Wheyming Tina Song

Simple Procedures for Selecting the Best Simulated System When the Number of Alternatives is Large

In this paper, we address the problem of finding the simulated system with the best (maximum or minimum) expected performance when the number of alternatives is finite, but large enough that ranking-and-selection (R&S) procedures may require too much computation to be practical. Our approach is to use the data provided by the first stage of sampling in an R&S procedure to screen out alternatives that are not competitive, and thereby avoid the (typically much larger) second-stage sample for these systems. Our procedures represent a compromise between standard R&S procedures--which are easy to implement, but can be computationally inefficient--and fully sequential procedures--which can be statistically efficient, but are more difficult to implement and depend on more restrictive assumptions. We present a general theory for constructing combined screening and indifference-zone selection procedures, several specific procedures and a portion of an extensive empirical evaluation.

On the performance of multiplexing independent regulated inputs

In this paper, we consider the performance analysis problem for a work conserving link with a large number of independent regulated inputs. For such a problem, we derive simple stochastic bounds under a general traffic constraint for the inputs. The bound for queue length is shown to be a stochastic extension of the deterministic worst case bound and it is asymptotically tighter than the bound in Kesidis and Konstantopoulos [23]. We also test the bound by considering periodic inputs with independent starting phases. Based on Sanovs theorem and importance sampling, we propose a fast simulation algorithm that achieves significant variance reduction. The simulations results are compared with our stochastic bound and the bound in [23].

Variance of the sample mean: properties and graphs of quadratic-form estimators

Many commonly used estimators of the variance of the sample mean from a covariance-stationary process can be written as quadratic forms. We study the class of quadratic-form estimators algebraically and graphically, including five specific types of estimators, some from the literature and some that are new. Finite and asymptotic bias, variance, and covariance are derived and examined, with emphasis on developing intuition and insight by interpreting these properties graphically. The graphs depict the nonoptimal statistical behavior of some of the simulation literature estimators such as nonoverlapping batch means, as well as the better behavior of estimators obtained by overlapping batches.

On the estimation of optimal batch sizes in the analysis of simulation output

Abstract The estimation of the variance of point estimators is a classical problem of stochastic simulation. A more specific problem addresses the estimation of the variance of a sample mean from a steady-state autocorrelated process. Many proposed estimators of the variance of the sample mean are parameterized by batch size. A critical problem is to find an appropriate batch size that provides a good tradeoff between bias and variance. This paper proposes a procedure for determining the optimal batch size to minimize the mean squared error of estimators of the variance of the sample mean. This paper also presents the results of empirical studies of the procedure. The experiments involve symmetric two-state Markov chain models, first-order autoregressive processes, seasonal autoregressive processes, and queue-waiting times for several M/M/1 queueing models. The empirical results indicate that the estimation procedure works nearly as well as it would if the parameters of the processes were known.

The Impact of Inpatient Boarding on ED Efficiency: A Discrete-Event Simulation Study

In this study, a discrete-event simulation approach was used to model Emergency Department’s (ED) patient flow to investigate the effect of inpatient boarding on the ED efficiency in terms of the National Emergency Department Crowding Scale (NEDOCS) score and the rate of patients who leave without being seen (LWBS). The decision variable in this model was the boarder-released-ratio defined as the ratio of admitted patients whose boarding time is zero to all admitted patients. Our analysis shows that the Overcrowded+ (a NEDOCS score over 100) ratio decreased from 88.4% to 50.4%, and the rate of LWBS patients decreased from 10.8% to 8.4% when the boarder-released-ratio changed from 0% to 100%. These results show that inpatient boarding significantly impacts both the NEDOCS score and the rate of LWBS patient and this analysis provides a quantification of the impact of boarding on emergency department patient crowding.

Omitting Meaningless Digits in Point Estimates: The Probability Guarantee of Leading-Digit Rules

Motivated by the question of which point-estimator digits to report in a statistical experiment, we study the probabilistic behavior of the digits as a function of the true performance measure and the point estimators standard error. We investigate the family of Leading-Digit Rules, which guarantees that every unreported digit has correctness probability below a given threshold. Choosing the threshold to be about 0.198 yields Yonedas rule. The easy-to-implement rule that reports the point estimate through the leading digit of the standard error has threshold (approximately) 0.117, which is not much larger than the one-in-ten probability of a uniformly distributed random digit being correct.

Inverse-Transformation Algorithms For Some Common Stochastic Processes

Realizations from common stochastic processes are often used by simulation-methodology researchers in Monte Carlo performance evaluation of new and existing methods for output analysis, variance reduction, and optimization. Typically realizations can be obtained easily from either the definition or simple properties of the process. We discuss using the inverse of the distribution function for generating realizations from some of these processes. The inverse transformation always possesses the advantage of correlation induction, useful for variance reduction. We consider the discrete-time processes ARMA, EAR, M/M/1-QT (time in queue), and M/M/1-ST (time in system, the sojourn time), and Markov chains. The inverse-transformation algorithms are sometimes slower (e.g., ARMA, M/M/1-ST), sometimes faster (e.g., M/M/1-QT), and often about the same speed as the usual algorithm. Some Fortran implementations are provided.Realizations from common stochastic processes are often used by simulation-methodology researchers in Monte Carlo performance evaluation of new and existing methods for output analysis, variance reduction, and optimization. Typically realizations can be obtained easily from either the definition or simple properties of the process. We discuss using the inverse of the distribution function for generating realizations from some of these processes. The inverse transformation always possesses the advantage of correlation induction, useful for variance reduction. We consider the discrete-time processes ARMA, EAR, M/M/1-QT (time in queue), and M/M/1-ST (time in system, the sojourn time), and Markov chains. The inverse-transformation algorithms are sometimes slower (e.g., ARMA, M/M/1-ST), sometimes faster (e.g., M/M/1-QT), and often about the same speed as the usual algorithm. Some Fortran implementations are provided.

Correlation among estimators of the variance of the sample mean

Various types of estimators have been proposed for estimating the variance of the sample mean, a fundamental quantity in simulation output analysis. When used with low degrees of freedom, several of these estimators have little bias. But the low degrees of freedom correspond to high variance. One approach to creating estimators with smaller variance while maintaining the negligible bias is to use linear combinations of known estimators. Whether linear combinations provide improved estimators — and, if so, the choice of estimators to be included in the linear combination — depends upon the correlations among the various estimators. Linear combinations of estimators having high positive correlation would provide little improvement while combinations of independent estimators would provide substantial gain. We investigate the correlation among four well-known estimators as a function of the type of stochastic process generating the data, the sample size, the estimator type, and estimator parameters.

Minimal-MSE linear combinations of variance estimators of the sample mean

We continue our investigation of linear combinations of variance-of-the-sample-mean estimators that are parameterized by batch size. First we state the mse-optimal linear-combination weights in terms of the bias vector and the covariance matrix of the component estimators for two cases: weights unconstrained and weights constrained to sum to one. Then we report a small numerical study that demonstrates mse reduction of about 80% for unconstrained weights and about 30% for constrained weights. The mses and the percent reductions are similar for all four estimator types considered. Such large mse reductions could not be achieved in practice, since they assume knowledge of unknown parameters, which would have to be estimated. Optimal-weight estimation is not considered here.

Batching methods in simulation output analysis: what we know and what we don't

As an advanced tutorial, we discuss batching methods for determining point-estimator precision for steady-state simulation experiments. We emphasize batching methods in which each batch provides a point estimator analogous to that of the experiment, but we mention other methods that use batches, especially the more-general idea of standardized time series. Despite the preponderance of literature on confidence-interval estimation for the mean using adjacent nonoverlapping batches, we focus on estimating the point estimators standard error and consider both general point estimators and general batching relationships. Literature on multivariate batching exists, but we focus on the univariate problem. We consider the initial-transient problem only in passing. Specific issues include form of the point estimator, definition of the batch statistics, form of the batch-statistics estimator, optimal batch size (including various definitions of optimal) and determining batch size. This paper is a short summary of the issues, with a fairly complete bibliography.