M. Drozdowski, Scheduling multiprocessor tasks - an overview, European Journal of Operational Research 94 (1996), 215-230.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....incompatible. Hence, tasks are subject to compatibility constraints. The present paper is concerned with scheduling independent multiprocessor tasks on dedicated processors, in both the preemptive case and the nonpreemptive case, and the goal is to minimize the makespan Cmax . Following the See [6] for some practical justifications for considering multiprocessor task systems, and a survey on the main results obtained in multiprocessor task scheduling. notations of [11,20] we will denote the problem by Pm jfix j ; pmtnjCmax in the preemptive case, and Pm jfix j jCmax in the non preemptive ....

M. Drozdowski. Scheduling Multiprocessor Tasks - An Overview. Private communication, (1996)

....[6] which require two processing elements simultaneously: the sender and the receiver. Multiprocessor tasks are also favorable for ef ciency reasons and represent coscheduled (also called gang scheduled) tasks [10, 19] An extensive description of the multiprocessor task concept can be found in [2, 8, 18]. We formulate now the considered scheduling problem. The computer system consists of set P = fP 1 ; Pmg of processors. The task set T = fT ; T ; T g is composed of subsets: T of n 1 tasks requiring one processor, T of n 2 tasks requiring two processors in ....

....j=1 c j , and mean weighted AEow time j=1 w j c j , where c j is the completion time of task T j . C max denotes schedule length (though it is not the optimality criterion analyzed in this work) To denote considered problems the three eld notation introduced in [11, 18] will be used (cf. also [2, 8]) Symbol P in the rst eld means that the number of processors is given in the particular instance of the problem. P2 means that the number of processors is equal 2 and xed by the formulation of the problem. According to [18] word size j in the task eld means that tasks may require arbitrary ....

Drozdowski, M., Scheduling multiprocessor tasks - An overview, European Journal of Operational Research, 1996, 94, 215-230.

.... Krandick considered independant MT with identical computing times. We refer the reader to Lep ere, Mouni e, Robi c Trystram [13] for more details and motivations of the MT model. MT are closely related to two other models, namely to the model of multiprocessor tasks (see e.g. Drozdowski [7]) and to the model of divisible tasks (Prasanna Musicus [17] The di erence between these models lies in the freedom allowed to the task allotment, that is, the number of processors which execute each task: A multiprocessor task requires to be executed by a xed integer number of processors, ....

M. Drozdowski [1996]. Scheduling multiprocessor tasks { An overview. European Journal of Operational Research 94, 215-230.

....from the outset. There are no additional arrivals later. The scheduler can then pack the jobs together in order to minimize the total processing time. Such a model is often suitable for space slicing, batch job schedulers and their performance can often be predicted using analytical methods [7]. It is also convenient for measuring the execution of real applications as scheduled by real schedulers. Alternatively, one can assume an on line model where jobs arrive over a period of time. In this case the scheduler must handle new jobs in real time, without the benefit of prior knowledge ....

M. Drozdowski, "Scheduling multiprocessor tasks --- an overview ". European J. Operational Research 94, pp. 215--230, 1996.

....problem [44] An on line scheduler deals with jobs that continually arrive to the system. In contrast, an off line scheduler assumes that all jobs are available from the outset. Off line scheduling is more amenable to analytical solutions and there is a great deal of research in the area [35]. However, the results of these investigations often cannot be applied to the online problem. There are a handful of supercomputer schedulers currently in production. These include the Easy [66] 82] PBS [58] Maui [69] and LSF [74] schedulers. Unfortunately, these schedulers can radically ....

....jobs that continually arrive to the system is called an on line scheduler [44] In contrast, an off line scheduler assumes that all jobs are available when the scheduler starts. Off line scheduling is more amenable to analytical solutions and there is a great deal of research done in this area [35]. However, the results of these investigations often cannot be applied to the on line problem. Likewise, much of the work in scheduling shared memory multiprocessors does not apply directly to distributed memory parallel computers. In principle, on line 102 schedulers designed for shared memory ....

M. Drozdowski. Scheduling Multiprocessor Tasks: An Overview. European Journal of Operational Research 94, pp. 215-230, 1996.

....the communications between the malleable tasks are usually neglected. We refer the reader to Lep ere, Mouni e, Robi c Trystram [11] for more details and for motivations of the MT model. MT are closely related to two other models, namely to the model of multiprocessor tasks (see e.g. Drozdowski [5]) and to the model of divisible tasks (Prasanna Musicus [15] The di erence between these models lies in the freedom allowed to the task allotment, that is, the number of processors which execute each task: A multiprocessor task requires to be executed by a xed integer number of processors, ....

M. Drozdowski [1996]. Scheduling multiprocessor tasks { An overview. European Journal of Operational Research 94, 215-230.

....a sequence of meetings where each meeting requires a certain group of people [5] 4. Diagnosable microprocessor systems, where a job must be performed on parallel processors in order to detect faults[12] 5. Testing of processors by one another requires at least two processors simultaneously [7]. 6. A file transfer(FTP) requires at least two processing elements simultaneously: the sender and receiver [7] The terms job and machine can be used interchangeably with terms task and processor, respectively (task and processor are commonly used when dealing with applications in computer ....

....systems, where a job must be performed on parallel processors in order to detect faults[12] 5. Testing of processors by one another requires at least two processors simultaneously [7] 6. A file transfer(FTP) requires at least two processing elements simultaneously: the sender and receiver [7]. The terms job and machine can be used interchangeably with terms task and processor, respectively (task and processor are commonly used when dealing with applications in computer science) To describe the 1 job on r machine pattern problem precisely, the notation used in scheduling literature ....

M.Drozdowski, Scheduling Multiprocessor Tasks-on overview, European Journal of Operations Research 94 (1996) 215-230 7

....proved there that under the same assumptions Pmjfix j ; pmtnjCmax with jfix j j = 2 can be solved in time O( P p j ) In this paper, we study the computational complexity of the preemptive variant of the problem. But here following the usual approach and assumptions in preemptive scheduling [4, 5] we do not assume (in contrast to [12] that starting times and preemptions are at integer points in time. Interestingly, without this assumption, the preemptive scheduling problem leads to fractional coloring of graphs. Hence we obtain by using a general complexity result for linear programs in ....

M. Drozdowski, Scheduling multiprocessor tasks - an overview, European Journal on Operations Research, 94 (1996), 215-230.

....these can also be obtained (as special cases) from the previously de ned general problem by requiring each task to consist of a single operation. Since both of the above special cases (jobshop and multiprocessor task scheduling) are NP hard even if there are only a constant number of machines [6, 7, 9, 16], it is natural to study how closely the optimum can be approximated by ecient algorithms. Focusing on the case where m and are xed, we will show that there are linear time approximation schemes for the problem providing a uni ed extension of recent approximability results for both of the above ....

....scheduling theory, each task is processed by only one processor at a time. However recently, due to the rapid development of parallel computer systems, new theoretical approaches have emerged to model scheduling on parallel architectures. One of these is scheduling multiprocessor tasks, see e.g. [6, 7]. The general (in contrast to dedicated, malleable, parallel) variant of non preemptive scheduling for independent multiprocessor tasks on a xed number of processors is denoted by Pmjset j jC max . Regarding the complexity, P3jset j jC max is strongly NP hard [3, 9] thus already this restricted ....

M. Drozdowski, Scheduling multiprocessor tasks - an overview, European Journal on Operations Research, 94 (1996), 215-230.

....scheduling theory, each task is processed by only one processor at a time. However recently, due to the rapid development of parallel computer systems, new theoretical approaches have emerged to model scheduling on parallel architectures. One of these is scheduling multiprocessor tasks, see e.g. [1, 4, 6, 8, 9, 11, 17, 23]. In this paper we address a multiprocessor scheduling problem, where a set T = fT 1 ; Tng of n tasks has to be executed by m processors such that each processor can execute at most one task at a time and a task must be processed simultaneously by several processors. Let M = f1; ....

....set of processors. The objective of the scheduling problems discussed in this paper is to minimize the makespan, i.e. the maximum completion time Cmax . We will mainly consider the parallel (or non malleable) version of the problem which has recently been discussed in several papers, see e.g. [4, 8, 9, 14, 16, 22]. We will focus on those preemptive schedules where migration is allowed, that is task T j may be assigned to di erent processor sets of size j during di erent execution phases [4, 8, 9] Approximation algorithms for preemptive scheduling without migration can be found e.g. in [21] The dedicated ....

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M. Drozdowski, Scheduling multiprocessor tasks - an overview, European Journal on Operations Research, 94 (1996), 215-230.

....scheduling theory, each task is processed by only one processor at a time. However recently, due to the rapid development of parallel computer systems, new theoretical approaches have emerged to model scheduling on parallel architectures. One of these is scheduling multiprocessor tasks, see e.g. [5, 8, 9]. In this paper we address some multiprocessor scheduling problems, where a set of n tasks has to be executed by m processors such that each processor can work on at most one task at a time and a task can (or may need to be) processed simultaneously by several processors. In the dedicated variant ....

M. Drozdowski, Scheduling multiprocessor tasks - an overview, European Journal on Operations Research, 94 (1996), 215-230.

....new results for several scheduling models of parallel jobs in order to minimize both (weighted) sum of completion times and makespan objectives. In these problems each job may demand more than one processor for execution, and hence is defined as 1 2 MU ALEM FEITELSON a parallel job. Drozdowski [5] gives a detailed overview on parallel jobs scheduling problems. All scheduling problems under consideration ask for minimization of some objective function. The most common (and apparently relatively simple to analyze) objective function is the makespan. The makespan of a schedule is the largest ....

....as well; in this case each job has a weight and we take the weighted sums. This captures the situation when some jobs are more important than the others. It seemed that significantly there are much more results in the area for approximating total completion times than for total flow times [5], although at optimality the two objectives are equivalent. However, the total completion times objective is concerned with maximizing the total number of finished jobs at any moment, and total flow times deals with fairness for each job [14] The models. We are given m identical processors and n ....

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M. Drozdowski, Scheduling multiprocessor tasks - An overview, European Journal of Operational Research 94 (1996) 215--230.

....Hence, tasks are subject to compatibility constraints. The present paper is concerned with scheduling independent multiprocessor tasks on dedicated processors, in both the preemptive case and the nonpreemptive case, and the goal is to minimize the makespan Cmax . Following the 1 See [6] for some practical justifications for considering multiprocessor task systems, and a survey on the main results obtained in multiprocessor task scheduling. notations of [11,20] we will denote the problem by Pm jfix j ; pmtnjCmax in the preemptive case, and Pm jfix j jCmax in the non preemptive ....

M. Drozdowski. Scheduling Multiprocessor Tasks - An Overview. Private communication, (1996)

....should be executed in the same time quantum on many processors rather than be scattered in various time quanta on di#erent processors. In such systems multiprocessor tasks are called coscheduled or gang scheduled tasks. An extensive description of the multiprocessor task concept can be found in [3, 4, 11, 26]. Now, we will formulate the considered deterministic scheduling problem. The computer system consists of two identical processors P 1 and P 2 .TasksetT is composed of two subsets: tasks requiring only one processor T 1 , T and tasks requiring two processors at the same moment of ....

....Cmax =max j maximum lateness Lmax =max j and the number of tasks completed after their due dates U j . Mean tardiness # j = j=1 max 0,c j is also mentioned in this work. To denote considered problems the three field notation introduced in [16, 26] will be used (cf. also [11]) In particular word size j in the task field stands for the fact that tasks require several processors simultaneously. A detailed survey of multiprocessor task scheduling can be found e.g. in [11] Now, we briefly review previous results for classical and multiprocessor tasks scheduling on two ....

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M. Drozdowski, Scheduling multiprocessor tasks -- An overview. Eur. J. Oper. Res. 94 (1996) 215-230.

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M. Drozdowski, Scheduling multiprocessor tasks - an overview, European Journal of Operational Research 94 (1996), 215-230.

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M. Drozdowski, Scheduling multiprocessor tasks - an overview, European Journal on Operations Research, 94 (1996), 215-230.

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M. Drozdowski, Scheduling multiprocessor tasks - an overview, European Journal on Operations Research, 94 (1996), 215-230.

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M. Drozdowski. Scheduling multiprocessor tasks - an overview. European Journal on Operations Research, pages 215-230, 1996.

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M. Drozdowski, Scheduling multiprocessor tasks - an overview, European Journal on Operations Research 94 (1996), 215-230.

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M. Drozdowski, Scheduling multiprocessor tasks - an overview, European Journal on Operations Research, 94 (1996), 215-230.

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DROZDOWSKI, M. Scheduling multiprocessor tasks - an overview. European Journal on Operations Research (1996), 215--230.

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M. Drozdowski. Scheduling multiprocessor tasks - an overview. European Journal of Operational Research, 94:215-230, 1996.

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