Both analytical (Chapter ??) and simulationand experimentation-based (Chapter ??) approaches to resilience assessment rely on models for the various phenomena that may affect the system under study. These models must be both accurate, in that they reflect the phenomenon well, and suitable for the chosen approach. Analytical methods require models that are analytically tractable, while methods f...

This paper describes generation of nonuniform random variates from Lipschitzcontinuous densities using acceptance/ rejection, and the class library ranlip which implements this method. It is assumed that the required distribution has Lipschitzcontinuous density, which is either given analytically or as a black box. The algorithm builds a piecewise constant upper approximation to the density (th...

Pseudo-random numbers – both uniform and non-uniform – are used in random sampling, simulation, and Monte-Carlo estimation. Base SAS software contains numerous random number, quantile, and probability functions allowing the user to generate a selection of nominal, discrete, and continuous random variates. Other variates may be generated with a data step, often making use of SAS functions. We wi...

Sometimes input probability distributions for stochastic models are not so simple that standard distributions suit. In this case, we model with weighted sums of standard distributions. These composed distributions may have many parameters which must be estimated. This is not easy with common estimation methods like maximum-likelihood. We use the genetic algorithm for that. The design of the com...

The standard algorithm for fast generation of Erdős-Rényi random graphs only works in the Real RAM model. The critical point is the generation of geometric random variates Geo(p), for which there is no algorithm that is both exact and efficient in any bounded precision machine model. For a RAM model with word size w = Ω(log log(1/p)), we show that this is possible and present an exact algorithm...

Providing accurate and automated input modeling support is one of the challenging problems in the application of computer simulation. In this paper, we present a general-purpose input-modeling tool for representing, fitting, and generating random variates from multivariate input processes to drive computer simulations. We explain the theory underlying the suggested data fitting and data generat...

Monte Carlo algorithms typically need to generate random variates from a probability distribution described by an unnormalized density or probability mass function. Perfect simulation algorithms generate random variates exactly from these distributions, but have a running time T that is itself an unbounded random variable. This article shows that commonly used protocols for creating perfect sim...

– For any problem that asks you to provide an algorithm, be sure to give a step-by-step algorithm. Do not explain how to implement your algorithm in Arena or Excel, but rather, you should provide an algorithm (i.e., pseudo-code) that can be implemented in any language. Also, for any random variates needed by your algorithm, be sure to explicitly provide the steps needed to generate the random v...