James R. Wilson

Variance Reduction Techniques for Digital Simulation

SYNOPTIC ABSTRACTIn the design and analysis of large-scale simulation experiments, It Is generally difficult to estimate model performance parameters with adequate precision at an acceptable sampling cost. This paper provides a state-of-the-art survey of the principal variance reduction techniques that can Improve the efficiency of such experiments.

Analysis of Space Shuttle ground operations

To assess the feasibility of proposed launch schedules for the Space Shuttle, we have developed a simulation model of the flow of activities comprising Shuttle turn around processing. Considering queueing delays caused by the limited capacity of ground facilities, the model estimates flight starting dates needed to meet a given launch schedule with a specified level of confi dence. The results of an extensive sensitivity analysis indicate that the currently projected schedules are optimistic and that the turnaround time will substan tially exceed the current goal of 28 days.

Multifractal detrended fluctuation analysis

To analyze financial time series exhibiting volatility clustering or other highly irregular behavior, we exploit multifractal detrended fluctuation analysis (MF-DFA). We summarize the use of local Holder exponents, generalized Hurst exponents, and the multifractal spectrum in characterizing the way that the sample paths of a multifractal stochastic process exhibit light- or heavy-tailed fluctuations as well as short- or long-range dependence on different time scales. We detail the development of a robust, computationally efficient software tool for estimating the multifractal spectrum from a time series using MF-DFA, with special emphasis on selecting the algorithms parameters. The software is tested on simulated sample paths of Brownian motion, fractional Brownian motion, and the binomial multiplicative process to verify the accuracy of the resulting multifractal spectrum estimates. We also perform an in-depth analysis of General Electrics stock price using conventional time series models, and we contrast the results with those obtained using MF-DFA.

Antithetic Sampling with Multivariate Inputs

SYNOPTIC ABSTRACTThis paper extends the “antithetic-variates theorem” to include the case of two or more random variables, each of which is generated by a sampling scheme requiring a fixed-dimension input vector of independent random numbers. Three examples illustrate the application of this result in Monte Carlo work.

Variance reduction: The current state

Estimation efficiency is an increasingly important issue in the design and analysis of large-scale simulation experiments. This paper surveys recent research on the major variance reduction techniques that have been developed for or adapted to Monte Carlo studies. Current unresolved problems and directions for future research are also discussed.

The inspection paradox in renewal-reward processes

To explore the inspection paradox in the context of a renewal-reward process, we obtain asymptotic expressions for the mean and distribution function of the reward associated with the spread (total life) of the process. These results also yield a simplified demonstration of the elementary renewal-reward theorem.

A sequential procedure for estimating the steady-state mean using standardized time series

We propose SPSTS, an automated sequential procedure for computing point and confidence-interval (CI) estimators for the steady-state mean of a simulation output process. This procedure is based on variance estimators computed from standardized time series, and it is characterized by its simplicity relative to methods based on batch means and its ability to deliver CIs for the variance parameter of the output process. The effectiveness of SPSTS is evaluated via comparisons with methods based on batch means. In preliminary experimentation with the steady-state waiting-time process for the M/M/1 queue with a server utilization of 90%, we found that SPSTS performed comparatively well in terms of its average required sample size as well as the coverage and average half-length of its delivered CIs.

A stochastic model of acute-care decisions based on patient and provider heterogeneity

The primary cause of preventable death in many hospitals is the failure to recognize and/or rescue patients from acute physiologic deterioration (APD). APD affects all hospitalized patients, potentially causing cardiac arrest and death. Identifying APD is difficult, and response timing is critical - delays in response represent a significant and modifiable patient safety issue. Hospitals have instituted rapid response systems or teams (RRT) to provide timely critical care for APD, with thresholds that trigger the involvement of critical care expertise. The National Early Warning Score (NEWS) was developed to define these thresholds. However, current triggers are inconsistent and ignore patient-specific factors. Further, acute care is delivered by providers with different clinical experience, resulting in quality-of-care variation. This article documents a semi-Markov decision process model of APD that incorporates patient and provider heterogeneity. The model allows for stochastically changing health states, while determining patient subpopulation-specific RRT-activation thresholds. The objective function minimizes the total time associated with patient deterioration and stabilization; and the relative values of nursing and RRT times can be modified. A case study from January 2011 to December 2012 identified six subpopulations. RRT activation was optimal for patients in “slightly concerning” health states (NEWS > 0) for all subpopulations, except surgical patients with low risk of deterioration for whom RRT was activated in “concerning” states (NEWS > 4). Clustering methods identified provider clusters considering RRT-activation preferences and estimation of stabilization-related resource needs. Providers with conservative resource estimates preferred waiting over activating RRT. This study provides simple practical rules for personalized acute care delivery.

Monitoring nonlinear profiles adaptively with a wavelet-based distribution-free CUSUM chart

A wavelet-based distribution-free tabular CUSUM chart based on adaptive thresholding, is designed for rapidly detecting shifts in the mean of a high-dimensional profile whose noise components have a continuous nonsingular multivariate distribution. First computing a discrete wavelet transform of the noise vectors for randomly sampled Phase I (in-control) profiles, uses a matrix-regularization method to estimate the covariance matrix of the wavelet-transformed noise vectors; then, those vectors are aggregated (batched) so that the non-overlapping batch means of the wavelet-transformed noise vectors have manageable covariances. Lower and upper in-control thresholds are computed for the resulting batch means of the wavelet-transformed noise vectors using the associated marginal Cornish–Fisher expansions that have been suitably adjusted for between-component correlations. From the thresholded batch means of the wavelet-transformed noise vectors, Hotelling’s -type statistics are computed to set the parameters of a CUSUM procedure. To monitor shifts in the mean profile during Phase II (regular) operation, computes a similar Hotelling’s -type statistic from successive thresholded batch means of the wavelet-transformed noise vectors using the in-control thresholds; then applies the CUSUM procedure to the resulting -type statistics. Experimentation with several normal and non-normal test processes revealed that outperformed existing non-adaptive profile-monitoring schemes.

Agent-based simulations of financial markets: zero- and positive-intelligence models

To analyze the impact of intelligent traders with differing fundamental motivations on agent-based simulations of financial markets, we construct both zero-intelligence and positive-intelligence models of those markets using the MASON agent-based modeling framework. We exploit our software implementation of multifractal detrended fluctuation analysis (MF-DFA) to analyze the price paths generated by both simulation models as well as the price paths of selected stocks traded on the New York Stock Exchange. We study the changes in the models’ macrolevel price paths when altering some of the microlevel agent behaviors; and we compare and contrast the multifractal properties of the zero- and positive-intelligence price paths with those properties of the selected real price paths. For the positive-intelligence and real price paths, we generally observed long-range dependence in the small-magnitude fluctuations and short-range dependence in the large-magnitude fluctuations. On the other hand, the zero-intelligence price paths failed to exhibit the multifractal properties seen in the selected real price paths.