Routing Messages with Release Time and Deadline Constraint

The problem of determining whether a set of real-time messages can be routed in a network is considered. Each message has five parameters-origin node, destination node, length, release time, and deadline. The complexity of the problem is considered under various restrictions of four parameters-origin node, destination node, release time, and deadline. It is shown that if the network is a arbitrary directed graph, the problem is NP-complete even when all four parameters are fixed; i.e., the messages have identical values in all four parameters. Motivated by the complexity of the problem, we consider a simple network-a unidirectional ring. For nonpreemptive transmission, it is shown that the problem is solvable in polynomial time if three of the four parameters are fixed, but becomes NP-complete if only two of them are fixed. The same kind of complexity results hold for preemptive transmission, except for the following two cases: (1) identical origin nodes and release times and (2) identical destination nodes and deadlines. The complexity of these two cases remains open. The issue of whether there is an optimal on-line algorithm is also considered. It is shown that no such algorithm can exist unless all of the remaining three parameters are fixed.     

Makespan minimization in preemptive two machine job shops

In this note we investigate the NP-complete problem of minimizing the makespan in a preemptive two machine job shop. We present a polynomial time approximation algorithm with worst case ratio 3/2 for this problem, and we also argue that this is the best possible result that can be derived via our line of approach.     

Scheduling hybrid flowshop with parallel batching machines and compatibilities

This paper considers a two-stage hybrid flowshop problem in which the first stage contains several identical discrete machines, and the second stage contains several identical batching machines. Each discrete machine can process no more than one task at time, and each batching machine can process several tasks simultaneously in a batch with the additional feature that the tasks of the same batch have to be compatible. A compatibility relation is defined between each pair of tasks, so that an undirected compatibility graph is obtained which turns out to be an interval graph. The batch processing time is equal to the maximal processing time of the tasks in this batch, and all tasks of the same batch start and finish together. The goal is to make batching and sequencing decisions in order to minimize the makespan. Since the problem is NP-hard, we develop several heuristics along with their worst cases analysis. We also consider the case in which tasks have the same processing time on the first stage, for which a polynomial time approximation scheme (PTAS) algorithm is presented.     

Single-machine batch scheduling to minimize the total setup cost in the presence of deadlines

We address the single-machine batch scheduling problem with the objective of minimizing the total setup cost. This problem arises when there are n jobs that are partitioned into F families and when setup operations are required whenever the machine switches from processing a job of one family to processing a job of another family. We assume that setups do not require time but are associated with a fixed cost which is identical for all setup operations. Each job has a processing time and an associated deadline. The objective is to schedule all jobs such that they are on time with respect to their deadlines and the total setup cost is minimized. We show that the decision version of this problem is NP-complete in the strong sense. Furthermore, we present properties of optimal solutions and an \(O(n\log n+nF)\) algorithm that approximates the cost of an optimal schedule by a factor of F. The algorithm is analyzed in computational tests.     

一种MapReduce实时调度算法设计及实现

MapReduce是云计算中重要的批数据处理框架,多任务共享MapReduce机群并满足任务实时性要求是调度算法急需解决的问题。提出两阶段实时调度算法,将调度划分为任务间调度和任务内调度。对于任务间调度,使用抽样法和经验值法确定子任务执行时间,利用该参数建立资源分配模型,动态确定任务优先级进行调度;对于子任务使用延迟调度策略进行调度,保证计算的本地性。实验结果显示,两阶段实时调度算法相比公平调度算法和FIFO算法,在保证吞吐量的同时能够满足任务实时性要求。     

一类具有资源约束和恶化效应的单机成组排序问题

讨论具有连续资源的单机成组排序问题.这一模型中同一组内的工件不允许分开加工,各工件组的安装时间是所消耗资源的非负减少连续函数.工件的加工时问是开工时问的严格减少函数.针对满足资源消耗总量限制条件下极小化最大完工时问的问题.以及在满足最大完工时间限制条件下极小化资源消耗总量的问题,讨论了最优排序的某些特征,分别给出了求解最优资源分配的方法.最后通过数值例子表明了所提出方法的正确性和有效性.     

Bounded parallel-batch scheduling on single and multi machines for deteriorating jobs

We consider the bounded parallel-batch scheduling problem in which the processing time of a job is a simple linear function of its starting time. The objective is to minimize the makespan. When the jobs have identical release dates, we present an optimal algorithm for the single-machine problem and an fully polynomial-time approximation scheme for the parallel-machine problem. When the jobs have distinct release dates, we show that the single-machine problem is NP-hard and present an optimal algorithm for one special case.     

Single-machine group scheduling with both learning effects and deteriorating jobs

In the paper two resource constrained single-machine group scheduling problems with both learning effects and deteriorating jobs are considered. By learning effects, deteriorating jobs and group technology assumption, we mean that the processing time of a job is defined by the function of its starting time and position in the group, and the group setup times of a group is a positive strictly decreasing continuous function of the amount of consumed resource. We present polynomial solutions for the makespan minimization problem under the constraint that the total resource consumption does not exceed a given limit, and the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit, respectively.     

混合自适应粒子群工作流调度优化算法

针对具有截止期的云工作流完成时间与执行成本冲突的问题,提出一种混合自适应粒子群工作流调度优化算法（HAPSO）。首先,基于截止期建立有向无环图（DAG）云工作流调度模型;然后,通过范数理想点与自适应权重的结合,将DAG调度模型转化为权衡DAG完成时间和执行成本的多目标优化问题;最后,在粒子群优化（PSO）算法的基础上引入自适应惯性权重、自适应学习因子、花朵授粉算法的概率切换机制、萤火虫算法（FA）和粒子越界处理方法,从而平衡粒子群的全局搜索与局部搜索能力,进而求解DAG完成时间与执行成本的目标优化问题。实验中对比分析了PSO、惯性权重粒子群算法（WPSO）、蚁群算法（ACO）和HAPSO的优化结果。实验结果表明,HAPSO在权衡工作流（30～300任务数）完成时间与执行成本的多目标函数值上降低了40.9%～81.1%,HAPSO在工作流截止期约束下有效权衡了完成时间与执行成本。此外,HAPSO在减少完成时间或降低执行成本的单目标上也有较好的效果,验证了HAPSO的普适性。     

Flowshop scheduling problem with a batching machine and task compatibilities

This paper deals with the problem of task scheduling in a flowshop with two (discrete and batching) machines. Each task has to be processed by both machines. All tasks visit the machines in the same order. The first machine is a discrete machine that can process no more than one task at a time, and the second machine is a batching machine that can process several tasks per batch with the additional feature that the tasks of the same batch have to be compatible. A compatibility relation is defined between each pair of tasks, so that an undirected compatibility graph is obtained which turns out to be an interval graph. The batch processing time is equal to the maximal processing time of the tasks in this batch and all tasks of the same batch start and finish together. The aim is to make batching and sequencing decisions and minimize the makespan.     

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.     

Makespan minimization in a no-wait flow shop problem with two batching machines

This paper deals with the problem of task scheduling in a no-wait flowshop with two batching machines. Each task has to be processed by both machines. All tasks visit the machines in the same order. Batching machines can process several tasks per batch so that all tasks of the same batch start and complete together. The batch processing time for the first machine is equal to the maximal processing time of the tasks in this batch, and for the second machine is equal to the sum of the processing times of the tasks in this batch. We assume that the capacity of any batch on the first machine is bounded, and that when a batch is completed on the first machine it is immediately transferred to the second machine. The aim is to make batching and sequencing decisions that allow the makespan to be minimized.     

A Cooperative Game Theoretical Technique for Joint Optimization of Energy Consumption and Response Time in Computational Grids

With the explosive growth in computers and the growing scarcity in electric supply, reduction of energy consumption in large-scale computing systems has become a research issue of paramount importance. In this paper, we study the problem of allocation of tasks onto a computational grid, with the aim to simultaneously minimize the energy consumption and the makespan subject to the constraints of deadlines and tasks' architectural requirements. We propose a solution from cooperative game theory based on the concept of Nash Bargaining Solution. In this cooperative game, machines collectively arrive at a decision that describes the task allocation that is collectively best for the system, ensuring that the allocations are both energy and makespan optimized. Through rigorous mathematical proofs we show that the proposed cooperative game in mere O(n mlog(m)) time (where n is the number of tasks and m is the number of machines in the system) produces a Nash Bargaining Solution that guarantees Pareto-optimally. The simulation results show that the proposed technique achieves superior performance compared to the Greedy and Linear Relaxation (LR) heuristics, and with competitive performance relative to the optimal solution implemented in LINDO for small-scale problems.     

Flow shop scheduling to minimize makespan with decreasing time-dependent job processing times

In this study, we consider an n-job, m-machine flow shop scheduling problem with decreasing time-dependent job processing times. By the decreasing time-dependent job processing times, we mean that the processing time is a decreasing function of its execution starting time. When some dominant relationships between m − 1 machines can be satisfied, we show that the makespan minimization problem can be solved in polynomial time.     

A hybrid evolutionary approach for heterogeneous multiprocessor scheduling

This article investigates the assignment of tasks with interdependencies in a heterogeneous multiprocessor environment; specific to this problem, task execution time varies depending on the nature of the tasks as well as with the processing element assigned. The solution to this heterogeneous multiprocessor scheduling problem involves the optimization of complete task assignments and processing order between the assigned processors to arrive at a minimum makespan, subject to a precedence constraint. To solve an NP-hard combinatorial optimization problem, as is typified by this problem, this paper presents a hybrid evolutionary algorithm that incorporates two local search heuristics, which exploit the intrinsic structure of the solution, as well as through the use of specialized genetic operators to promote exploration of the search space. The effectiveness and contribution of the proposed features are subsequently validated on a set of benchmark problems characterized by different degrees of communication times, task, and processor heterogeneities. Preliminary results from simulations demonstrate the effectiveness of the proposed algorithm in finding useful schedule sets based on the set of new benchmark problems.     

Utilization Bounds for EDF Scheduling on Real-Time Multiprocessor Systems

The utilization bound for earliest deadline first (EDF) scheduling is extended from uniprocessors to homogeneous multiprocessor systems with partitioning strategies. First results are provided for a basic task model, which includes periodic and independent tasks with deadlines equal to periods. Since the multiprocessor utilization bounds depend on the allocation algorithm, different allocation algorithms have been considered, ranging from simple heuristics to optimal allocation algorithms. As multiprocessor utilization bounds for EDF scheduling depend strongly on task sizes, all these bounds have been obtained as a function of a parameter which takes task sizes into account. Theoretically, the utilization bounds for multiprocessor EDF scheduling can be considered a partial solution to the bin-packing problem, which is known to be NP-complete. The basic task model is extended to include resource sharing, release jitter, deadlines less than periods, aperiodic tasks, non-preemptive sections, context switches, and mode changes.     

Scheduling jobs under decreasing linear deterioration

This paper considers the scheduling problems under decreasing linear deterioration. Deterioration of a job means that its processing time is a function of its execution start time. Optimal algorithms are presented respectively for single machine scheduling of minimizing the makespan, maximum lateness, maximum cost and number of late jobs. For two-machine flow shop scheduling problem to minimize the makespan, it is proved that the optimal schedule can be obtained by Johnson's rule. If the processing times of operations are equal for each job, flow shop scheduling problems can be transformed into single machine scheduling problems.     

Series production in a basic re-entrant shop to minimize makespan or total flow time

This paper addresses a real life shop scheduling problem in a manufacturing company. In this problem, a set of n identical jobs are to be processed on two machines. Every job visits one of the machines more than once. This is therefore a re-entrant shop. Due to the fact that the jobs are identical, the decision version of this problem is even not in the class NP. We give an optimal schedule to minimize the makespan. Since the total flow time depends on the relations between the processing times, we decompose this problem into sub-problems according to the relations between the processing times. We prove various properties of optimal solutions and, based on these properties, we provide an optimal solution for all the sub-problems except one of them. For the sole remaining sub-problem, we prove a dominance property which allows to consider a part of schedules to find an optimal one.     

Static resource allocation for heterogeneous computing environments with tasks having dependencies,priorities, deadlines,and multiple versions

Heterogeneous computing (HC) environments composed of interconnected machines with varied computational capabilities are well suited to meet the computational demands of large, diverse groups of tasks. One aspect of resource allocation in HC environments is matching tasks with machines and scheduling task execution on the assigned machines. We will refer to this matching and scheduling process as mapping. The problem of mapping these tasks onto the machines of a distributed HC environment has been shown, in general, to be NP-complete. Therefore, the development of heuristic techniques to find near-optimal solutions is required. In the HC environment investigated, tasks have deadlines, priorities, multiple versions, and may be composed of communicating subtasks. The best static (off-line) techniques from some previous studies are adapted and applied to this mapping problem: a genetic algorithm (GA), a GENITOR-style algorithm, and a two phase greedy technique based on the concept of Min–min heuristics. Simulation studies compare the performance of these heuristics in several overloaded scenarios, i.e., not all tasks can be executed by their deadlines. The performance measure used is the sum of weighted priorities of tasks that completed before their deadline, adjusted based on the version of the task used. It is shown that for the cases studied here, the GENITOR technique finds the best results, but the faster two phase greedy approach also performs very well.     

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