Identical Parallel Processors Research Articles

Architecture and enhanced-algorithms to manage servers-processes into network: a management system.

This work investigates minimizing the makespan of multiple servers in the case of identical parallel processors. In the case of executing multiple tasks through several servers and each server has a fixed number of processors. The processors are generally composed of two processors (core duo) or four processors (quad). The meaningful format of the number of processors is 2k, and k≥0. The problem is to find a schedule that minimizes the makespan on 2k processors. This problem is identified as NP-hard one. A new network architecture is proposed based on the addition of server management. In addition, two novel algorithms are proposed to solve the addressed scheduling problems. The proposed algorithms are based on the decomposition of the main problem in several sub-problems that are applied to develop new heuristics. In each level of the generated tree, some results are saved and used to decompose the set of processes into subsets for the next level. The proposed methods are experimentally examined showing that the running time of the proposed heuristics is remarkably better than its best rival from the literature. The application of this method is devoted to the network case when there are several servers to be exploited. The experimental results show that in 87.9% of total instances, the most loaded and least loaded subset-sum heuristic (MLS) reaches the best solution. The best-proposed heuristic reaches in 87.4% of cases the optimal solution in an average time of 0.002 s compared with the best of the literature which reaches a solution in an average time of 1.307 s.

A NOTE ON HARDNESS OF MULTIPROCESSOR SCHEDULING WITH SCHEDULING SOLUTION SPACE TREE

We study the computational complexity of the non-preemptive scheduling problem of a listof independent jobs on a set of identical parallel processors with a makespan minimizationobjective. We make a maiden attempt to explore the combinatorial structure showing theexhaustive solution space of the problem by defining the Scheduling Solution Space Tree(SSST) data structure. The properties of the SSST are formally defined and characterizedthrough our analytical results. We develop a unique technique to show the problemNP using the SSST and the Weighted Scheduling Solution Space Tree (WSSST) datastructures. We design the first non-deterministic polynomial-time algorithm named MagicScheduling (MS) for the problem based on the reduction framework. We also define anew variant of multiprocessor scheduling by including the user as an additional inputparameter. We formally establish the complexity class of the variant by the reductionprinciple. Finally, we conclude the article by exploring several interesting open problemsfor future research investigation.

Fair Distribution Heuristics for Parallel Processors

This paper studies the machine covering problem to satisfy the fair distribution of several tasks with different execution times to be run on several parallel processors. My work deals with process scheduling on identical parallel processors and how to find the best solution to this problem. The goal is to maximize the finishing time for the processor with the least time regarding all other system processors. Some algorithms were proposed that can approximately solve the studied problem by minimizing the difference between the finishing time of all processors in the system.

Max-Min Processors Scheduling

This paper focuses on the maximization of the minimum completion time on identical parallel processors. The objective of this maximization is to ensure fair distribution. Let a set of jobs to be assigned to several identical parallel processors. This problem is shown as NP-hard. The research work of this paper is based essentially on the comparison of the proposed heuristics with others cited in the literature review. Our heuristics are developed using essentially the randomization method and the iterative utilization of the knapsack problem to solve the studied problem. Heuristics are assessed by several instances represented in the experimental results. The results show that the knapsack based heuristic gives almost a similar performance than heuristic in a literature review but in better running time.

Cyclic Scheduling for Parallel Processors with Precedence Constrains

The goal of this paper is to prepare algorithms of the cyclic scheduling problem, in which some set of jobs V is to be repeated an infinite number of times. We consider the multiprocessors problem when a set of jobs is done on identical parallel processors. Cyclic scheduling problems arise (for example) in manufacturing, timesharing of processors in embedded systems. The goal is to find a periodic schedule that minimizes the cycle time under precedence constraints. Although the problem is NP-hard, we show that the special case, where the precedence graph G is a tree or there are only two processors and all jobs have a unit processing time, can be solved in polynomial time.

Interruptible algorithms for multiproblem solving

In this paper, we address the problem of designing an interruptible system in a setting which involves n problem instances. The system schedules executions of a contract algorithm (which offers a trade-off between allowable computation time and quality of the solution) in m identical parallel processors. When an interruption occurs, the system outputs the currently best solution to each of the n problem instances. The quality of this output is then compared to the best possible algorithm that has foreknowledge of the interruption time and must, likewise, produce solutions to all n problem instances. This extends the well-studied setting in which only one problem instance is queried at interruption time. In this work, we first introduce new measures for evaluating the performance of interruptible systems in this setting. In particular, we propose the deficiency of a schedule as a performance measure that meets the requirements of the problem at hand. We then present a schedule whose performance we prove that is within a small factor from optimal in the general, multiprocessor setting. We also show several lower bounds on the deficiency of schedules on a single processor. More precisely, we prove a general lower bound of $$(n+1)/n$$ , an improved lower bound for the two-problem setting ( $$n=2$$ ), and a tight lower bound for the class of round-robin schedules. Our techniques can also yield a simpler, alternative proof of the main result of Bernstein et al. (in: Proceedings of the 18th International Joint Conference on Artificial Intelligence (IJCAI), pp 1211–1217, 2003) concerning the performance of cyclic schedules in multiprocessor environments.

Activity Scheduling on Identical Parallel Processors

The efficiency of parallel processors is achieved for the purpose of quick computing is mainly depending on the scheduling of activity. The most important factor for scheduling of activities are depend on the waiting time which is directly influence the computation time of overall activity. Minimizing the Variance of Waiting Time otherwise known as Waiting Time Variance (WTV) is one of the metrics of Quality of Services (QoS) which enhance the efficiency of activity scheduling. Allocate the activity from a set of activity pool and schedule them for each identical parallel processor for execution in a large scale by minimizing WTV is the main focusing area of this paper. In case of large scale computing activities are complex in nature. A prior knowledge of each activity must be known before the preparation of activity scheduling for efficient and rapid computing. A snake walks style of activity distribution among the parallel processor is presented in this paper for minimization problem. The minimization of WTV is measured with the help of three heuristic intend methods named as RSS, VS and BS. The results of the experiment are compared with current conspires and demonstrate the new snake style conspire is presenting the best practices for proven conspires and challenges in a wide range of activity. The algorithm's predictable findings appear as illustrated with graph.

The Mean-field Behavior of Processor Sharing Systems with General Job Lengths Under the SQ(d) Policy

In this paper, we derive the mean-field behavior of empirical distributions of large systems that consist of N (large) identical parallel processor sharing servers with Poisson arrival process having intensity Nλ and generally distributed job lengths under the randomized SQ(d) load balancing policy. Under this policy, an arrival is routed to the server with the least number of progressing jobs among d randomly chosen servers. The mean-field is then used to approximate the statistical properties of the system. In particular, we show that in the limit as N grows, individual servers are statistically independent of others (propagation of chaos) and more importantly, the equilibrium point of the mean-field is insensitive to the job length distributions. This has important engineering relevance for the robustness of such routing policies that are often used in web server farms. We use a measure-valued process approach and martingale techniques to obtain our results. We also provide numerical results to support our analysis.

Completion time variance minimisation on two identical parallel processors

The problem of scheduling jobs to minimise completion time variance (CTV) is a well-known problem in scheduling research. CTV is categorized as a non-regular performance measure and its value may decrease by increasing the job completion times. This objective is relevant in situations where providing uniform service to customers is important, and is in-line with just-in-time philosophy. The problem concerned in this paper is to schedule n jobs on two identical parallel machines to minimise CTV. We consider the unrestricted version of the problem. The problem is said to be restricted when a machine is not allowed to remain idle when jobs are available for processing. It may be necessary to delay the start of job processing on a machine in order to reduce the completion time deviations. This gives rise to the unrestricted version of the problem. We discuss several properties of an optimal schedule to the problem. In this paper, we develop a lower bound on CTV for a known partial schedule and propose a branch and bound algorithm to solve the problem. Optimal solutions are obtained and results are reported.

Multi-processor Search and Scheduling Problems with Setup Cost

We study two optimization problems in a multiprocessor environment in the presence of set-up costs. The first problem involves multiple parallel searchers (e.g., robots) that must locate a target which lies in one of many concurrent rays, and at an unknown position from their common origin. Every time a searcher turns direction, it incurs a turn cost. The objective is to derive a search strategy for locating the target as efficiently as possible. The second problem involves contract algorithms, namely algorithms in which the available computation time is specified prior to their execution. In particular, we seek a schedule of executions of contract algorithms for several different problems in identical parallel processors so as to efficiently simulate an interruptible algorithm, assuming that each execution incurs a given set-up cost. The performance of the search and scheduling strategies are evaluated by means of well-established measures, namely the competitive ratio and the acceleration ratio, respectively. In this paper we provide near-optimal strategies for the above problems, using an approach based on infinite linear-programming formulations. More precisely, we present a search strategy (resp. schedule) which is optimal when the number of rays (resp. problems) is a multiple of the number of searchers (resp. processors). For the general case, we show that the corresponding solutions are very close to optimal.

An improved meta-heuristic approach for solving identical parallel processor scheduling problem

This article considers the problem of scheduling n jobs on m identical parallel processors where an optimal schedule is defined as one that produces minimum makespan (the completion time of the last job) and total tardiness among the set of schedules. Such a problem is known as identical parallel processor makespan and total tardiness problem. In order to minimize makespan and total tardiness of identical parallel processors, improved versions of particle swarm optimization and harmony search algorithm are proposed to enhance scheduling performance with less computational burden. The major drawback of particle swarm optimization in terms of premature convergence at initial stage of iterations is avoided through the use of mutation, a commonly used operator in genetic algorithm, by introducing diversity in the solution. The proposed algorithm is termed as particle swarm optimization with mutation. The convergence rate of harmony search algorithm is improved by fine tuning of parameters such as pitch adjusting rate and bandwidth for improving the solution. The performance of the schedules is evaluated in terms of makespan and total tardiness. The results are analyzed in terms of percentage deviation of the solution from the lower bound on makespan. The results indicate that particle swarm optimization with mutation produces better solutions when compared with genetic algorithm and particle swarm optimization in terms of average percentage deviation. However, harmony search algorithm outperforms genetic algorithm, particle swarm optimization, and particle swarm optimization with mutation in terms of average percentage deviation. In certain instances, the solution obtained by harmony search algorithm outperforms existing clonal selection particle swarm optimization.

Online scheduling in Minimizing Makespan on Identical Parallel Processor with Release Date

In this paper, we address a non-preemptive task scheduling problem with an objective function of minimizing the makespan. We consider online scheduling with release date on identical parallel processing system with centralized and no splitting structure. Multi-steps heuristic algorithms are proposed to solve this non-deterministic scheduling problem. A computational experiment is conducted to examine the effectiveness of the proposed multi-steps method in different size problem. The computational results show that all the proposed heuristics obtain good results with the gap between optimal solutions are less than 10% even for a large date set. The experiment is performed using Microsoft Visual C++ programming software in windows environment. Keywords: Online scheduling; Minimizing makespan; Identical parallel processor; Release date. 2010 Mathematics Subject Classification: 68M20, 90B36, 90C27.

Optimal Scheduling of Contract Algorithms for Anytime Problem-Solving

A contract algorithm is an algorithm which is given, as part of the input, a specified amount of allowable computation time. The algorithm must then complete its execution within the allotted time. An interruptible algorithm, in contrast, can be interrupted at an arbitrary point in time, at which point it must report its currently best solution. It is known that contract algorithms can simulate interruptible algorithms using iterative deepening techniques. This simulation is done at a penalty in the performance of the solution, as measured by the so-called acceleration ratio. In this paper we give matching (i.e., optimal) upper and lower bounds for the acceleration ratio under such a simulation. We assume the most general setting in which n problem instances must be solved by means of scheduling executions of contract algorithms in $m$ identical parallel processors. This resolves an open conjecture of Bernstein, Filkenstein, and Zilberstein who gave an optimal schedule under the restricted setting of round robin and length-increasing schedules, but whose optimality in the general unrestricted case remained open. Lastly, we show how to evaluate the average acceleration ratio of the class of exponential strategies in the setting of n problem instances and m parallel processors. This is a broad class of schedules that tend to be either optimal or near-optimal, for several variants of the basic problem.

A nature inspired intelligent water drops evolutionary algorithm for parallel processor scheduling with rejection

Scheduling has become a popular area for artificial intelligence and expert system researchers during last decade. In this paper, a new metaheuristic algorithm entitled intelligent water drops (IWD) is adapted for solving a generalized kind of order scheduling problem where rejection of received orders is allowed with a penalty cost. At the beginning of production period, a set of orders are received by manufacturer. Due to capacity limit, the manufacturer can only process a subset of orders and has to decide to reject some of undesirable orders. The accepted orders are proceed to be scheduled by a set of identical parallel processors in shop floor. The objective is to select the best set of orders with high contribution in manufacturer's benefit and then find the appropriate schedule of accepted orders minimizing the number of tardy orders. To effectively solve the suggested problem, the Lexicographic utility function is customized to address different objectives and then an IWD algorithm, which is based on the process of the natural rivers and the interactions among water drops in a river, is devised. To further enhance the performance of basic IWD, an Iterated Local Search (ILS) heuristic is also incorporated into the main algorithm. To demonstrate the applicability of suggested problem and also show the effectiveness of enhanced IWD with ILS, a real-world application in commercial printing industry is presented and the performance of algorithm is compared with traditional algorithms like GA, DE and ACO.

Modeling sequence scrambling and related phenomena in mixed-model production lines

In this paper we examine the various effects that workstations and rework loops with identical parallel processors and stochastic processing times have on the performance of a mixed-model production line. Of particular interest are issues related to sequence scrambling. In many production systems (especially those operating on just-in-time or in-line vehicle sequencing principles), the sequence of orders is selected carefully to optimize line efficiency while taking into account various line balancing and product spacing constraints. However, this sequence is often altered due to stochastic factors during production. This leads to significant economic consequences, due to either the degraded performance of the production line, or the added cost of restoring the sequence (via the use of systems such as mix banks or automated storage and retrieval systems). We develop analytical formulas to quantify both the extent of sequence scrambling caused by a station of the production line, and the effects of this scrambling on downstream performance. We also develop a detailed Markov chain model to analyze related issues regarding line stoppages and throughput. We demonstrate the usefulness of our methods on a range of illustrative numerical examples, and discuss the implications from a managerial point of view.

Minimizing the total weighted late work in scheduling of identical parallel processors with communication delays

This paper addresses a certain type of scheduling problem that arises when a parallel computation is to be executed on a set of identical parallel processors. It is assumed that if two precedence-related tasks are processed on two different processors, due to the information transferring, there will be a task-dependent communication delay between them. For each task, a processing time, a due date and a weight is given while the goal is to minimize the total weighted late work. An integer linear mathematical programming model and a branch-and-bound algorithm have been developed for the proposed problem. Comparing the results obtained by the proposed branch-and-bound algorithm with those obtained by CPLEX, indicates the effectiveness of the method.

Minimizing workload balancing criteria on identical parallel machines

This paper considers the problem of scheduling nonpreemptive jobs on identical parallel processors to minimize workload balancing criteria. While workload balancing is an important practical criterion given the need of production systems to efficiently use all of their resources, there is no established measure of performance in the scheduling literature that characterizes total workload balance. In this paper, the normalized standard deviation, the normalized mean deviation, and the normalized mean difference are proposed as criteria that measure the balance of the workloads among the machines associated to a schedule. A local search algorithm, which performs multiple exchanges of jobs among machines, is presented. The results of a wide computational experimentation demonstrate that the proposed algorithm performs well for all the proposed measures.

On multiprocessor temperature-aware scheduling problems

We study temperature-aware scheduling problems under the model introduced in [Chrobak et al. AAIM 2008], where unit-length jobs of given heat contributions and common release dates are to be scheduled on a set of parallel identical processors. We consider three optimization criteria: makespan, maximum temperature and (weighted) average temperature. On the positive side, we present polynomial time approximation algorithms for the minimization of the makespan and the maximum temperature, as well as, optimal polynomial time algorithms for minimizing the average temperature and the weighted average temperature. On the negative side, we prove that there is no approximation algorithm of absolute ratio $$\frac{4}{3}-\epsilon $$ for the problem of minimizing the makespan for any $$\epsilon > 0$$ , unless $$\mathcal{P}=\mathcal{NP}$$ .

Power-aware scheduling of preemptable jobs on identical parallel processors to meet deadlines

This paper deals with a power-aware scheduling of preemptable independent jobs on identical parallel processors where ready time for each job is given and its completion time has to meet a given deadline. Jobs are described by (different) continuous, strictly concave functions relating their processing speeds at a time to the amount of power allotted at the moment. Power is a continuous, doubly constrained resource, i.e. both: its availability at each time instant and consumption over scheduling horizon are constrained. A methodology based on properties of minimum-length schedules is utilized to determine the existence of a feasible schedule for given amounts of energy and power. The question about minimum levels of power and energy ensuring the existence of a feasible schedule for a given set of jobs is also studied.

Solving a new mathematical model for a hybrid flow shop scheduling problem with a processor assignment by a genetic algorithm

This paper presents a new mathematical model for a hybrid flow shop scheduling problem with a processor assignment that minimizes makespan (i.e., C max) and cost of assigning a number of processors to stages. In this problem, it is assumed that there are a number of parallel identical processors which are assigned to all of the stages with an unlimited intermediate storage between any two successive stages. To solve such a hard problem, first a new heuristic algorithm is proposed to compute the makespan that is embedded in the proposed genetic algorithm in order to find the best sequence of jobs, and then processors are assigned to the stages simultaneously. A number of test problems have been solved and related results are illustrated and analyzed.