Regenerative Simulation for Queueing Networks with Exponential or Heavier Tail Arrival Distributions

Multiclass open queueing networks find wide applications in communication, computer and fabrication networks. Often one is interested in steady-state performance measures associated with these networks. Conceptually, under mild conditions, a regenerative structure exists in multiclass networks, making them amenable to regenerative simulation for estimating the steady-state performance measures. However, typically, identification of a regenerative structure in these networks is difficult. A well known exception is when all the interarrival times are exponentially distributed, where the instants corresponding to customer arrivals to an empty network constitute a regenerative structure. In this paper, we consider networks where the interarrival times are generally distributed but have exponential or heavier tails. We show that these distributions can be decomposed into a mixture of sums of independent random variables such that at least one of the components is exponentially distributed. This allows an easily implementable embedded regenerative structure in the Markov process. We show that under mild conditions on the network primitives, the regenerative mean and standard deviation estimators are consistent and satisfy a joint central limit theorem useful for constructing asymptotically valid confidence intervals. We also show that amongst all such interarrival time decompositions, the one with the largest mean exponential component minimizes the asymptotic variance of the standard deviation estimator.Comment: A preliminary version of this paper will appear in Proceedings of Winter Simulation Conference, Washington, DC, 201

Estimation of calorific value of biomass from its elementary components by regression analysis

The calorific value is one of the most important properties of biomass fuels for design calculations or numerical simulations in thermochemical conversion systems for biomass. There are a number of formulae proposed in the literature to estimate the calorific value of biomass fuels from its elementary components by i.e. proximate, ultimate and chemical analysis composition. In this thesis, these correlations were evaluated statistically by Regression Analysis based on a larger database of biomass samples collected from the open literature. It was found that the correlations based on linear multiple regression analysis is the most accurate. The correlations based on the non-linear regression analysis have very low accuracy. The low accuracy of previous correlations is mainly due to the limitation of samples used for deriving them. To achieve a higher accuracy, new correlations were proposed to estimate the Calorific value by Regression analysis based on present database. The new correlation between the Calorific value and elemental components of biomass could be conveniently used to estimate the Calorific Value from Regression analysis. The new formula, based on the composition of main elements (in wt. %) C, H, O, N and S based on nonlinear regression analysis is C2+ C × O2+ 0.03 C × H + 0.60 C – O + 0.11 O × N + 0.53 S – 0.33 S × O = Calorific Value (Mj/Kg) whose R-squared value is 0.95

Column Subset Selection and Nystr\"om Approximation via Continuous Optimization

We propose a continuous optimization algorithm for the Column Subset Selection Problem (CSSP) and Nystr\"om approximation. The CSSP and Nystr\"om method construct low-rank approximations of matrices based on a predetermined subset of columns. It is well known that choosing the best column subset of size $k$ is a difficult combinatorial problem. In this work, we show how one can approximate the optimal solution by defining a penalized continuous loss function which is minimized via stochastic gradient descent. We show that the gradients of this loss function can be estimated efficiently using matrix-vector products with a data matrix $X$ in the case of the CSSP or a kernel matrix $K$ in the case of the Nystr\"om approximation. We provide numerical results for a number of real datasets showing that this continuous optimization is competitive against existing methods

Generalized Linear Models via the Lasso: To Scale or Not to Scale?

The Lasso regression is a popular regularization method for feature selection in statistics. Prior to computing the Lasso estimator in both linear and generalized linear models, it is common to conduct a preliminary rescaling of the feature matrix to ensure that all the features are standardized. Without this standardization, it is argued, the Lasso estimate will unfortunately depend on the units used to measure the features. We propose a new type of iterative rescaling of the features in the context of generalized linear models. Whilst existing Lasso algorithms perform a single scaling as a preprocessing step, the proposed rescaling is applied iteratively throughout the Lasso computation until convergence. We provide numerical examples, with both real and simulated data, illustrating that the proposed iterative rescaling can significantly improve the statistical performance of the Lasso estimator without incurring any significant additional computational cost

Variance Reduction for Matrix Computations with Applications to Gaussian Processes

In addition to recent developments in computing speed and memory, methodological advances have contributed to significant gains in the performance of stochastic simulation. In this paper, we focus on variance reduction for matrix computations via matrix factorization. We provide insights into existing variance reduction methods for estimating the entries of large matrices. Popular methods do not exploit the reduction in variance that is possible when the matrix is factorized. We show how computing the square root factorization of the matrix can achieve in some important cases arbitrarily better stochastic performance. In addition, we propose a factorized estimator for the trace of a product of matrices and numerically demonstrate that the estimator can be up to 1,000 times more efficient on certain problems of estimating the log-likelihood of a Gaussian process. Additionally, we provide a new estimator of the log-determinant of a positive semi-definite matrix where the log-determinant is treated as a normalizing constant of a probability density.Comment: 20 pages, 3 figure