J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 200--209, June 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....incurred due to preemptive scheduling algorithms may be much larger in parallel and distributed systems, and especially in the networks of workstations model. When the overhead is prohibitive, then results from theoretical studies on non preemptive execution of parallel jobs may be more relevant [25, 26, 21], but these results require complete information about jobs in the system. In this work, we consider the scheduling problem on a p processor system where n jobs all arrive at time 0 and no other jobs arrive thereafter. We present a new job model that applies to a large class of parallel All ....

....thereafter. We present a new job model that applies to a large class of parallel All four authers were partially supported by NSERC. Deng was also funded by a grant of HKRGC (CityU 1049 98E) and a grant of City University of Hong Kong. jobs, including those job models discussed in Turek et al. [25]. Our metric of performance is the mean response time of the jobs. To provide flexibility in modeling these costs, we classify scheduling algorithms by the number of preemptions they are allowed, ranging from none to an infinite number. We also explore job classes, categorized by their execution ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 200--209, June 1994.

....the adversary can choose, increases the knowledge of the non clairvoyant scheduler, or increases the power of the scheduler in some way. By covering many of these issues, we bring many of these paths of research together. 1. 3 Advantages Given to the Non Clairvoyant Scheduler One line of research [25, 5, 7], advantages the non clairvoyant scheduler by considering only batch jobs, i.e. all the jobs are released at time zero. However, in most practical settings, this not the case. Hence, we allow the jobs to be released at arbitrary times. Some results consider only fully parallelizable jobs (or ....

....with one processor) In practice, however, parallel programs can have a wide variety of execution characteristics. The parallelism profile of a job was introduced by Kumar [11] and extended by Deng and Koutsoupias [6] using a DAG model to represent the data dependency within the job. Turek et al. [25] model this more simply with a speedup function, Gamma. This specifies the rate at which work is completed as a function of the number of processors allocated to it. They require only that the speedup function be sublinear and nondecreasing, which in practice is reasonable. Edmonds, Chinn, ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 200--209, June 1994.

....the adversary can choose, increases the knowledge of the non clairvoyant scheduler, or increases the power of the scheduler in some way. By covering many of these issues, we bring many of these paths of research together. 1. 3 Advantages Given to the Non Clairvoyant Scheduler One line of research [25, 5, 7], advantages the non clairvoyant scheduler by considering only batch jobs, i.e. all the jobs are released at time zero. However, in most practical settings, this not the case. Hence, we allow the jobs to be released at arbitrary times. Some results consider only fully parallelizable jobs (or ....

....with one processor) In practice, however, parallel programs can have a wide variety of execution characteristics. The parallelism profile of a job was introduced by Kumar [11] and extended by Deng and Koutsoupias [6] using a DAG model to represent the data dependency within the job. Turek et al. [25] model this more simply with a speedup function, Gamma. This specifies the rate at which work is completed as a function of the number of processors allocated to it. They require only that the speedup function be sublinear and nondecreasing, which in practice is reasonable. Edmonds, Chinn, ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 200--209, June 1994.

.... of processor scheduling, and various algorithms have been proposed for different QoS metrics such as completion time, maximum response time and, weighted response time [6] In the parallel scheduling literature, there has been significant work on scheduling of malleable tasks, see for example [7, 8, 9, 10, 11]. Our multidimensional malleable scheduling problem has not been studied previously. In wireless networks, job scheduling has been addressed in the context of downlink broadcast scheduling [12] There a single transmission may satisfy multiple users or requests which is a model that is ....

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schweigelshohn, and P. S. Yu, "Scheduling parallelizable tasks to minimize average response time," in In Proc. of the 6th Annual Symposium on Parallel Algorithms and Architectures, 1994, pp. 200--209.

....incurred due to preemptive scheduling algorithms may be much larger in parallel and distributed systems, and especially in the networks of workstations model. When the overhead is prohibitive, then results from theoretical studies on non preemptive execution of parallel jobs may be more relevant [25, 26, 21], but these results require complete information about jobs in the system. To appear in the Journal of Scheduling y All four authers were partially supported by NSERC. Deng was also funded by a grant of HKRGC (CityU 1049 98E) and a grant of City University of Hong Kong. 1 In this work, we ....

....of Hong Kong. 1 In this work, we consider the scheduling problem on a p processor system where n jobs all arrive at time 0 and no other jobs arrive thereafter. We present a new job model that applies to a large class of parallel jobs, including those job models discussed in Turek et al. [25]. Our metric of performance is the mean response time of the jobs. To provide exibility in modeling these costs, we classify scheduling algorithms by the number of preemptions they are allowed, ranging from none to an in nite number. We also explore job classes, categorized by their execution ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 200-209, June 1994.

.... number of di#erent possibilities exist for CPU schedulers in a general purpose multiuser computing environment [31] Nevertheless, minimizing the mean completion time (the sum of the times at which each job completes, divided by the number of jobs) is a commonly used objective function [22] 18] [34], 35] 27] We can equivalently just consider the sum of the completion times. In this paper, the phrase completion times is used to imply that all jobs are available for execution at time zero, while the phrase response time implies that there are new job arrivals. Several recent analytic ....

....University of Waterloo, Waterloo, ON Canada N2L 3G1 (brecht cs.uwaterloo.ca) Department of Computer Science, TsingHua University, Beijing, China, 100084 (lkc dcs mail. tsinghua.edu.cn) 145 146 XIAOTIE DENG, NIAN GU, TIM BRECHT, AND KAICHENG LU job information is completely known [35] [34], 27] 18] These results initiated the first (theoretical) step toward understanding the general problem. Our work takes the next significant step and is distinguished from these results in that we remove the unrealistic assumption that the job execution time is known. Knowledge of execution ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J.L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. Yu, Scheduling parallelizable tasks to minimize average response time, in Proceedings of the Sixth Annual ACM Symposium on Parallel Algorithms and Architectures, ACM, New York, 1994, pp. 200--209.

.... number of different possibilities exist for CPU schedulers in a general purpose multi user computing environment [31] Nevertheless, minimizing the mean completion time (the sum of the times at which each job completes, divided by the number of jobs) is a commonly used objective function [22] 18] [34] [35] 27] We can equivalently just consider the sum of the completion times. In this paper, the phrase completion times is used to imply that all jobs are available for execution at time zero, while the phrase response time implies that there are new job arrivals. Several recent analytic ....

....at time zero, while the phrase response time implies that there are new job arrivals. Several recent analytic results have been obtained for the problem of minimizing mean completion times using non preemptive scheduling algorithms which assume that job information is completely known [35] [34] [27] 18] These results initiated the first (theoretical) step toward understanding the general problem. Our work takes the next significant step and is distinguished from these results in that we remove the unrealistic assumption that the job execution time is known. Knowledge of execution ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, P. Yu, Scheduling Parallelizable Tasks to Minimize Average Response Time, Proceedings of the 6th Annual Symposiumon Parallel Algorithms and Architectures, June, 1994, pp. 200--209.

....This problem is NP complete. Various heuristics have been developed for the different cases (e.g. for different requirements on the work, and for a possible requirement that the allocated PEs be contiguous) These heuristics lead to schedules that are within a factor of 2 or 3 from the optimal [587, 586, 608, 585]. Note that like many other results in scheduling theory, these algorithms are for off line scheduling, where all the jobs are given in advance. They do not handle on line scheduling, where jobs arrive in an unpredictable manner. As a result, the feedback effect alluded to earlier is avoided. ....

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu, "Scheduling parallelizable tasks to minimize average response time". In 6th Symp. Parallel Algorithms & Architectures, pp. 200--209, Jun 1994.

....incurred due to preemptive scheduling algorithms may be much larger in parallel and distributed systems, and especially in the networks of workstations model. When the overhead is prohibitive, then results from theoretical studies on non preemptive execution of parallel jobs may be more relevant [10, 19, 20, 16], but those results would require complete information of jobs in the system. In this work, we consider the scheduling problem on a p processor system where n jobs all arrive at time 0 and no other jobs arrive thereafter. We present a new job model that applies to a large class of parallel jobs, ....

....of jobs in the system. In this work, we consider the scheduling problem on a p processor system where n jobs all arrive at time 0 and no other jobs arrive thereafter. We present a new job model that applies to a large class of parallel jobs, including those job models discussed in Turek et al. [19]. Our metric of performance is the mean response time of the jobs. 1 The approach of Equi partition was first introduced to parallel scheduling by Tucker and Gupta as a process control policy [18] and later modified to the preemptive scheduling environment as DEQ by Zahorjan and McCann [21] ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 200--209, June 1994.

....the task graph structure. The NP hardness of the special case of independent tasks a fortiori means that the scheduling problem (in either the switched or mixed model) is also NP hard. The best algorithms known are constant factor approximations, with worst case factors in the range 2 2. 6 [111]. Unfortunately, a constant factor of this magnitude (which we will call packing loss ) may substantially mask the benefits which would otherwise be obtained from mixed parallelism. Furthermore, we know of no tighter analysis of this constant for a given graph, and the worst case constant may not ....

....special cases of the resource scheduling problem had previously known approximation algorithms; these are discussed below and summarized in Table 4.1. No precedence. If the precedence graph is empty, i.e. jobs are independent) then a number of approaches are known to get approximation bounds [57, 87, 113, 112, 111]. In the database scenario, it is possible to collapse each query, consisting of several jobs with a precedence relation among them, into one job, i.e. allocate maximum resources over all the jobs in the query, and then apply the results for independent jobs [119] This has a serious drawback in ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schweigelshohn, and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In Symposium on Parallel Algorithms and Architectures (SPAA). ACM, 1994.

....or another, unless we abandon some requirement. In what follows we show examples of this. No precedence. If the precedence graph were empty, i.e. independent jobs) then a number of approaches are known to get approximation bounds, even with additional restrictions like sub linear speedup [8, 17, 26, 25, 24]. In the database scenario, it is possible to collapse each query (consisting of several jobs with a precedence relation amongst them) into one job (allocating maximum resources over all the jobs in the query) and then apply the results for independent jobs [27] This has a serious drawback in ....

J. Turek, W. Ludwig, J. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schweigelshohn,and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In Symposium on Parallel Algorithms and Architectures (SPAA). ACM, 1994.

....the adversary can choose, increases the knowledge of the non clairvoyant scheduler, or increases the power of the scheduler in some way. By covering many of these issues, we bring many of these paths of research together. 1. 3 Advantages Given to the Non Clairvoyant Scheduler One line of research [25, 5, 7], advantages the non clairvoyant scheduler by considering only batch jobs, i.e. all the jobs are released at time zero. However, in most practical settings, this not the case. Hence, we allow the jobs to be released at arbitrary times. Some results consider only fully parallelizable jobs (or ....

....one processor) In practice, however, parallel programs can have a wide variety of execution characteristics. The parallelism profile of a job was introduced by Kumar [11] and extended by Deng and Koutsoupias [6] using a DAG model to represent the data dependency within the job. Turek et al. [25] model this more simply with a speedup function, Gamma. This specifies the rate at which work is completed as a function of the number of processors allocated to it. They require only that the speedup function be sublinear and nondecreasing, which in practice is reasonable. Edmonds, Chinn, ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 200--209, June 1994.

....the object sequences) so that the scheduler can effectively minimize some scheduling performance metric such as schedule length or average response time. This is obviously a very complex problem that, in many ways, generalizes recently proposed malleable multiprocessor scheduling problems [32]. The general sliding problem, as outlined above, has yet to be addressed in the scheduling or multimedia literature. Our results for the sequence packing problem indicate that simple, greedy scheduling algorithms based on Graham s list scheduling method [18] can guarantee provably ....

J. Turek, W. Ludwig, J.L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P.S. Yu. "Scheduling Parallelizable Tasks to Minimize Average Response Time". In Proc. of the 6th Annual ACM Symp. on Parallel Algorithms and Architectures, June 1994.

....incurred due to preemptive scheduling algorithms may be much larger in parallel and distributed systems, and especially in the networks of workstations model. When the overhead is prohibitive, then results from theoretical studies on non preemptive execution of parallel jobs may be more relevant [19, 20, 15], but these results require complete information about jobs in the system. In this work, we consider the scheduling problem on a p processor system where n jobs all arrive at time 0 and no other jobs arrive thereafter. We present a new job model that applies to a large class of parallel jobs, ....

....about jobs in the system. In this work, we consider the scheduling problem on a p processor system where n jobs all arrive at time 0 and no other jobs arrive thereafter. We present a new job model that applies to a large class of parallel jobs, including those job models discussed in Turek et al. [19]. Our metric of performance is the mean response time of the jobs. To provide flexibility in modeling these costs, we classify scheduling algorithms by the number of preemptions they are allowed, ranging from none to an infinite number. We also explore job classes, categorized by their execution ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 200--209, June 1994.

....model. In Section 3, we show that the average completion time of DEQ is within a constant factor of the optimal average completion time for any set of DAGs. We use notions of squashed area bound and height bound originally introduced for the nonpreemptive scheduling of parallel jobs [16] 29] 30] [28] and adapt some proof techniques of [5] In Section 4, we consider jobs characterized by BSP programs and discuss positive results in average completion time for a large class of good BSP programs on distributed memory multiprocessors. In Section 5, we conclude the paper with some remarks and ....

....time is a scheduling policy of the same competitive ratio for average completion time. For simplicity, we discuss the total completion time here. Any job represented by a DAG G would require at least D(G) execution time. Therefore we immediately have the following height bound [16] 29] 30] [28] on the completion time. Lemma 1 OPT (J ) P n i=1 D(G i ) Let the DAGs be ordered according to the number of nodes to be executed: jV 1 j jV 2 j Delta Delta Delta jV n j. We define the squashed area bound [16] 29] 30] 28] A(J ) to be P n i=1 (n Gamma i 1) jV i j P . Notice ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, P. S. Yu, "Scheduling Parallelizable Tasks to Minimize Average Response Time", Proceedings of the 6th Annual Symposium on Parallel Algorithms and Architectures, pp. 200-209, June, 1994.

....Dept. of CS, York University, North York, Canada M3J 1P3. email: gu cs.yorku.ca x Dept. of CS, York University, North York, Canada M3J 1P3. email: brecht cs.yorku.ca Dept. of CS, TsingHua University, Beijing, China, 100084. email:qhdata attmail.com job information is completely known [26] [25] [27] 11] These results initiated the first (theoretical) step toward understanding the general problem. Our work takes the next significant step and is distinguished from these results in that we remove the unrealistic assumption that the job execution time is known. Knowledge of execution ....

....which assume that job information is completely known. The first significant work is that of Turek, et al. who introduce an approximation algorithm of 32 times the optimum [26] This Preemptive Scheduling of Parallel Jobs on Multiprocessors 3 result has been subsequently improved and extended [25] [27] 11] A number of different preemptive policies have been proposed and studied for scheduling parallel jobs in multiprocessors [24] 20] 29] 16] 19] 7] In particular, experimental and simulation studies have shown that the DEQ yields low mean response times under a variety of workloads ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, P. S. Yu, "Scheduling Parallelizable Tasks to Minimize Average Response Time", Proceedings of the 6th Annual Sym- 8 X. Deng, N. Gu, T. Brecht, K. Lu posium on Parallel Algorithms and Architectures, pp. 200-209, June, 1994.

....the adversary can choose, increases the knowledge of the non clairvoyant scheduler, or increases the power of the scheduler in some way. By covering many of these issues, we bring many of these paths of research together. 1. 3 Advantages Given to the Non Clairvoyant Scheduler One line of research [25, 5, 7], advantages the non clairvoyant scheduler by considering only batch jobs, i.e. all the jobs are released at time zero. However, in most practical settings, this not the case. Hence, we allow the jobs to be released at arbitrary times. Some results consider only fully parallelizable jobs (or ....

....one processor) In practice, however, parallel programs can have a wide variety of execution characteristics. The parallelism profile of a job was introduced by Kumar [11] and extended by Deng and Koutsoupias [6] using a DAG model to represent the data dependency within the job. Turek et al. [25] model this more simply with a speedup function, Gamma. This specifies the rate at which work is completed as a function of the number of processors allocated to it. They require only that the speedup function be sublinear and nondecreasing, which in practice is reasonable. Edmonds, Chinn, ....

[Article contains additional citation context not shown here]

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu. Scheduling parallelizable tasks to minimize average response time. In 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 200--209, June 1994.

....assigned processors and that the tasks can be delayed for arbitrarily long periods of time before they are serviced. They evaluate the makespan for a set of tasks, instead of the response time for each single task, thus forsaking the issue of real time service. There are a number of studies, e.g. [2, 19, 8] and references therein, on the on line problem of allocating tasks to a set of servers. However, in their model, servers are independent; therefore, topology is not considered to be an issue. Further, the algorithms in [8] preempts tasks at any time without considering the cost involved. In all ....

J. Turek, W. Ludwig, J.L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelsohn, P.S. Yu (1994): Scheduling parallelizable tasks to minimize average response time. 6th ACM Symp. on Parallel Algorithms and Architectures.

....writing the application with the intention of promoting it to one of the later types, the better a good scheduler can perform with respect to both the particular job, and the whole workload. Generally, a scheduler can start a job sooner if the job is moldable or even malleable than if it is rigid [87]. If jobs are moldable, then processor allocations can be selected in accordance with the current system load, which delays the onset of saturation as system load increases [25] It is generally not difficult to write an application so that it is moldable, and is able to execute with processor ....

....be enhanced with a procedure to specifically handle those situations. For instance Kawaguchi and Kyan s LRF schedule [41] can be easily extended to parallel jobs. As long as no parallel job requires more than 50 of the processors, this will only increase the approximation factor from 1. 21 to 2 [87]. However, if jobs requiring more processors are allowed in addition, no constant approximation factor can be guaranteed. 2.2 Some Specific Studies Workload Characterization Several workload characterization studies of production high performance computing facilities have been carried out. They ....

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu, "Scheduling parallelizable tasks to minimize average response time". In 6th Symp. Parallel Algorithms & Architectures, pp. 200--209, Jun 1994.

.... [7] or scheduling with unknown job execution times [3] Similarly, completion time scheduling algorithms with a constant approximation factor have been provided with respect to o line scheduling [8] randomized scheduling [9] preemptive scheduling [10] scheduling of moldable (malleable) jobs [11] and scheduling with unknown job execution times [12] In general a parallel job schedule S determines for each job i its starting time and the subset of nodes M i assigned to this job. The starting time of job i must be greater than its submission time or release date r i and node subsets of two ....

....increase the cost of a schedule while C ( remains unchanged. Therefore, we have C S C ( C S 0 C ( 0 ) This concludes the proof for the completion time bound. The same bound for CS C can also be derived by a generalization of Lemma 4. 1 in a paper by Turek et al. [11]. For the makespan rst note that C max;S 0 C max;S and C max ( 0 ) C max ( hold with respect to all transformations described above. Also, the optimal makespan is bound by C max ( 0 ) max i2 0 fp i g and C max ( 0 ) P i2 0 p i m x 2 . This ....

J.J. Turek, W. Ludwig, J.L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. Yu. Scheduling parallelizable tasks to minimize average response time. In Proceedings of the 6 th Annual Symposium on Parallel Algorithms and Architectures, Cape May, NJ, pages 200-209, June 1994.

....et al. A preliminary version of this paper appeared in the Proceedings of the European Symposium of Algorithms ESA 96, Springer Lecture Notes in Science Computer 1136 showed that the SMART algorithm generates shelf based schedules with an approximation factor of 8. 53 [10] Turek et al. [14] proved that a generalization of Kawaguchi s and Kyan s LRF method produces a tight approximation factor of 2 for parallel jobs with unique weights if the resource requirement of each job is at most 50 of the maximum number of processors. However, when allowing arbitrary jobs this method may ....

....each job is at most 50 of the maximum number of processors. However, when allowing arbitrary jobs this method may result in schedules which deviate significantly from the optimum. Other results include Chakrabarti et al. 1] who addressed for instance the scheduling of malleable jobs similar to [14] and proved an expected performance within 8.67 of optimal for a randomized on line algorithm. Deng et al. 2] also discussed preemptive response time scheduling for malleable jobs with unique weights and variable resource requirements. But their model is related to a multithreaded environment ....

[Article contains additional citation context not shown here]

J.J. Turek, W. Ludwig, J.L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. Yu. Scheduling parallelizable tasks to minimize average response time. In Proceedings of the 6th Annual Symposium on Parallel Algorithms and Architectures, Cape May, NJ, pages 200--209, June 1994.

....of x 2 and the relations x 2 x1 2 and minfx 2 ; h i g maxfh i Gamma x 2 ; 0g = h i for all jobs i this results in 6 2c opt ( 2c opt ( 0 ) ffi c S 0 ffi c S : Note that the bound for cS copt can also be derived by a generalization of Lemma 4. 1 in a paper by Turek et al. [15]. For the makespan m opt h i and m opt t i Gammah i 2 holds for all jobs i 2 . With j being the job that finishes last in the schedule, we have mS m opt = t j m opt = t j Gamma h j m opt h j m opt 3: Note that no job system with jobs in 0 2 can generate a worst case ....

J.J. Turek, W. Ludwig, J.L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. Yu. Scheduling parallelizable tasks to minimize average response time. In Proceedings of the 6th Annual Symposium on Parallel Algorithms and Architectures, Cape May, NJ, pages 200--209, June 1994.

....writing the application with the intention of promoting it to one of the later types, the better a good scheduler can perform with respect to both the particular job, and the whole workload. Generally, a scheduler can start a job sooner if the job is moldable or even malleable than if it is rigid [88]. If jobs are moldable, then processor allocations can be selected in accordance with the current system load, which delays the onset of saturation as system load increases [26] It is generally not difficult to write an application so that it is moldable, and is able to execute with processor ....

....with a procedure to specifically handle those situations. Example 6 For instance Kawaguchi and Kyan s LRF schedule [42] can be easily extended to parallel jobs. As long as no parallel job requires more than 50 of the processors, this will only increase the approximation factor from 1. 21 to 2 [88]. However, if jobs requiring more processors are allowed in addition, no constant approximation factor can be guaranteed. Finally, as already mentioned the costs of the schedules generated by theoretical approximation methods are usually very low for the average workload. Even if they do not ....

J. Turek, W. Ludwig, J. L. Wolf, L. Fleischer, P. Tiwari, J. Glasgow, U. Schwiegelshohn, and P. S. Yu, "Scheduling parallelizable tasks to minimize average response time". In 6th Symp. Parallel Algorithms & Architectures, pp. 200--209, Jun 1994.

No context found.

John Turek, Walter Ludwig, Joel L. Wolf, Lisa Fleischer, Prasoon Tiwari, Jason Glasgow, Uwe Schwiegelshohn, and Philip S. Yu. "Scheduling Parallelizable Tasks to Minimize Average Response Time". In Proceedings of the Sixth Annual ACM Symposium on Parallel Algorithms and Architectures, pages 200--209, Cape May, New Jersey, June 1994.

No context found.

John Turek, Walter Ludwig, Joel L. Wolf, Lisa Fleischer, Prasoon Tiwari, Jason Glasgow, Uwe Schwiegelshohn, and Philip S. Yu. Scheduling parallelizable tasks to minimize average response time. In 6th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 200--209, 1994.

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