SLO-aware Colocation of Data Center Tasks Based on Instantaneous Processor Requirements

In a cloud data center, a single physical machine simultaneously executes dozens of highly heterogeneous tasks. Such colocation results in more efficient utilization of machines, but, when tasks' requirements exceed available resources, some of the tasks might be throttled down or preempted. We analyze version 2.1 of the Google cluster trace that shows short-term (1 second) task CPU usage. Contrary to the assumptions taken by many theoretical studies, we demonstrate that the empirical distributions do not follow any single distribution. However, high percentiles of the total processor usage (summed over at least 10 tasks) can be reasonably estimated by the Gaussian distribution. We use this result for a probabilistic fit test, called the Gaussian Percentile Approximation (GPA), for standard bin-packing algorithms. To check whether a new task will fit into a machine, GPA checks whether the resulting distribution's percentile corresponding to the requested service level objective, SLO is still below the machine's capacity. In our simulation experiments, GPA resulted in colocations exceeding the machines' capacity with a frequency similar to the requested SLO.Comment: Author's version of a paper published in ACM SoCC'1

Distributed linear regression by averaging

Distributed statistical learning problems arise commonly when dealing with large datasets. In this setup, datasets are partitioned over machines, which compute locally, and communicate short messages. Communication is often the bottleneck. In this paper, we study one-step and iterative weighted parameter averaging in statistical linear models under data parallelism. We do linear regression on each machine, send the results to a central server, and take a weighted average of the parameters. Optionally, we iterate, sending back the weighted average and doing local ridge regressions centered at it. How does this work compared to doing linear regression on the full data? Here we study the performance loss in estimation, test error, and confidence interval length in high dimensions, where the number of parameters is comparable to the training data size. We find the performance loss in one-step weighted averaging, and also give results for iterative averaging. We also find that different problems are affected differently by the distributed framework. Estimation error and confidence interval length increase a lot, while prediction error increases much less. We rely on recent results from random matrix theory, where we develop a new calculus of deterministic equivalents as a tool of broader interest.Comment: V2 adds a new section on iterative averaging methods, adds applications of the calculus of deterministic equivalents, and reorganizes the pape

A statistical approach to the inverse problem in magnetoencephalography

Magnetoencephalography (MEG) is an imaging technique used to measure the magnetic field outside the human head produced by the electrical activity inside the brain. The MEG inverse problem, identifying the location of the electrical sources from the magnetic signal measurements, is ill-posed, that is, there are an infinite number of mathematically correct solutions. Common source localization methods assume the source does not vary with time and do not provide estimates of the variability of the fitted model. Here, we reformulate the MEG inverse problem by considering time-varying locations for the sources and their electrical moments and we model their time evolution using a state space model. Based on our predictive model, we investigate the inverse problem by finding the posterior source distribution given the multiple channels of observations at each time rather than fitting fixed source parameters. Our new model is more realistic than common models and allows us to estimate the variation of the strength, orientation and position. We propose two new Monte Carlo methods based on sequential importance sampling. Unlike the usual MCMC sampling scheme, our new methods work in this situation without needing to tune a high-dimensional transition kernel which has a very high cost. The dimensionality of the unknown parameters is extremely large and the size of the data is even larger. We use Parallel Virtual Machine (PVM) to speed up the computation.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS716 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

TaskPoint: sampled simulation of task-based programs

Sampled simulation is a mature technique for reducing simulation time of single-threaded programs, but it is not directly applicable to simulation of multi-threaded architectures. Recent multi-threaded sampling techniques assume that the workload assigned to each thread does not change across multiple executions of a program. This assumption does not hold for dynamically scheduled task-based programming models. Task-based programming models allow the programmer to specify program segments as tasks which are instantiated many times and scheduled dynamically to available threads. Due to system noise and variation in scheduling decisions, two consecutive executions on the same machine typically result in different instruction streams processed by each thread. In this paper, we propose TaskPoint, a sampled simulation technique for dynamically scheduled task-based programs. We leverage task instances as sampling units and simulate only a fraction of all task instances in detail. Between detailed simulation intervals we employ a novel fast-forward mechanism for dynamically scheduled programs. We evaluate the proposed technique on a set of 19 task-based parallel benchmarks and two different architectures. Compared to detailed simulation, TaskPoint accelerates architectural simulation with 64 simulated threads by an average factor of 19.1 at an average error of 1.8% and a maximum error of 15.0%.This work has been supported by the Spanish Government (Severo Ochoa grants SEV2015-0493, SEV-2011-00067), the Spanish Ministry of Science and Innovation (contract TIN2015-65316-P), Generalitat de Catalunya (contracts 2014-SGR-1051 and 2014-SGR-1272), the RoMoL ERC Advanced Grant (GA 321253), the European HiPEAC Network of Excellence and the Mont-Blanc project (EU-FP7-610402 and EU-H2020-671697). M. Moreto has been partially supported by the Ministry of Economy and Competitiveness under Juan de la Cierva postdoctoral fellowship JCI-2012-15047. M. Casas is supported by the Ministry of Economy and Knowledge of the Government of Catalonia and the Cofund programme of the Marie Curie Actions of the EUFP7 (contract 2013BP B 00243). T.Grass has been partially supported by the AGAUR of the Generalitat de Catalunya (grant 2013FI B 0058).Peer ReviewedPostprint (author's final draft

Tackling Exascale Software Challenges in Molecular Dynamics Simulations with GROMACS

GROMACS is a widely used package for biomolecular simulation, and over the last two decades it has evolved from small-scale efficiency to advanced heterogeneous acceleration and multi-level parallelism targeting some of the largest supercomputers in the world. Here, we describe some of the ways we have been able to realize this through the use of parallelization on all levels, combined with a constant focus on absolute performance. Release 4.6 of GROMACS uses SIMD acceleration on a wide range of architectures, GPU offloading acceleration, and both OpenMP and MPI parallelism within and between nodes, respectively. The recent work on acceleration made it necessary to revisit the fundamental algorithms of molecular simulation, including the concept of neighborsearching, and we discuss the present and future challenges we see for exascale simulation - in particular a very fine-grained task parallelism. We also discuss the software management, code peer review and continuous integration testing required for a project of this complexity.Comment: EASC 2014 conference proceedin

Predicting Scheduling Failures in the Cloud

Cloud Computing has emerged as a key technology to deliver and manage computing, platform, and software services over the Internet. Task scheduling algorithms play an important role in the efficiency of cloud computing services as they aim to reduce the turnaround time of tasks and improve resource utilization. Several task scheduling algorithms have been proposed in the literature for cloud computing systems, the majority relying on the computational complexity of tasks and the distribution of resources. However, several tasks scheduled following these algorithms still fail because of unforeseen changes in the cloud environments. In this paper, using tasks execution and resource utilization data extracted from the execution traces of real world applications at Google, we explore the possibility of predicting the scheduling outcome of a task using statistical models. If we can successfully predict tasks failures, we may be able to reduce the execution time of jobs by rescheduling failed tasks earlier (i.e., before their actual failing time). Our results show that statistical models can predict task failures with a precision up to 97.4%, and a recall up to 96.2%. We simulate the potential benefits of such predictions using the tool kit GloudSim and found that they can improve the number of finished tasks by up to 40%. We also perform a case study using the Hadoop framework of Amazon Elastic MapReduce (EMR) and the jobs of a gene expression correlations analysis study from breast cancer research. We find that when extending the scheduler of Hadoop with our predictive models, the percentage of failed jobs can be reduced by up to 45%, with an overhead of less than 5 minutes