Adaptive Importance Sampling Simulation of Queueing Networks

In this paper, a method is presented for the efficient estimation of rare-event (overflow) probabilities in Jackson queueing networks using importance sampling. The method differs in two ways from methods discussed in most earlier literature: the change of measure is state-dependent, i.e., it is a function of the content of the buffers, and the change of measure is determined using a cross-entropy-based adaptive procedure. This method yields asymptotically efficient estimation of overflow probabilities of queueing models for which it has been shown that methods using a stateindependent change of measure are not asymptotically efficient. Numerical results demonstrating the effectiveness of the method are presented as well

Simulation and the Monte Carlo Method

This accessible new edition explores the major topics in Monte Carlo simulation Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo Variance reduction techniques such as the transform likelihood ratio method and the screening method The score function method for sensitivity analysis The stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization The cross-entropy method to rare events estimation and combinatorial optimization Application of Monte Carlo techniques for counting problems, with an emphasis on the parametric minimum cross-entropy method An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly for advanced readers. A generous sampling of applied examples is positioned throughout the book, emphasizing various areas of application, and a detailed appendix presents an introduction to exponential families, a discussion of the computational complexity of stochastic programming problems, and sample MATLAB programs. Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method

Heavy Tails, Importance Sampling and Cross-Entropy

We consider the problem of estimating P (Y1+ ... +Yn > x) by importance sampling when the Yi are i.i.d. and heavy-tailed. The idea is to exploit the cross-entropy method as a tool for choosing good parameters in the importance sampling distribution; in doing so, we use the asymptotic description that given P(Y1+ ... +Yn > x,) n-1 of the Yi have distribution F and one the conditional distribution of Y given Y > x. We show in some parametric examples (Pareto and Weibull) how this leads to precise answers, which as demonstrated numerically, are close to being variance minimal within the parametric class under consideration. Related problems for M/G/1 and GI/G/1 queues are also discussed

The cross-entropy method for continuous multi-extremal optimization

In recent years, the cross-entropy method has been successfully applied to a wide range of discrete optimization tasks. In this paper we consider the cross-entropy method in the context of continuous optimization. We demonstrate the effectiveness of the cross-entropy method for solving difficult continuous multi-extremal optimization problems, including those with non-linear constraints

Diversifying focused testing for unit testing

Software changes constantly because developers add new features or modifications. This directly affects the effectiveness of the testsuite associated with that software, especially when these new modifications are in a specific area that no test case covers. This paper tackles the problem of generating a high quality test suite to cover repeatedly a given point in a program, with the ultimate goal of exposing faults possibly affecting the given program point. Both search based software testing and constraint solving offer ready, but low quality, solutions to this: ideally a maximally diverse covering test set is required whereas search and constraint solving tend to generate test sets with biased distributions. Our approach, Diversified Focused Testing (DFT), uses a search strategy inspired by GödelTest. We artificially inject parameters into the code branching conditions and use a bi-objective search algorithm to find diverse inputs by perturbing the injected parameters, while keeping the path conditions still satisfiable. Our results demonstrate that our technique, DFT, is able to cover a desired point in the code at least 90% of the time. Moreover, adding diversity improves the bug detection and the mutation killing abilities of the test suites. We show that DFT achieves better results than focused testing, symbolic execution and random testing by achieving from 3% to 70% improvement in mutation score and up to 100% improvement in fault detection across 105 software subjects

Simulation and the monte carlo method/ Rubinstein

275 hal.; 21 cm