Showing papers in "ACM Transactions on Modeling and Computer Simulation in 2003"

ACM Transactions on Modeling and Computer Simulation: Guest Editorial

Abstract: Genetic testing is an area of medicine that will affect the way insurers and medical directors conduct business in the future. To what degree, has yet to be determined. Nevertheless, it is a certainty, that the insurance playing field will be different. Many factors are coming into play: the speed at which the mushrooming cloud of knowledge is expanding faster than anticipated; the crossover from merely predictors of genetic diseases into mainstream medicine for common ailments like cancer, heart disease, and diabetes, and, much to our concern, the ever increasing number of legislative bans on insurers’ use of this technology. In recognition of these concerns the American Council of Life Insurance, with the American Academy of Insurance Medicine, Canadian Life Insurance Medical Officers Association, and Health Insurance Association of America, sponsored a conference in February 1996, entitled: \"Genetic Issues Seminar-Update ’96.\" During the two and half days of presentations, attendees could hear about the latest developments regarding genetic testing both in the clinical and insurance arenas. The topics were quite diverse. Topics covered were from, \"Genetics and Obesity,\" to the latest developments in the Human Genome Project. We are now privileged to publish selected articles from those presentations. In this issue you will find an article by Michael Youngman, vice president of Northwestern Mutual’s Government Relations. He outlines the political history of genetic tests and gives an eye opening look at possible developments. Is everyone entitled to life insurance? Some legislators think so. I challenged David Holland, who has a unique perspective as both an actuary and CEO, to develop a protocol that might illustrate the possible consequences of life insurance entitlement. I think you will find his article quite .fascinating. Apolipoprotein E has shown possible value as a predictor of both heart disease and Alzheimer’s disease. Dr. Perls, a geriatrician from Harvard Medical School, discusses the association between Apolipoprotein E and Alzheimer’s. In addition, Dr. Engman, medical director from Lincoln National, presents data regarding the BRCA1 and BRCA2 models he has constructed. Finally, Dr. Culver, director of Gene Therapy Research at OncorMed, gives us a peek into the future of genetic therapy and Andre Chuffart, vice president of Swiss Re, shares his insights about how the genetic revolution is evolving in Europe. One outcome of the conference was the opening of communication channels between the genetics and insurance communities. After the conference, Dr.Pokorksi’s article, \"Use of Genetic Tests to Predict and Diagnose Cancer: An Insurance Perspective,’1 was published in the Journal of Tumor Marker Oncology. I would like to think that this conference had at least a small part in bringing these two groups together. I highly recommend this article as a primer on our concerns about genetic testing, legislation, and clinical medicine. I know you will find these articles both enlightening and thought provoking and my thanks goes to all who helped to make the conference a success.

Discrete-event simulation optimization using ranking, selection, and multiple comparison procedures: A survey

Abstract: An important use for discrete-event simulation models lies in comparing and contrasting competing design alternatives without incurring any physical costs. This article presents a survey of the literature for two widely used classes of statistical methods for selecting the best design from among a finite set of k alternatives: ranking and selection (RS guidelines for procedure application are offered.

Variable-sample methods for stochastic optimization

Abstract: In this article we discuss the application of a certain class of Monte Carlo methods to stochastic optimization problems. Particularly, we study variable-sample techniques, in which the objective function is replaced, at each iteration, by a sample average approximation. We first provide general results on the schedule of sample sizes, under which variable-sample methods yield consistent estimators as well as bounds on the estimation error. Because the convergence analysis is performed pathwisely, we are able to obtain our results in a flexible setting, which requires mild assumptions on the distributions and which includes the possibility of using different sampling distributions along the algorithm. We illustrate these ideas by studying a modification of the well-known pure random search method, adapting it to the variable-sample scheme, and show conditions for convergence of the algorithm. Implementation issues are discussed and numerical results are presented to illustrate the ideas.

Modeling and generating multivariate time-series input processes using a vector autoregressive technique

Abstract: We present a model for representing stationary multivariate time-series input processes with marginal distributions from the Johnson translation system and an autocorrelation structure specified through some finite lag. We then describe how to generate data accurately to drive computer simulations. The central idea is to transform a Gaussian vector autoregressive process into the desired multivariate time-series input process that we presume as having a VARTA (Vector-Autoregressive-To-Anything) distribution. We manipulate the autocorrelation structure of the Gaussian vector autoregressive process so that we achieve the desired autocorrelation structure for the simulation input process. We call this the correlation-matching problem and solve it by an algorithm that incorporates a numerical-search procedure and a numerical-integration technique. An illustrative example is included.

Behavior of the NORTA method for correlated random vector generation as the dimension increases

Abstract: The NORTA method is a fast general-purpose method for generating samples of a random vector with given marginal distributions and given correlation matrix. It is known that there exist marginal distributions and correlation matrices that the NORTA method cannot match, even though a random vector with the prescribed qualities exists. We investigate this problem as the dimension of the random vector increases. Simulation results show that the problem rapidly becomes acute, in the sense that NORTA fails to work with an increasingly large proportion of correlation matrices. Simulation results also show that if one is willing to settle for a correlation matrix that is "close" to the desired one, then NORTA performs well with increasing dimension. As part of our analysis, we develop a method for sampling correlation matrices uniformly (in a certain precise sense) from the set of all such matrices. This procedure can be used more generally for sampling uniformly from the space of all symmetric positive definite matrices with diagonal elements fixed at positive values.

Variance with alternative scramblings of digital nets

Abstract: There have been many proposals for randomizations of digital nets. Some of those proposals greatly reduce the computational burden of random scrambling. This article compares the sampling variance under different scrambling methods. Some scrambling methods adversely affect the variance, even to the extent of deteriorating the rate at which variance converges to zero. Surprisingly, a new scramble proposed here, has the effect of improving the rate at which the variance converges to zero, but so far, only for one dimensional integrands. The mean squared L2 discrepancy is commonly used to study scrambling schemes. In this case, it does not distinguish among some scrambles with different convergence rates for the variance.

A combined procedure for optimization via simulation

Abstract: We propose an optimization-via-simulation algorithm for use when the performance measure is estimated via a stochastic, discrete-event simulation, and the decision variables may be subject to deterministic linear integer constraints. Our approach---which consists of a global guidance system, a selection-of-the-best procedure, and local improvement---is globally convergent under very mild conditions.

Two-timescale simultaneous perturbation stochastic approximation using deterministic perturbation sequences

Abstract: Simultaneous perturbation stochastic approximation (SPSA) algorithms have been found to be very effective for high-dimensional simulation optimization problems. The main idea is to estimate the gradient using simulation output performance measures at only two settings of the N-dimensional parameter vector being optimized rather than at the N + 1 or 2N settings required by the usual one-sided or symmetric difference estimates, respectively. The two settings of the parameter vector are obtained by simultaneously changing the parameter vector in each component direction using random perturbations. In this article, in order to enhance the convergence of these algorithms, we consider deterministic sequences of perturbations for two-timescale SPSA algorithms. Two constructions for the perturbation sequences are considered: complete lexicographical cycles and much shorter sequences based on normalized Hadamard matrices. Recently, one-simulation versions of SPSA have been proposed, and we also investigate these algorithms using deterministic sequences. Rigorous convergence analyses for all proposed algorithms are presented in detail. Extensive numerical experiments on a network of M/G/1 queues with feedback indicate that the deterministic sequence SPSA algorithms perform significantly better than the corresponding randomized algorithms.

Continuous random variate generation by fast numerical inversion

Abstract: The inversion method for generating nonuniform random variates has some advantages compared to other generation methods, since it monotonically transforms uniform random numbers into non-uniform random variates. Hence, it is the method of choice in the simulation literature. However, except for some simple cases where the inverse of the cumulative distribution function is a simple function we need numerical methods. Often inversion by "brute force" is used, applying either very slow iterative methods or linear interpolation of the CDF and huge tables. But then the user has to accept unnecessarily large errors or excessive memory requirements, that slow down the algorithm. In this article, we demonstrate that with Hermite interpolation of the inverse CDF we can obtain very small error bounds close to machine precision. Using our adaptive interval splitting method, this accuracy is reached with moderately sized tables that allow for a fast and simple generation procedure.

Empirical evidence concerning AES

Abstract: AES, the Advanced Encryption Standard, is one of the most important algorithms in modern cryptography. Certain randomness properties of AES are of vital importance for its security. At the same time, these properties make AES an interesting candidate for a fast nonlinear random number generator for stochastic simulation. In this article, we address both of these two aspects of AES. We study the performance of AES in a series of statistical tests that are related to cryptographic notions like confusion and diffusion. At the same time, these tests provide empirical evidence for the suitability of AES in stochastic simulation. A substantial part of this article is devoted to the strategy behind our tests and to their relation to other important test statistics like Maurer's Universal Test.

Modeling methodology for integrated simulation of embedded systems

Abstract: Developing a single embedded application involves a multitude of different development tools including several different simulators. Most tools use different abstractions, have their own formalisms to represent the system under development, utilize different input and output data formats, and have their own semantics. A unified environment that allows capturing the system in one place and one that drives all necessary simulators and analysis tools from this shared representation needs a common representation technology that must support several different abstractions and formalisms seamlessly. Describing the individual formalisms by metamodels and carefully composing them is the underlying technology behind MILAN, a Model-based Integrated Simulation Framework. MILAN is an extensible framework that supports multigranular simulation of embedded systems by seamlessly integrating existing simulators into a unified environment. Formal metamodels and explicit constraints define the domain-specific modeling language developed for MILAN that combines hierarchical, heterogeneous, parametric dataflow representation with strong data typing. Multiple modeling aspects separate orthogonal concepts. The language also allows the representation of the design space of the application, not just a point solution. Nonfunctional requirements are captured as formal, application-specific constraints. MILAN has integrated tool support for design-space exploration and pruning. The models are used to automatically configure the integrated functional simulators, high-level performance and power estimators, cycle-accurate performance simulators, and power-aware simulators. Simulation results are used to automatically update the system models. The article focuses on the modeling methodology and briefly describes how the integrated models are utilized in the framework.

A system of high-dimensional, efficient, long-cycle and portable uniform random number generators

Abstract: We propose a system of multiple recursive generators of modulus p and order k where all nonzero coefficients of the recurrence are equal. The advantage of this property is that a single multiplication is needed to compute the recurrence, so the generator would run faster than the general case. For p = 231 − 1, the most popular modulus used, we provide tables of specific parameter values yielding maximum period for recurrence of order k = 102 and 120. For p = 231 − 55719 and k = 1511, we have found generators with a period length approximately 1014100.5.

HAVEGE: A user-level software heuristic for generating empirically strong random numbers

Abstract: Random numbers with high cryptographic quality are needed to enhance the security of cryptography applications. Software heuristics for generating empirically strong random number sequences rely on entropy gathering by measuring unpredictable external events. These generators only deliver a few bits per event. This limits them to being used as seeds for pseudorandom generators.General-purpose processors feature a large number of hardware mechanisms that aim to improve performance: caches, branch predictors, …. The state of these components is not architectural (i.e., the result of an ordinary application does not depend on it). It is also volatile and cannot be directly monitored by the user. On the other hand, every operating system interrupt modifies thousands of these binary volatile states.In this article, we present and analyze HAVEGE (HArdware Volatile Entropy Gathering and Expansion), a new user-level software heuristic to generate practically strong random numbers on general-purpose computers. The hardware clock cycle counter of the processor can be used to gather part of the entropy/uncertainty introduced by operating system interrupts in the internal states of the processor. Then, we show how this entropy gathering technique can be combined with pseudorandom number generation in HAVEGE. Since the internal state of HAVEGE includes thousands of internal volatile hardware states, it seems impossible even for the user itself to reproduce the generated sequences.

Dynamic structure multiparadigm modeling and simulation

Abstract: This article presents the Heterogeneous Flow System Specification (HFSS), a formalism aimed to represent hierarchical and modular hybrid flow systems with dynamic structure. The concept of hybrid flow systems provides a generalization of the conventional concept of hybrid system and it can represent a whole plethora of systems, namely: discrete event systems, multicomponent and multirate numerical methods, multirate and multicomponent sampling systems, event locators and time-varying systems. The ability to join all these types of models makes HFSS an excellent framework for merging components built in different paradigms. We present several examples of model definition in the HFSS formalism and we also exploit the ability of the HFSS formalism to represent mutirate numerical integrators.

Computing the distribution function of a conditional expectation via monte carlo: Discrete conditioning spaces

Abstract: We examine different ways of numerically computing the distribution function of conditional expectations where the conditioning element takes values in a finite or countably infinite outcome space. Both the conditional expectation and the distribution function itself are computed via Monte Carlo simulation. Given a limited (and fixed) computer budget, the quality of the estimator is gauged by the inverse of its mean square error. It is a function of the fraction of the budget allocated to estimating the conditional expectation versus the amount of sampling done relative to the "conditioning variable." We will present the asymptotically optimal rates of convergence for different estimators and resolve the trade-off between the bias and variance of the estimators. Moreover, central limit theorems are established for some of the estimators proposed. We will also provide algorithms for the practical implementation of two of the estimators and illustrate how confidence intervals can be formed in each case. Major potential application areas include calculation of Value at Risk (VaR) in the field of mathematical finance and Bayesian performance analysis.

Flexible reference trace reduction for VM simulations

Abstract: The unmanageably large size of reference traces has spurred the development of sophisticated trace reduction techniques. In this article we present two new algorithms for trace reduction: Safely Allowed Drop (SAD) and Optimal LRU Reduction (OLR). Both achieve high reduction factors and guarantee exact simulations for common replacement policies and for memories larger than a user-defined threshold. In particular, simulation on OLR-reduced traces is accurate for the LRU replacement algorithm, while simulation on SAD-reduced traces is accurate for the LRU and OPT algorithms. Both policies can easily be modified and extended to maintain timing information, thus allowing for exact simulation of the Working Set and VMIN policies. OLR also satisfies an optimality property: for a given original trace and chosen memory size, it produces the shortest possible reduced trace that has the same LRU behavior as the original for a memory of at least the chosen size. We present a proof of this optimality of OLR, and show that SAD, while not optimal, yields nearly optimal performance in practice.Our approach has multiple applications, especially in simulating virtual memory systems; many page replacement algorithms are similar to LRU in that more recently referenced pages are likely to be resident. For several replacement algorithms in the literature, SAD- and OLR-reduced traces yield exact simulations. For many other algorithms, our trace reduction eliminates information that matters little: we present extensive measurements to show that the error for simulations of the clock and segq (segmented queue) replacement policies (the most common LRU approximations) is under 3p for the vast majority of memory sizes. In nearly all cases, the error is much smaller than that incurred by the well-known stack deletion technique.SAD and OLR have many desirable properties. In practice, they achieve reduction factors up to several orders of magnitude. The reduction translates to both storage savings and simulation speedups. Both techniques require little memory and perform a single forward traversal of the original trace, making them suitable for online trace reduction. Neither requires that the simulator be modified to accept the reduced trace.

Efficient multiply-with-carry random number generators with maximal period

Abstract: In this (largely expository) article, we propose a simple modification of the multiply-with-carry random number generators of Marsaglia [1994] and Couture and L'Ecuyer [1997]. The resulting generators are both efficient (since they may be configured with a base b which is a power of 2) and exhibit maximal period. These generators are analyzed using a simple but powerful algebraic technique involving b-adic numbers.

Efficient simulation of queues in heavy traffic

Abstract: When simulating queues in heavy traffic, estimators of quantities such as average delay in queue d converge slowly to their true values. This problem is exacerbated when interarrival and service distributions are irregular. For the GI/G/1 queue, delay moments can be expressed in terms of moments of idle period I. Instead of estimating d directly by a standard regenerative estimator that we call DD, a method we call DI estimates d from estimated moments of I. DI was investigated some time ago and shown to be much more efficient than DD in heavy traffic. We measure efficiency as the factor by which variance is reduced. For the GI/G/1 queue, we show how to generate a sequence of realized values of the equilibrium idle period, Ie, that are not independent and identically distributed, but have the correct statistical properties in the long run. We show how to use this sequence to construct a new estimator of d, called DE, and of higher moments of delay as well. When arrivals are irregular, we show that DE is more efficient than DI, in some cases by a large factor, independent of the traffic intensity. Comparing DE with DD, these factors multiply. For GI/G/c, we construct a control-variates estimator of average delay in queue dc that is efficient in heavy traffic. It uses DE to estimate the average delay for the corresponding fast single server. We compare the efficiency of this method with another method in the literature. For M/G/c, we use insensitivity to construct another control-variates estimator of dc. We compare the efficiency of this estimator with the two c-server estimators above.

Declaration of unknowns in DAE-based hybrid system specification

Abstract: The majority of hybrid languages are based on the assumption that discontinuities in differential variables at discrete events are modeled by explicit mappings. When there are algebraic equations restricting the allowed new values of the differential variables, explicit remapping of differential variables forces the modeler to solve the algebraic equations. To overcome this difficulty, hybrid languages use many different language elements. This article shows that only one language element is needed for this purpose: an unknown declaration, which allows the explicit declaration of a variable as unknown. The syntax and semantics of unknown declarations are discussed. Examples are given, using the Chi language, in which unknown declarations are used for modeling multi-body collision, steady-state initialization, and consistent initialization of higher index systems. It is also illustrated how the declaration of unknowns can help to clarify the structure of the system of equations, and how it can help the modeler detect structurally singular systems of equations.

Guest introduction

Abstract: Pseudorandom numbers are basic ingredients for a wide range of practical applications involving computers; for example, simulation, statistics, numerical analysis, computer games, lotteries, and cryptology. Those applications often have different requirements, which in a sense makes things more interesting. Recurring desiderata are efficiency (high speed and small memory usage) and a long period. For simulation, it is often argued that the set of all vectors of (say) t successive output values produced by a uniform random number generator (RNG), from all its admissible seeds, should be very evenly distributed over the t-dimensional unit hypercube (more uniformly than random points), because this set can be viewed as a finite sample space from which vectors are drawn at random to approximate the continuous uniform distribution over the unit hypercube. In other words, a RNG should be designed to produce a highly uniform point set (HUPS) over its full period. This should be guaranteed by a rigourous mathematical analysis based on a good understanding of the structure of the RNG. This structure should not be too simplistic, for otherwise departure from ran-domness would be too easy to detect by statistical tests. The quest for faster RNGs, with a long period and a good structure in all dimensions t up to some large enough integer, is still going on. New candidates are proposed and studied in this special issue. One of the main methods for implementing long-period RNGs is via a linear recurrence of order k > 1, modulo a large prime m. A fast implementation is easier to obtain when the coefficients of the recurrence are small and most of them are zero. However, it is also known that the structure of the points produced by the generator cannot be good when the sum of squares of the coefficients is small. In the first article of this special issue, Deng and Xu construct new generators based on linear recurrences where all nonzero coefficients are equal to a common value b. These generators are fast because they require a single multiplication modulo m at each step of the recurrence, even if many coefficients are nonzero. The authors provide specific parameter sets and concrete implementations for m near 2 31 and k = 102, 120, and 1511. In the latter case, the generator has period length near 2 46841 and Permission to make digital or hard copies of part or all of this work for …