for soft real-time systems

Real-time systems are often designed using preemptive scheduling and worst-case execution time estimates to guarantee the execution of high priority tasks. There is, however, an interest in exploring non-preemptive scheduling models for real-time systems, particularly for soft real-time multimedia applications. In this paper, we propose a new algorithm that uses multiple scheduling strategies for efficient non-preemptive scheduling of tasks. Our goal is to improve the success ratio of the well-known Earliest Deadline First (EDF) approach when the load on the system is very high and to improve the overall performance in both underloaded and overloaded conditions. Our approach, known as group-EDF (gEDF) is based on dynamic grouping of tasks with deadlines that are very close to each other, and using Shortest Job First (SJF) technique to schedule tasks within the group. We will present results comparing gEDF with other real-time algorithms including, EDF, Best-effort, and Guarantee, by using randomly generated tasks with varying execution times, release times, deadlines and tolerance to missing deadlines, under varying workloads. We believe that grouping tasks dynamically with similar deadlines and utilizing a secondary criteria, such as minimizing the total execution time (or other metrics such as power or resource availability) for scheduling tasks within a group, can lead to new and more efficient real-time scheduling algorithms.     

Dynamic non-preemptive single machine scheduling

Considering a dynamic single machine problem in which operations cannot be split, we first develop a decision theory based heuristic called DT-TD (Decision Theory-Tactically Delayed) of computational complexity O(n²). Using a simple look-ahead procedure, it produces, actically delayed (TD) schedules. We then develop a branch-and-bound (BB) algorithm (which uses DT-TD to obtain the initial upper bound) to obtain the optimum schedule. The optimum schedules are examined to identify conditions where TD schedules are necessary. Results based on 540 test problems suggest that TD schedules are important, for job shop scheduling under the range of conditions examined, when due dates are arbitrary and utilization is low. Additional test results indicate that the difference between the optimum schedule and the optimum non-delay schedule could be substantial. Finally, the performance of the DT-TD heuristic is analyzed by comparing its solution to the optimum solution obtained using the BB algorithm. The results indicate that the DT-TD heuristic is effective.     

A decomposition approach to non-preemptive real-time scheduling

Consider the problem of scheduling a set ofn tasks on a uniprocessor such that a feasible schedule that satisfies each task's time constraints is generated. Traditionally, researchers have looked at all the tasks as a group and applied heuristic or enumeration search to it. We propose a new approach called thedecomposition scheduling where tasks are decomposed into a sequence of subsets. The subsets are scheduled independently, in the order of the sequence. It is proved that a feasible schedule can be generated as long as one exists for the tasks. In addition, the overall scheduling cost is reduced to the sum of the scheduling costs of the tasks in each subset.Simulation experiments were conducted to analyze the performance of decomposition scheduling approach. The results show that in many cases decomposition scheduling performs better than the traditional branch-and-bound algorithms in terms of scheduling cost, and heuristic algorithms in terms of percentage of finding feasible schedules over randomly-generated task sets.     

Precautious-RM: a predictable non-preemptive scheduling algorithm for harmonic tasks

A major requirement of many real-time embedded systems is to have time-predictable interaction with the environment. More specifically, they need fixed or small sampling and I/O delays, and they cannot cope with large delay jitters. Non-preemptive execution is a known method to reduce the latter delay; however, the corresponding scheduling problem is NP-Hard for periodic tasks. In this paper, we present Precautious-RM as a predictable linear-time online non-preemptive scheduling algorithm for harmonic tasks which can also deal with the former delay, namely sampling delay. We derive conditions of optimality of Precautious-RM and show that satisfying those conditions, tight bounds for best- and worst-case response times of the tasks can be calculated in polynomial-time. More importantly, response time jitter of the tasks is analyzed and it is proven that under specific conditions, each task has either one or two values for response time, which leads to improving the predictability of the system interaction with the environment. Simulation results demonstrate efficiency of Precautious-RM in increasing accuracy of control applications.     

Line search method for solving a non-preemptive strictly periodic scheduling problem

We study a non-preemptive strictly periodic scheduling problem. This problem arises for example in the avionic field where a set of \(N\) periodic tasks (measure of a sensor, data presentation, etc.) has to be scheduled on \(P\) processors distributed on the plane. In this article, we consider an existing heuristic which is based on the notion of equilibrium. Following a game theory analogy, each task tries successively to optimize its own schedule and, therefore, to produce the best response, given the other schedules. This iterative process continues until an equilibrium is reached. We present a new method to compute the best response which significantly improves the previously proposed heuristic, and compares favorably with MILP solutions.     

Preemptive and non-preemptive scheduling of optical switches with configuration delay

Utilizing optical technologies for the design of packet switches and routers offers several advantages in terms of scalability, high bandwidth, power consumption, and cost. However, the configuration delays of optical crossbars are much longer than that of the electronic counterpart, which makes the conventional slot-by-slot scheduling methods no longer the feasible solution. Therefore, some tradeoff must be found between the empty time slots and configuration overhead. This paper classifies such scheduling problems into preemptive and non-preemptive scenarios, each has its own advantages and disadvantages. Although non-preemptive scheduling is inherently not good at achieving the above-mentioned tradeoff, it is shown, however, that the proposed maximum weight matching (MWM) based greedy algorithm is guaranteed to achieve an approximation 2 for arbitrary configuration delay, and with a relatively low time complexity O(N2). For preemptive scheduling, a novel 2-approximation heuristic is presented. Each time in finding a switch configuration, the 2-approximation heuristic guarantees the covering cost of the remaining traffic matrix to have 2-approximation. Simulation results demonstrate that 2-approximation heuristic (1) performs close to the optimal scheduling, and (2) outperforms ADJUST and DOUBLE in terms of traffic transmission delay and time complexity.     

Learning and backtracking in non-preemptive scheduling of tasks under timing constraints

We propose two novel heuristic search techniques to address the problem of scheduling tasks under hard timing constraints on a single processor architecture. The underlying problem is NP-hard in the strong sense and it is a fundamental challenge in feedback-control theory and automated cybernetics. The proposed techniques are a learning-based approaches and they take much less memory space. A partial feasible schedule is maintained and extended over a repeated problem solving trials, previously assigned priorities are refined according to the gained information about the problem to lead the convergence to a complete feasible schedule if one exists. First, we present the learning in hard-real-time with single learning (LHRTS-SL) algorithm where a single learning function is utilized, then we discuss its drawback and we propose the LHRTS with double learning algorithm in which a second learning function is integrated to cope up with LHRTS-SL drawback. Experimental results show the efficiency of the proposed techniques in terms of success ratio when used to schedule randomly generated problem instances.     

Genetic algorithm with fuzzy logic controller for preemptive and non-preemptive job-shop scheduling problems

In this paper, we propose a new genetic algorithm (GA) with fuzzy logic controller (FLC) for dealing with preemptive job-shop scheduling problems (p-JSP) and non-preemptive job-shop scheduling problems (np-JSP). The proposed algorithm considers the preemptive cases of activities among jobs under single machine scheduling problems. For these preemptive cases, we first use constraint programming and secondly develop a new gene representation method, a new crossover and mutation operators in the proposed algorithm.However, the proposed algorithm, as conventional GA, also has a weakness that takes so much time for the fine-tuning of genetic parameters. FLC can be used for regulating these parameters.In this paper, FLC is used to adaptively regulate the crossover ratio and the mutation ratio of the proposed algorithm. To prove the performance of the proposed FLC, we divide the proposed algorithm into two cases: the GA with the FLC (pro-fGA) and the GA without the FLC (pro-GA).In numerical examples, we apply the proposed algorithms to several job-shop scheduling problems and the results applied are analyzed and compared. Various experiments show that the results of pro-fGA outperform those of pro-GA.     

An analysis of the non-preemptive mixed-criticality match-up scheduling problem

Many applications have a mixed-criticality nature. They contain tasks with a different criticality, meaning that a task with a lower criticality can be skipped if a task with a higher criticality needs more time to be executed. This paper deals with a mixed-criticality scheduling problem where each task has a criticality given by a positive integer number. The exact processing time of the task is not known. Instead, we use different upper bounds of the processing time for different criticality levels of the schedule. A schedule with different criticality levels is generated off-line, but its on-line execution switches among the criticality levels depending on the actual values of the processing times. The advantage is that after the transient prolongation of a higher criticality task, the system is able to match up with the schedule on a lower criticality level. While using this model, we achieve significant schedule efficiency (assuming that the prolongation of the higher criticality task rarely occurs), and at the same time, we are able to grant a sufficient amount of time to higher criticality tasks (in such cases, some of the lower criticality tasks may be skipped). This paper shows a motivation for the non-preemptive mixed-criticality match-up scheduling problem arising from the area of the communication protocols. Using a polynomial reduction from the 3-partition problem, we prove the problem to be \(\mathcal {NP}\)-hard in the strong sense even when the release dates and deadlines are dropped and only two criticality levels are considered.     

Multi-mode resource-constrained project scheduling problems with non-preemptive activity splitting

In this paper, we explore the difference between preemption and activity splitting in the resource-constrained project scheduling problem (RCPSP) literature and identify a new set of RCPSPs that only allows non-preemptive activity splitting. Each activity can be processed in multiple modes and both renewable and non-renewable resources are considered. Renewable resources have time-varying resource constraints and vacations. Multi-mode RCPSP (MRCPSP) with non-preemptive activity splitting is shown to be a generalization of the RCPSP with calendarization. Activity ready times and due dates are considered to study the impact on project makespan. Computational experiments are conducted to compare optimal makespans under three different problem settings: RCPSPs without activity splitting (P1), RCPSPs with non-preemptive activity splitting (P2), and preemptive RCPSPs (P3). A precedence tree-based branch-and-bound algorithm is modified as an exact method to find optimal solutions. Resource constraints are included into the general time window rule and priority rule-based simple heuristics are proposed to search for good initial solutions to tighten bounding rules. Results indicate that there are significant makespan reductions possible when non-preemptive activity splitting or preemptions are allowed. The higher the range of time-varying renewable resource limits and the tighter the renewable resource limits are, the bigger the resulting makespan reduction can be.     

Evaluation of mixed integer programming formulations for non-preemptive parallel machine scheduling problems

Mixed integer programming (MIP) formulations for scheduling problems can be classified based on the decision variables upon which they rely. In this paper, four different MIP formulations based on four different types of decision variables are presented for various parallel machine scheduling problems. The goal of this research is to identify promising optimization formulation paradigms that can subsequently be used to either (1) solve larger practical scheduling problems of interest to optimality and/or (2) be used to establish tighter lower solution bounds for those under study. We present the computational results and discuss formulation efficacy for total weighted completion time and maximum completion time problems for the identical parallel machine case.     

An efficient approach for the multiprocessor non-preemptive strictly periodic task scheduling problem

Strict periodicity constraint is of great importance since it concerns some hard real-time systems where missing deadlines leads to catastrophic situations. However, the problem of schedulability analysis for non-preemptive strictly periodic tasks on a multiprocessor platform is even more intractable than the one with the common periodicity. In order to implement such systems, designers need effective tools based on fast and near-optimal solutions.This paper presents a schedulability analysis which results mainly in a, two versions, task assignment and start-time calculation algorithm. The first one targets the harmonic task periods case while the second one targets the non-harmonic task periods case. Each version is based on a sufficient uniprocessor schedulability test. In addition, for the non-harmonic case which is the most intractable, the uniprocessor sufficient schedulability test uses the strictly periodic task utilization factor. This factor stands for the fraction of time spent to execute a task while its strict periodicity and the ones of the already scheduled tasks are met. As a result, an efficient and easily implementable scheduling algorithm is proposed which begins by assigning tasks to processors then attributes a start-time to every task in such a way that strict periodicity and deadline constraints are met. The effectiveness of the proposed scheduling algorithm, in both versions, has been shown by a performance evaluation and comparisons with an optimal and a similar suboptimal solution.     

Minimizing the makespan in the non-preemptive job-shop scheduling with limited machine availability

This paper addresses the makespan minimization in a job-shop environment where the machines are not available during the whole planning horizon. The disjunctive graph model is used to represent the schedules and the concept of blocks is generalized to include the unavailability periods of machines. To solve the problem, we develop a taboo thresholding heuristic that uses a new block-based neighborhood function. Some sufficient conditions to eliminate the evaluation of non-improving moves are proposed. Experiments performed on existing problem instances of the literature show the efficiency of the proposed heuristic.     

Exact and metaheuristic approaches for unrelated parallel machine scheduling

Journal of Scheduling - In this paper, we study an important real-life scheduling problem that can be formulated as an unrelated parallel machine scheduling problem with sequence-dependent setup...     

Exact search-space size for the refactoring scheduling problem

Ouni et al. “Maintainability defects detection and correction: a multi-objective approach” proposed a search-based approach for generating optimal refactoring sequences. They estimated the size of the search space for the refactoring scheduling problem using a formulation that is incorrect; the search space is estimated to be too much larger than it is. We provide in this paper the exact expression for computing the number of possible refactoring sequences of a software system. This could be useful for researchers and practitioners interested in developing new approaches to automate refactoring.     

Integrating non-preemptive open shops scheduling with sequence-dependent setup times using advanced metaheuristics

In this article, we consider non-preemptive open shops scheduling problem (OSSP) where setup times are sequence-dependent (SDST) on each machine to minimize makespan. The contributions of this article are threefold. Firstly, we incorporate a very practical assumption in our problem, SDST, which, according to Allahverdi et al. (2008) [Allahverdi, A., Ng, C. T., Cheung, T. C. E., & Kovalyov, Y. M. (2008). A survey of scheduling problems with setup times or costs. European Journal of Operational Research, 187(3), 985–1032], no paper has ever attempted to integrate into OSSP. Secondly, we propose two new advanced metaheuristics: multi-neighborhood search simulated annealing and hybrid simulated annealing to tackle the problem at hand. Thirdly, for the first time, we adapt two well-known constructive heuristics: longest total processing time and longest total remaining processing from the literature so as to consider the case of SDSTs. We also apply genetic algorithm from the literature of OSSP to embrace the concepts of SDST. Since there is no standard SDST-OSSP benchmark, we make certain adaptations on the Taillard’s benchmark [Taillard, E. (1993). Benchmarks for basic scheduling problems. European Journal of Operational Research, 64, 278–285] to include setup times. An experimental design based on foregoing benchmark is conducted to evaluate the competitiveness and robustness of our proposed algorithm against some effective algorithms in the literature. The obtained results strongly support the high performance of our proposed algorithms with respect to other well-known heuristic and metaheuristic algorithms.