A novel approach for distributed application scheduling based on prediction of communication events

The evolution of commodity computing lead to the possibility of efficient usage of interconnected machines to solve computationally-intensive tasks, which were previously solvable only by using expensive supercomputers. This, however, required new methods for process scheduling and distribution, considering the network latency, communication cost, heterogeneous environments and distributed computing constraints. An efficient distribution of processes over such environments requires an adequate scheduling strategy, as the cost of inefficient process allocation is unacceptably high. Therefore, a knowledge and prediction of application behavior is essential to perform effective scheduling. In this paper, we overview the evolution of scheduling approaches, focusing on distributed environments. We also evaluate the current approaches for process behavior extraction and prediction, aiming at selecting an adequate technique for online prediction of application execution. Based on this evaluation, we propose a novel model for application behavior prediction, considering chaotic properties of such behavior and the automatic detection of critical execution points. The proposed model is applied and evaluated for process scheduling in cluster and grid computing environments. The obtained results demonstrate that prediction of the process behavior is essential for efficient scheduling in large-scale and heterogeneous distributed environments, outperforming conventional scheduling policies by a factor of 10, and even more in some cases. Furthermore, the proposed approach proves to be efficient for online predictions due to its low computational cost and good precision. (C) 2009 Elsevier B.V. All rights reserved.

Positive solutions for the p-Laplacian involving critical and supercritical nonlinearities with zeros

In this paper we show the existence of multiple solutions to a class of quasilinear elliptic equations when the continuous non-linearity has a positive zero and it satisfies a p-linear condition only at zero. In particular, our approach allows us to consider superlinear, critical and supercritical nonlinearities. (C) 2009 Elsevier Masson SAS. All rights reserved.

Black-box decomposition approach for computational hemodynamics: One-dimensional models

Increasing efforts exist in integrating different levels of detail in models of the cardiovascular system. For instance, one-dimensional representations are employed to model the systemic circulation. In this context, effective and black-box-type decomposition strategies for one-dimensional networks are needed, so as to: (i) employ domain decomposition strategies for large systemic models (1D-1D coupling) and (ii) provide the conceptual basis for dimensionally-heterogeneous representations (1D-3D coupling, among various possibilities). The strategy proposed in this article works for both of these two scenarios, though the several applications shown to illustrate its performance focus on the 1D-1D coupling case. A one-dimensional network is decomposed in such a way that each coupling point connects two (and not more) of the sub-networks. At each of the M connection points two unknowns are defined: the flow rate and pressure. These 2M unknowns are determined by 2M equations, since each sub-network provides one (non-linear) equation per coupling point. It is shown how to build the 2M x 2M non-linear system with arbitrary and independent choice of boundary conditions for each of the sub-networks. The idea is then to solve this non-linear system until convergence, which guarantees strong coupling of the complete network. In other words, if the non-linear solver converges at each time step, the solution coincides with what would be obtained by monolithically modeling the whole network. The decomposition thus imposes no stability restriction on the choice of the time step size. Effective iterative strategies for the non-linear system that preserve the black-box character of the decomposition are then explored. Several variants of matrix-free Broyden`s and Newton-GMRES algorithms are assessed as numerical solvers by comparing their performance on sub-critical wave propagation problems which range from academic test cases to realistic cardiovascular applications. A specific variant of Broyden`s algorithm is identified and recommended on the basis of its computer cost and reliability. (C) 2010 Elsevier B.V. All rights reserved.

Predicting random effects with an expanded finite population mixed model

Prediction of random effects is an important problem with expanding applications. In the simplest context, the problem corresponds to prediction of the latent value (the mean) of a realized cluster selected via two-stage sampling. Recently, Stanek and Singer [Predicting random effects from finite population clustered samples with response error. J. Amer. Statist. Assoc. 99, 119-130] developed best linear unbiased predictors (BLUP) under a finite population mixed model that outperform BLUPs from mixed models and superpopulation models. Their setup, however, does not allow for unequally sized clusters. To overcome this drawback, we consider an expanded finite population mixed model based on a larger set of random variables that span a higher dimensional space than those typically applied to such problems. We show that BLUPs for linear combinations of the realized cluster means derived under such a model have considerably smaller mean squared error (MSE) than those obtained from mixed models, superpopulation models, and finite population mixed models. We motivate our general approach by an example developed for two-stage cluster sampling and show that it faithfully captures the stochastic aspects of sampling in the problem. We also consider simulation studies to illustrate the increased accuracy of the BLUP obtained under the expanded finite population mixed model. (C) 2007 Elsevier B.V. All rights reserved.