Despite extensive research focused on enabling QoS for grid users through economic and intelligent resource provisioning, no consensus has emerged on the most promising strategies. On top of intrinsically challenging problems, the complexity and size of data has so far drastically limited the number of comparative experiments. An alternative to experimenting on real, large, and complex data, is to look for well-founded and parsimonious representations. This study is based on exhaustive information about the gLite-monitored jobs from the EGEE grid, representative of a significant fraction of e-science computing activity in Europe. Our main contributions are twofold. First we found that workload models for this grid can consistently be discovered from the real data, and that limiting the range of models to piecewise linear time series models is sufficiently powerful. Second, we present a bootstrapping strategy for building more robust models from the limited samples at hand.

We consider the problem of modelling piecewise fractional autoregressive integrated moving-average (FARIMA) model signal. The number m of break points as well as their locations, the order (p, q) and the parameters of each regime are assumed to be unknown. To estimate the unknown parameters, we propose a criterion based on the minimum description length (MDL) principle of Rissanen. A genetic algorithm is implemented to optimize this criterion. Monte Carlo simulation results show that criterion performs well for estimating the break points number as well as their locations, the order and the parameters of each regime.

This paper presents a new robust method to estimate the parameters of ARMA models. This method makes use of the autocorrelations estimates based on the ratio of medians together with a robust filter cleaner able to reject a large fraction of outliers, and a Gaussian maximum likelihood estimation which handles missing values. The main advantages of the procedure are its easiness, robustness and fast execution. Its effectiveness is demonstrated on an example of the forecasting of the French daily electricity consumptions.

We present a new unscented particle filter for dynamic systems that outperforms the general particle filter and the unscented particle filter when the variance of the observation noise is small. Our algorithm uses a bank of unscented Kalman filters to refine the prediction in particle filter. The key difference with the traditional unscented particle filter is the introduction of an auxiliary model and a bank of unscented Kalman filter with this auxiliary model to generate the importance distribution in the particle filter. This structure makes efficient use of the latest observation information. Our new algorithm use fewer particles than the general particle filters and its performance outperforms them.

The problem of predicting a discrete-time stationary signal whose past is altered by some missing observations with arbitrary pattern is investigated. The autoregressive (AR) representation of the optimal linear mean-square predictor is obtained under the classical sufficient conditions of existence of such a representation for the predictor based on the complete past. These conditions hold for instance for an ARMA signal. The calculation of the AR representation requires to invert a matrix whose dimension depends on the number of missing values but is independent of their pattern, and whose elements depend only on the AR parameters of the signal. Some properties of the AR representation of the predictor for a finite order AR signal are derived.

Existing methods for estimating linearly s future values of a m-variate stationary random process using a record of p vectors from the past consist in first solving the one-step prediction problem and then all the h-step prediction problems for 2/spl les/h/spl les/s independently. When the Levinson (1947) algorithm is used, each prediction problem is solved with a numerical complexity proportional to p/sup 2/. We propose new methods to solve the h-step prediction problems for h/spl ges/2 with a numerical complexity proportional to p.

We consider the problem of synthesizing feasible signals in the presence of inconsistent convex constraints, some of which are hard in the sense that they must absolutely be satisfied. This problem is formalized as that of minimizing an objective function measuring the degree of unfeasibility with respect to the soft constraints over the intersection of the sets associated with the hard constraints. We first investigate the process of aggregating soft constraints in order to define relevant objectives and then address the question of solving the resulting convex programs. Finally, we provide numerical results to illustrate the benefits of our analysis.

The problem of minimum mean-square (m.s.) interpolation of a discrete-time stationary stochastic process using a class of infinite extent nonlinear interpolators is studied. These interpolators consist of a finite number p of nonlinear instantaneous transformations followed by a p input one output infinite extent linear filter. The expressions of the optimal interpolator and of the approximation error are derived and generalize the corresponding relations known in linear interpolation theory. As an extension, the estimation problem with several missing observations is also investigated.

We address the problem of linear mean-square estimation with arbitrary convex constraints for dependent processes. Two algorithms are proposed and their convergence is established. The first algorithm, which is deterministic, covers the case of known correlation structures; the second, which is stochastic and adaptive, covers the case of unknown correlation structures. Since existing algorithms can handle at most one simple constraint this contribution is relevant to signal processing problems in which arbitrary convex inequality constraints are present.

We consider a multivariable polynomial with random variables as arguments. All the monoids of this polynomial are arranged to define a random vector for which we study the correlation matrix. We establish necessary and sufficient invertibility conditions of this matrix, and investigate some applications.>

Quadratic systems appear in various fields of signal processing, in particular in detection and estimation. In this paper, we establish some conditions to determine the order and identify the coefficients of any discrete and finite extent quadratic system driven by a sequence of independent and identically distributed random variables. The input sequence is assumed unobservable and the conditions are based on some properties of the output cumulant functions up to the third order. Necessary and sufficient conditions ensuring the determination of the order are given. A sufficient condition of uniqueness to recover the parameters is presented. Lastly, some examples are given.>

The problem of estimating the amplitude of a signal is addressed using higher-order statistics. The probability distribution of the noise is assumed to be unknown so that the maximum likelihood estimator cannot be calculated. The estimator is taken as a polynomial of the observation, the coefficients of which are determined so that the estimate is unbiased with minimum variance. This method generalizes the linear approach, and the estimate variance is reduced. The ease of linear-quadratic estimation is detailed, and numerical examples are presented.>

The problem of estimating the amplitude of a signal appears in many aspects of signal processing such as, for example, amplitude modulation in communication theory. When the probability distribution of the noise is unknown, the calculation of the maximum likelihood estimator is impossible. Generally a linear estimator without bias and with minimum variance is used because it is simple to calculate and only requires the knowledge of the covariance matrix of the noise. The amplitude is estimated here with a polynomial of the observations. The coefficients of the polynomial are determined such that the estimator is unbiased with minimum variance regardless of the amplitude. This method is quite general since it only requires the knowledge of some higher-order moments of the noise.>

The bispectrum modelling problem using linear or quadratic filters is investigated. In the linear case, the third-order cumulant function C/sub 3/ of the output of a finite impulse response filter, driven by a white noise, is zero outside a finite domain. It is proven that this property is still valid if the filter is quadratic. The inverse problem is also considered. It is shown that, if the function C/sub 3/ is zero outside a finite domain, then the impulse response is necessarily finite in the linear case and may or may not be finite in the quadratic case. It is proven that every factorizable bispectrum can also be modeled with a quadratic filter, and an example to establish that the converse is false is given.>