On the Heterogeneity Bias of Cost Matrices for Assessing Scheduling Algorithms

Canon, Louis-Claude; Philippe, Laurent

doi:10.1109/tpds.2016.2629503

Cited by 4 publications

(21 citation statements)

References 134 publications

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“…The shuffling and noise‐based methods were later proposed in Canon and Philippe and Canon and Philippe . They both start with an initial cost matrix that is equivalent to a uniform instance (any cost is the product of a task weight and a machine cycle time).…”

Section: Related Workmentioning

confidence: 99%

“…More than 200 unique settings used for generating instances were collected from the literature and synthesized in Canon and Philippe . For each of them, we computed the correlations using the formulas from Table .…”

Section: Correlation Between Tasks and Processorsmentioning

confidence: 99%

“…Proof The expected value and the coefficient of variation of the costs in a matrix generated with the noise‐based method are μ and

\sqrt{V_{task}^{2} V_{mach}^{2} V_{noise}^{2} + V_{task}^{2} V_{mach}^{2} + V_{task}^{2} V_{noise}^{2} + V_{mach}^{2} V_{noise}^{2} + V_{task}^{2} + V_{mach}^{2} + V_{noise}^{2} ‾}

, respectively , Proposition . Replacing V task , V mach , and V noise by their definitions on Lines 3 to 5 leads to an expression that simplifies as V .□…”

Section: Controlling the Correlationmentioning

confidence: 99%

“…Of course, the performance of any scheduling algorithm depends on the properties of the input instance. Generating instances is thus a crucial problem in algorithm assessment …”

Section: Introductionmentioning

confidence: 99%

“…In a previous study, we already studied the problem of generating random matrices to assess the performance of scheduling algorithms in the unrelated case. In particular, we showed that the heterogeneity was previously not properly controlled despite having a significant impact on the relative performance of scheduling heuristics.…”

Section: Introductionmentioning

confidence: 99%

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Controlling the correlation of cost matrices to assess scheduling algorithm performance on heterogeneous platforms

Canon

Héam

Philippe

2017

Concurrency and Computation

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Summary Bias in the performance evaluation of scheduling heuristics has been shown to undermine the scope of existing studies. Improving the assessment step leads to stronger scientific claims when validating new optimization strategies. This article considers the problem of allocating independent tasks to unrelated machines such as to minimize the maximum completion time. Testing heuristics for this problem requires the generation of cost matrices that specify the execution time of each task on each machine. Numerous studies showed that the task and machine heterogeneities belong to the properties impacting heuristics performance the most. This study focuses on orthogonal properties, the average correlations between each pair of rows and each pair of columns, which measure the proximity with uniform instances. Cost matrices generated with 2 distinct novel generation methods show the effect of these correlations on the performance of several heuristics from the literature. In particular, EFT performance depends on whether the tasks are more correlated than the machines and HLPT performs the best when both correlations are close to one.

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Section: Related Workmentioning

confidence: 99%

Section: Correlation Between Tasks and Processorsmentioning

confidence: 99%

“…Proof The expected value and the coefficient of variation of the costs in a matrix generated with the noise‐based method are μ and

\sqrt{V_{task}^{2} V_{mach}^{2} V_{noise}^{2} + V_{task}^{2} V_{mach}^{2} + V_{task}^{2} V_{noise}^{2} + V_{mach}^{2} V_{noise}^{2} + V_{task}^{2} + V_{mach}^{2} + V_{noise}^{2} ‾}

, respectively , Proposition . Replacing V task , V mach , and V noise by their definitions on Lines 3 to 5 leads to an expression that simplifies as V .□…”

Section: Controlling the Correlationmentioning

confidence: 99%

“…Of course, the performance of any scheduling algorithm depends on the properties of the input instance. Generating instances is thus a crucial problem in algorithm assessment …”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Controlling the correlation of cost matrices to assess scheduling algorithm performance on heterogeneous platforms

Canon

Héam

Philippe

2017

Concurrency and Computation

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Scheduling DAG Applications for Time Sharing Systems

Ren

et al. 2018

Algorithms and Architectures for Parallel Processing

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Scheduling independent stochastic tasks on heterogeneous cloud platforms

Gao

Canon

Robert

et al. 2019

2019 IEEE International Conference on Cluster Computing (CLUSTER)

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This work introduces scheduling strategies to maximize the expected number of independent tasks that can be executed on a cloud platform within a given budget and under a deadline constraint. The cloud platform is composed of several types of virtual machines (VMs), where each type has a unit execution cost that depends upon its characteristics. The amount of budget spent during the execution of a task on a given VM is the product of its execution length by the unit execution cost of that VM. The execution lengths of tasks follow a variety of standard probability distributions (exponential, uniform, half-normal, lognormal, gamma, inverse-gamma and Weibull) whose mean and standard deviation both depend upon the VM type. Finally, there is a global available budget and a deadline constraint, and the goal is to successfully execute as many tasks as possible before the deadline is reached or the budget is exhausted (whichever comes first). On each VM, the scheduler can decide at any instant to interrupt the execution of a (long) running task and to launch a new one, but the budget already spent for the interrupted task is lost. The main questions are which VMs to enroll, and whether and when to interrupt tasks that have been executing for some time. We assess the complexity of the problem by showing its NP-completeness and providing a 2-approximation for the asymptotic case where budget and deadline both tend to infinity. Then we introduce several heuristics and compare their performance by running an extensive set of simulations.

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On the Heterogeneity Bias of Cost Matrices for Assessing Scheduling Algorithms

Cited by 4 publications

References 134 publications

Controlling the correlation of cost matrices to assess scheduling algorithm performance on heterogeneous platforms

Controlling the correlation of cost matrices to assess scheduling algorithm performance on heterogeneous platforms

Scheduling DAG Applications for Time Sharing Systems

Scheduling independent stochastic tasks on heterogeneous cloud platforms

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