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- MaxMin is a traditional two-phase heuristic which considers the makespan
objective in both phases. In the first phase the task t with the largest compute
time is selected. In the second phase task t is assigned to the machine which
minimizes the makespan.
- MaxMIN is a two-phase heuristic which considers the makespan objective in
the first phase and the energy consumption in the second. In the first phase
the task t with the largest compute time is selected. In the second phase
task t is assigned to the machine which minimizes the energy consumption.
- SuffMIN again considers the makespan objective in the first phase and the
energy consumption in the second. In the first phase the task t which suffers
the most if not assigned right away is selected. In the second phase task t is
assigned to the machine which minimizes the energy consumption.
- Min and MIN are one-phase greedy heuristics that assign tasks as they
arrive, considering the makespan ( Min ) and the energy consumption ( MIN ).
5 Modeling Uncertainty
In this work we consider two sources of uncertainty, the task execution time (ET)
and the machine energy consumption (EC). We present here the task execution
time model and the energy consumption model proposed in this work.
5.1 The Task Execution Time Uncertainty Model
One of the most popular models for modelling execution time uncertainty is
the f -model [15]. This model assumes the task's EET is uniformly distributed
within [ ET, ( f +1) ET ], where f is some positive factor. When f =0then
ʔ ET = 0 hence estimates are identical to execution times, and the larger the
f -value the greater the user inaccuracy in the system. In this work we perform
some empirical analysis and show the f -model does not fit the empirical data
considered in the analysis, hence we deduce some simple model from the data in
order to model task execution time uncertainty in this work.
In order to construct a model for uncertainty in the tasks execution time
we performed an empirical study using workloads from three real-world HPC
infrastructures. The analysis is two-fold, first we studied the EET of the tasks
to characterize the user behavior when requesting execution time for their tasks,
and second we studied the ʔ ET of the tasks considering their requested EET.
The first analyzed infrastructure is the CEA Curie system, a large HPC in-
frastructure with 93312 cores during the considered time span. A workload with
773138 tasks, which spans for 20 months (Feb. 2011-Oct. 2012), was used. We
also studied the RICC infrastructure, a medium sized system with 9216 cores. A
workload with 447794 tasks, which spans for 5 months (May 2010 to Sept. 2010)
was used. Finally, we studied the Cluster FING system, a small sized system
which was comprised of 408 cores during the considered time span. For the
Cluster FING system a 31 months period was analyzed, in this period dated
between November 2011 and June 2014, a total of 500000 tasks were executed.
 
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