Abstract Scheduling is essentially a decision-making process that enables resource sharing among a number of activities by determining their execution order on the set of available resources. The emergence of distributed systems brought new challenges on scheduling in computer systems, including clusters, grids, and more recently clouds. On the other hand, the plethora of research makes it hard for both newcomers researchers to understand the relationship among different scheduling problems and strategies proposed in the literature, which hampers the identification of new and relevant research avenues. In this paper we introduce a classification of the scheduling problem in distributed systems by presenting a taxonomy that incorporates recent developments, especially those in cloud computing. We review the scheduling literature to corroborate the taxonomy and analyze the interest in different branches of the proposed taxonomy. Finally, we identify relevant future directions in scheduling for distributed systems.
@cite_75 present a taxonomy in the scheduling problem for workflows considering multiple criteria optimization in grid computing environments. The authors separate the multi-criteria scheduling taxonomy in @math , namely , and , each facet describing the problem from a different point of view. These facets are expanded to classify existing works in a smaller granularity, pointing out where current research can be expanded and the work in each facet.
@cite_75
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The workflow scheduling problem which is considered difficult on the Grid becomes even more challenging when multiple scheduling criteria are used for optimization. The existing approaches can address only certain variants of the multi-criteria workflow scheduling problem, usually considering up to two contradicting criteria being scheduled in some specific Grid environments. A comprehensive description of the problem can be an important step towards more general scheduling approaches. Based on the related work and on our own experience, we propose several novel taxonomies of the multi-criteria workflow scheduling problem, considering five facets which may have a major impact on the selection of an appropriate scheduling strategy: scheduling process, scheduling criteria, resource model, task model, and workflow model. We analyze different existing workflow scheduling approaches for the Grid, and classify them according to the proposed taxonomies, identifying the most common use cases and the areas which have not been sufficiently explored yet. Abstract In many domains of science, scientific applications are represented by workflows. In this paper, we introduce a resource management strategy to maximize the success rate of concurrent workflow applications constrained by individual deadline and budget values. The Multi-Workflow Deadline-Budget Scheduling (MW-DBS) algorithm can schedule multiple workflows that can arrive in the system at any time, with the aim of satisfying individual job requirements. MW-DBS produces schedules without performing optimizations but guarantees that the deadline and budget defined for each job are not exceeded. Experimental results show that our strategy increases the scheduling success rate of finding valid solutions. The problem considered here is the same as the one discussed in [G. Galambos and G. J. Woeginger, eds., SIAM J. Comput., 22 (1993), pp. 349--355]. It is an m-machine online scheduling problem in which we wish to minimize the competitive ratio for the makespan objective. In this paper, we show that @math is a lower bound on this competitive ratio for m=4. In particular, we show how to force a lower bound of @math for any positive @math . This reduces the gap between the performance of known algorithms [S. Albers, in Proceedings of the 29th Annual ACM Symposium on Theory of Computing, ACM, New York, 1997, pp. 130--139] and the lower bound. The method used introduces an approach to building the task master's strategy. In heterogeneous distributed environment, it is a great challenge to schedule multiple workflows submitted at different times. Particularly, scheduling of concurrent workflows with deadline and budget constraints makes the problem become more complex. Recent studies have proposed dynamic scheduling strategies for concurrent workflows which have limitations in inconsistent environments. Therefore, this paper presents a new dynamic scheduling algorithm for concurrent workflows. This algorithm proposes a uniform ranking that considers the time and costs for both workflows and workgroups to assign priorities for tasks. In the resource selection phase, it controls the resource selection range for each task based on an optimistic budget for the current task and selects resources for the current task according to a defined bi-factor. The experimental results show that our algorithm outperforms the existing algorithms in both consistent and inconsistent environments. Scheduling theory has received a growing interest since its origins in the second half of the 20th century. Developed initially for the study of scheduling problems with a single objective, the theory has been recently extended to problems involving multiple criteria. However, this extension has still left a gap between the classical multi-criteria approaches and some real-life problems in which not all jobs contribute to the evaluation of each criterion. In this book, we close this gap by presenting and developing multi-agent scheduling models in which subsets of jobs sharing the same resources are evaluated by different criteria. Several scenarios are introduced, depending on the definition and the intersection structure of the job subsets. Complexity results, approximation schemes, heuristics and exact algorithms are discussed for single-machine and parallel-machine scheduling environments. Definitions and algorithms are illustrated with the help of examples and figures. We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give a linear-time algorithm to compute all non-dominated solutions for the general uniprocessor problem and a fast arbitrarily-good approximation for multiprocessor problems when every job requires the same amount of work. We also show that the multiprocessor problem becomes NP-hard when jobs can require different amounts of work. For total flow, we show that the optimal flow corresponding to a particular energy budget cannot be exactly computed on a machine supporting exact real arithmetic, including the extraction of roots. This hardness result holds even when scheduling equal-work jobs on a uniprocessor. We do, however, extend previous work by to give an arbitrarily-good approximation for scheduling equal-work jobs on a multiprocessor. Sequential decision-making problems with multiple objectives arise naturally in practice and pose unique challenges for research in decision-theoretic planning and learning, which has largely focused on single-objective settings. This article surveys algorithms designed for sequential decision-making problems with multiple objectives. Though there is a growing body of literature on this subject, little of it makes explicit under what circumstances special methods are needed to solve multi-objective problems. Therefore, we identify three distinct scenarios in which converting such a problem to a single-objective one is impossible, infeasible, or undesirable. Furthermore, we propose a taxonomy that classifies multi-objective methods according to the applicable scenario, the nature of the scalarization function (which projects multi-objective values to scalar ones), and the type of policies considered. We show how these factors determine the nature of an optimal solution, which can be a single policy, a convex hull, or a Pareto front. Using this taxonomy, we survey the literature on multi-objective methods for planning and learning. Finally, we discuss key applications of such methods and outline opportunities for future work. In a heterogeneous system, the efficient exploitation of parallelism requires scheduling strategies that account for heterogeneity among processors to achieve an effective mapping of computations to processors. The paper presents a scheduling heuristic specialized for heterogeneous multiprocessor systems which make use of several different types of processors. The new algorithm is based on the greedy strategy: no processor remains idle if there is some task available that it could process. A graph called the classified typed task graph is used to describe the current status of tasks of different types at each scheduling step. With the graph, the algorithm dynamically evaluates the priorities of tasks only when there are multiply executable candidates, and then schedules an appropriate one onto the currently available processors of the corresponding type. A preliminary evaluation shows that this algorithm has promising performance. > We consider the power-aware problem of scheduling non-preemptively a set of jobs on a single speed-scalable processor so as to minimize the maximum lateness. We consider two variants of the problem: In the budget variant we aim in finding a schedule minimizing the maximum lateness for a given budget of energy, while in the aggregated variant our objective is to find a schedule minimizing a linear combination of maximum lateness and energy. We present polynomial time algorithms for both variants of the problem without release dates and we prove that both variants become strongly ( NP )-hard in the presence of arbitrary release dates. Moreover, we show that, for arbitrary release dates, there is no O(1)-competitive online algorithm for the budget variant and we propose a 2-competitive one for the aggregated variant. A companion paper Part I considers the problem of minimizing the weighted earliness and tardiness of jobs scheduled on a single machine around a common due date, d, which is unrestrictively late. This paper Part II considers the problem of minimizing the unweighted earliness and tardiness of jobs, allowing the possibility that d is early enough to constrain the scheduling decision. We describe several optimality conditions. The recognition version of the problem is shown to be NP-complete in the ordinary sense, confirming a well known conjecture. Moreover, this complexity definition is precise, since we describe a dynamic programming algorithm which runs in pseudopolynomial time. This algorithm is also extremely efficient computationally, providing an improvement over earlier procedures, of almost two orders of magnitude in the size of instance that can be solved. Finally, we describe a special case of the problem which is polynomially solvable. We consider the following scheduling problem. The input is a set of jobs with equal processing times, where each job is specified by its release time and deadline. The goal is to determine a single-processor nonpreemptive schedule that maximizes the number of completed jobs. In the online version, each job arrives at its release time. We give two online algorithms with competitive ratios below @math and show several lower bounds on the competitive ratios. First, we give a barely random @math -competitive algorithm that uses only one random bit. We also show a lower bound of @math on the competitive ratio of barely random algorithms that randomly choose one of two deterministic algorithms. If the two algorithms are selected with equal probability, we can further improve the bound to @math . Second, we give a deterministic @math -competitive algorithm in the model that allows restarts, and we show that in this model the ratio @math is optimal. For randomized algorithms with restarts we show a lower bound of @math . Scheduling workflows in cloud service environment has attracted great enthusiasm, and various approaches have been reported up to now. However, these approaches often ignored the uncertainties in the scheduling environment. Ignoring these uncertain factors often leads to the violation of workflow deadlines and increases service renting costs of executing workflows. This study devotes to improving the performance for cloud service platforms by minimizing uncertainty propagation in scheduling workflow applications that have both uncertain task execution time and data transfer time. To be specific, a novel scheduling architecture is designed to control the count of workflow tasks directly waiting on each service instance (e.g., virtual machine). Based on this architecture, we develop an unceRtainty-aware Online Scheduling Algorithm (ROSA) to schedule dynamic and multiple workflows with deadlines. The proposed ROSA skillfully integrates both the proactive and reactive strategies. Then, on the basis of real-world workflow traces, five groups of simulation experiments are carried out to compare ROSA with five typical algorithms. The comparison results reveal that ROSA performs better than the five compared algorithms with respect to costs (up to 56 ), deviation (up to 70 ), resource utilization (up to 37 ) and fairness (up to 37). Two major decisions are made when scheduling the operations of a fossil-fuel power-generating system over a short time horizon. The “unit commitment” decision indicates what generating units are to be in use at each point in time. The “economic dispatch” decision is the allocation of system demand among the generating units in operation at any point in time. Both these decisions must be considered to achieve a least-cost schedule over the short time horizon. In this paper we present a mixed integer programming model for the short time horizon power-scheduling problem. The objective of the model is to minimize the sum of the unit commitment and economic dispatch costs subject to demand, reserve, and generator capacity and generator schedule constraints. A branch-and-bound algorithm is proposed using a Lagrangian method to decompose the problem into single generator problems. A sub gradient method is used to select the Lagrange multipliers that maximize the lower bound produced by the relaxation. We present... Static scheduling of a program represented by a directed task graph on a multiprocessor system to minimize the program completion time is a well-known problem in parallel processing. Since finding an optimal schedule is an NP-complete problem in general, researchers have resorted to devising efficient heuristics. A plethora of heuristics have been proposed based on a wide spectrum of techniques, including branch-and-bound, integer-programming, searching, graph-theory, randomization, genetic algorithms, and evolutionary methods. The objective of this survey is to describe various scheduling algorithms and their functionalities in a contrasting fashion as well as examine their relative merits in terms of performance and time-complexity. Since these algorithms are based on diverse assumptions, they differ in their functionalities, and hence are difficult to describe in a unified context. We propose a taxonomy that classifies these algorithms into different categories. We consider 27 scheduling algorithms, with each algorithm explained through an easy-to-understand description followed by an illustrative example to demonstrate its operation. We also outline some of the novel and promising optimization approaches and current research trends in the area. Finally, we give an overview of the software tools that provide scheduling mapping functionalities. Previous work on assigning tasks to robots has proposed extensive categorizations of allocation of tasks with and without constraints. The main contribution of this paper is a specific categorization of problems that have temporal and ordering constraints. We propose a novel taxonomy that emphasizes the differences between temporal and ordering constraints, and organizes the current literature according to the nature of those constraints. We summarize widely used models and methods from the task allocation literature and related areas, such as vehicle routing and scheduling problems, showing similarities and differences. One of the classic results in scheduling theory is the @math -approximation algorithm by Lenstra, Shmoys, and Tardos for the problem of scheduling jobs to minimize makespan on unrelated machines; i.e., job @math requires time @math if processed on machine @math . More than two decades after its introduction it is still the algorithm of choice even in the restricted model where processing times are of the form @math . This problem, also known as the restricted assignment problem, is NP-hard to approximate within a factor less than @math , which is also the best known lower bound for the general version. Our main result is a polynomial time algorithm that estimates the optimal makespan of the restricted assignment problem within a factor @math , where @math is an arbitrarily small constant. The result is obtained by upper bounding the integrality gap of a certain strong linear program, known as the configuration LP, that was previously successfu... We consider the problem of speed scaling to conserve energy in a multiprocessor setting where there are precedence constraints between tasks, and where the performance measure is the makespan. That is, we consider an energy bounded version of the classic problem Pm|prec|Cmax . We extend the standard 3-field notation and denote this problem as Sm|prec, energy|Cmax . We show that, without loss of generality, one need only consider constant power schedules. We then show how to reduce this problem to the problem Qm|prec|Cmax to obtain a poly-log(m)-approximation algorithm. Many text classification tasks are known to be highly domain-dependent. Unfortunately, the availability of training data can vary drastically across domains. Worse still, for some domains there may not be any annotated data at all. In this work, we propose a multinomial adversarial network (MAN) to tackle the text classification problem in this real-world multidomain setting (MDTC). We provide theoretical justifications for the MAN framework, proving that different instances of MANs are essentially minimizers of various f-divergence metrics (Ali and Silvey, 1966) among multiple probability distributions. MANs are thus a theoretically sound generalization of traditional adversarial networks that discriminate over two distributions. More specifically, for the MDTC task, MAN learns features that are invariant across multiple domains by resorting to its ability to reduce the divergence among the feature distributions of each domain. We present experimental results showing that MANs significantly outperform the prior art on the MDTC task. We also show that MANs achieve state-of-the-art performance for domains with no labeled data. This paper aims to address the problem of scheduling large workflows onto multiple execution sites with storage constraints. Three heuristics are proposed to first partition the workflow into sub-workflows. Three estimators and two schedulers are then used to schedule sub-workflows to the execution sites. Performance with three real-world workflows shows that this approach is able to satisfy storage constraints and improve the overall runtime by up to 48 over a default whole-workflow scheduling. We consider one of the basic, well-studied problems of scheduling theory, that of nonpreemptively scheduling n independent tasks on m identical, parallel processors with the objective of minimizing the “makespan,” i.e., the total timespan required to process all the given tasks. Because this problem is @math -complete and apparently intractable in general, much effort has been directed toward devising fast algorithms which find near-optimal schedules. The well-known LPT (Largest Processing Time first) algorithm always finds a schedule having makespan within @math of the minimum possible makespan, and this is the best such bound satisfied by any previously published fast algorithm. We describe a comparably fast algorithm, based on techniques from “bin-packing,” which we prove satisfies a bound of 1.220. On the basis of exact upper bounds determined for each @math , we conjecture that the best possible general bound for our algorithm is actually @math .