Algorithms for multiprocessor scheduling with machine release times

A new polynomial algorithm is developed for the classical multiprocessor scheduling problem in which independent jobs are nonpreemptively scheduled on identical parallel machines with the objective of minimizing the makespan, i.e. the latest job finishing time. The algorithm at first generates and merges a set of partial solutions in order to obtain a feasible solution for the multiprocessor scheduling problem. Then a set of bin packing problems are solved in order to improve the solution, by iteratively using a MultiFit type procedure on different job sets. The effectiveness of this approach is evaluated by solving a large number of benchmark instances. The results indicate that the proposed algorithm, called PSMF, is very competitive with well known constructive algorithms for a wide range of instances. Furthermore, PSMF is competitive with respect to some of the best heuristics for parallel machine scheduling problems only when it uses a 2-exchange procedure.

The way the processes in a parallel program are scheduled on the processors of a multiprocessor system affects the performance significantly. Finding a schedule of processes to processors which results in minimum completion time is NP-hard. Therefore, one has to resort to heuristic schedules. However, it is often difficult to determine if a specific schedule is close to the optimal case or if it is worthwhile to look for other schedules. Based on information from previous executions of the parallel program, we present a formula for an upper bound on the minimum completion time of the program. The bound is a function of a set of parameters. Some of these parameters are obtained from the previous executions of the program and the others describe the target multiprocessor architecture for which we want to bound the minimum completion time. The bound is optimal when it is based on information from one previous execution. Using these results, we are able to decide if a certain schedule is close to optimal or if it is worthwhile to look for other schedules. This is demonstrated by evaluating the completion time of a specific schedule of a particular program. The proofs used for obtaining the bound are based on program transformations and combinatorial mathematics.

In real production processes, various problems may occur. Cost minimization, make span minimization, and energy consumption minimization are often the topics that are studied to eliminate problems in production. In this study, it is aimed to minimize the make span of a job assigned to workers working on identical and parallel machines in a welding workshop. Minimum completion time has been obtained by assigning the jobs in accordance with the objective function in a problem which has demand constraints according to worker capacity, worker ability and welding types. The mathematical models made in order to obtain the minimum makespan during which the given welding work can be realized were calculated in the LINGO 17.0 program.

This paper proposed an efficient real time scheduling algorithm using global scheduling paradigm running in multicore environment known as Global Preemptive Utility Accrual Scheduling (GPUAS) algorithm. The existing TUF/UA multiprocessor scheduling algorithms known as Greedy-Global Utility Accrual (G-GUA) and Non Greedy-Global Utility Accrual (NG-GUA) algorithms is seen to overlook the efficiency on its task scheduling algorithm. These algorithms have adapted the task migration attribute considering the load balancing problem in multi core platform. The existing PUAS uniprocessor scheduling algorithm is mapped into the multicore scheduling environment that consists of the global scheduling schemes considering the migration attribute of the executed tasks. The main principal of global scheduling is that it allows the executed tasks to migrate from one processor to the other processors whenever a scheduling event occurs in the system. The proposed GPUAS algorithm inherits the characteristics of PUAS in uniprocessor where it can preempt the highest PUD task at any event that occurs in the system. In this research, the proposed GPUAS algorithm enhanced the existing NG-GUA and G-GUA algorithms. The developed simulator has derived the set of parameter, events and performance metrics according to a detailed analysis of the base model. The proposed GPUAS algorithm achieved the highest accrued utility for the entire load range. The proposed GPUAS algorithm is more efficient than the existing algorithms, producing the highest accrued utility ratio and less abortion ratio making it more suitable and efficient for real time application domain.

A heuristic algorithm is developed for the classical scheduling problem in which independent jobs are nonpreemptively scheduled on identical parallel machines with the objective of minimizing the makespan with load balancing. The algorithm uses iteratively the LPT procedure to be successful computational tools in many hard Combinatorial Optimization problems. We present an approximation algorithm based on balance the Hopfild with binary decision variables which are a kind of assignment variables for the classical deterministic scheduling problem of minimizing the makespan on identical machines. These problems are characterized by their complexity, known as NP-hard in most cases. Computational results indicate that the proposed algorithm is very competitive with respect to well-known constructive algorithms for a large number of benchmark.

Workflow scheduling is one of the significant issues for scientific applications among virtual machine migration, database management, security, performance, fault tolerance, server consolidation, etc. In this paper, existing time-based scheduling algorithms, such as first come first serve (FCFS), min–min, max–min, and minimum completion time (MCT), along with dependency-based scheduling algorithm MaxChild have been considered. These time-based scheduling algorithms only compare the burst time of tasks. Based on the burst time, these schedulers, schedule the sub-tasks of the application on suitable virtual machines according to the scheduling criteria. During this process, not much attention was given to the proper utilization of the resources. A novel dependency and time-based scheduling algorithm is proposed that considers the parent to child (P2C) node dependencies, child to parent node dependencies, and the time of different tasks in the workflows. The proposed P2C algorithm emphasizes proper utilization of the resources and overcomes the limitations of these time-based schedulers. The scientific applications, such as CyberShake, Montage, Epigenomics, Inspiral, and SIPHT, are represented in terms of the workflow. The tasks can be represented as the nodes, and relationships between the tasks can be represented as the dependencies in the workflows. All the results have been validated by using the simulation-based environment created with the help of the WorkflowSim simulator for the cloud environment. It has been observed that the proposed approach outperforms the mentioned time and dependency-based scheduling algorithms in terms of the total execution time by efficiently utilizing the resources.

Fog computing (FC) is an emerging paradigm that extends computation, communication, and storage facilities towards the edge of a network. In this heterogeneous and distributed environment, resource allocation is very important. Hence, scheduling will be a challenge to increase productivity and allocate resources appropriately to the tasks. We schedule tasks in fog computing devices based on classification data mining technique. A key contribution is that a novel classification mining algorithm I‐Apriori is proposed based on the Apriori algorithm. Another contribution is that we propose a novel task scheduling model and a TSFC (Task Scheduling in Fog Computing) algorithm based on the I‐Apriori algorithm. Association rules generated by the I‐Apriori algorithm are combined with the minimum completion time of every task in the task set. Furthermore, the task with the minimum completion time is selected to be executed at the fog node with the minimum completion time. We finally evaluate the performance of I‐Apriori and TSFC algorithm through experimental simulations. The experimental results show that TSFC algorithm has better performance on reducing the total execution time of tasks and average waiting time.

Serial and within-stage independent parallel model equivalence on the minimum completion time

Real-time systems are subject to fundamental user requirements, such as correctness of the systems, taking into account timeliness and simultaneity, a high degree of predictability. This means that the scheduling algorithm is an important component of these systems. A scheduling algorithm is used to determine a schedule for a set of tasks so that the task's deadlines and resource requirements are satisfied. The potential speedup of applications has motivated the widespread use of multiprocessors in recent years. In this paper, recent results on multiprocessor real-time scheduling algorithms are reviewed. The review takes the form of an analysis of the problems presented by different application requirements and characteristics. A scheduling algorithm for real-time systems to be implemented on multiprocessors is proposed. This algorithm is appropriate for real-time tasks with the precedence constraints.

When multiple participants work on a workflow that represents a large, collaborative activity, it is important to have a well defined process to determine the portions of the workflow that each participant is responsible for executing. In this paper, we describe a process and related algorithms required to assign tasks in a workflow, to hosts that are willing to carry out the execution of these tasks, and thereby contributing to the completion of the activity. This problem is a stylized form of the multi-processor scheduling algorithm which has been shown to be NP-Hard. Further complicating the issue is that we are targeting our approach to mobile ad hoc networks, where hosts are physically mobile, communication links are frequently interrupted, and spatiotemporal considerations become increasingly important. We describe a distributed approach to task allocation in mobile ad hoc networks that employs heuristics to assign tasks in a workflow to mobile hosts based on their capabilities and their mobility patterns. We have implemented our algorithms in the context of CiAN, a workflow management system (WfMS) supporting collaborations in a mobile environment. In addition, we also present performance data of our algorithm and compare it to naive and brute force approaches.

Preemptive scheduling problems on parallel machines are classic problems. Given the goal of minimizing the makespan, they are polynomially solvable even for the most general model of unrelated machines. In these problems, a set of jobs is to be assigned to be executed on a set of m machines. A job can be split into parts arbitrarily and these parts are to be assigned to time slots on the machines without parallelism, that is, for every job, at most one of its parts can be processed at each time.Motivated by sensitivity analysis and online algorithms, we investigate the problem of designing robust algorithms for constructing preemptive schedules. Robust algorithms receive one piece of input at a time. They may change a small portion of the solution as an additional part of the input is revealed. The capacity of change is based on the size of the new input. For scheduling problems, the maximum ratio between the total size of the jobs (or parts of jobs) which may be re-scheduled upon the arrival of a new job j, and the size of j, is called migration factor.We design a strongly optimal algorithm with the migration factor \(1-\frac 1m\) for identical machines. Such algorithms avoid idle time and create solutions where the (non-increasingly) sorted vector of completion times of the machines is minimal lexicographically. In the case of identical machines this results not only in makespan minimization, but the created solution is also optimal with respect to any ℓ p norm (for p > 1). We show that an algorithm of a smaller migration factor cannot be optimal with respect to makespan or any other norm, thus the result is best possible in this sense as well. We further show that neither uniformly related machines nor identical machines with restricted assignment admit an optimal algorithm with a constant migration factor. This lower bound holds both for makespan minimization and for any ℓ p norm. Finally, we analyze the case of two machines and show that in this case it is still possible to maintain an optimal schedule with a small migration factor in the cases of two uniformly related machines and two identical machines with restricted assignment.

Optimal on-line algorithms for the uniform machine scheduling problem with ordinal data

This paper deals with the problem of scheduling dependent tasks with release time, deadline and due time on identical parallel machines. Based on decomposition-coordination methodology in large scale systems theory and Lagrangian relaxation technique, a multilayer hierarchical scheduling algorithm is presented. By making the most of structural properties of the precedence graph of partial ordering task set and introducing the concept of feasible start time interval , the proposed algorithm can be used for solving the scheduling problem under study effectively.

The potential speedup of applications has motivated the widespread use of multiprocessors in recent years. Future real-time systems are likely to be built on multiprocessor architectures. Efficient scheduling algorithms for multiprocessors are needed so that tasks will have predictable behaviors. In this paper, recent results on multiprocessor real-time scheduling algorithms are reviewed. The review takes the form of an analysis of the problems presented by different application requirements and characteristics. A scheduling algorithm for real-time systems to be implemented on multiprocessors is proposed. This algorithm is appropriate for real-time tasks with precedence constraints.

The problem of scheduling of tasks in distributed, heterogeneous, and multiprocessing computing environment like grid and cloud computing is considered as one of the most important issue from research perspective. As the performance of such kind of systems is highly depends upon the way, how tasks are allocated among the multiple processing units for their efficient execution. The underlying objective of any task scheduling mechanism is to minimize the overall makespan for the execution of given set of jobs/tasks and computing machines. Scheduling of tasks in cloud computing falls in the class of NP-hard optimization problem. As a result, many meta-heuristic algorithms have been applied and tested to solve this problem but still lot of scope is there for the better strategies. The characteristic of the good algorithm is that it must be adaptable to the dynamic environment. Through this paper, we are proposing task scheduling mechanism based on particle swarm optimization (PSO) in which opposition-based learning technique is used to avoid premature convergence and to accelerate the convergence of standard PSO and compared same with the well-established task scheduling strategies based on PSO, mPSO (modified PSO), genetic algorithm GA, max–min, minimum completion time and minimum execution time. The results obtained for the various class of experiments clearly establish that the proposed opposition-based learning inspired particle swarm optimization based scheduling strategy performs better in comparison to its peers which are taken into the consideration.