Averill M. Law

A Sequential Procedure for Determining the Length of a Steady-State Simulation

A common problem faced by simulators is that of constructing a confidence interval for the steady-state mean of a stochastic process. We have reviewed the existing procedures for this problem and found that all but one either produce confidence intervals with coverages which may be considerably lower than desired or have not been adequately tested. Thus, in many cases simulators will have more confidence in their results than is justified. In this paper we present a new sequential procedure based on the method of batch means for constructing a confidence interval with coverage close to the desired level. The procedure has the advantage that it does not explicitly require a stochastic process to have regeneration points. Empirical results for a large number of stochastic systems indicate that the new procedure performs quite well.

Simulation of manufacturing systems

This paper discusses how simulation is used to design and analyze manufacturing or warehousing systems. Topics discussed include: manufacturing issues investigated by simulation, techniques for building valid and credible models, manufacturing simulation software, statistical considerations, and simulation pitfalls. A case study is included.

A procedure for selecting a subset of size m containing the l best of k independent normal populations, with applications to simulation

In this paper we state and justify a two-stage sampling procedure for selecting a subset of size m containing the t best of k independent normal populations, when the ranking parameters are the population means. We do not assume that the variances of the populations are known or equal. Discrete event simulation studies are often concerned with choosing one or more system designs which are best in some sense. We present empirical results from a typical simulation application for which the observations are not normally distributed.

Secrets of successful simulation studies

In many simulation studies, the primary focus is on simulation software selection and programming. The authors believe, however, that only 30 to 40 percent of the total effort in most successful simulation projects is actually model coding. They discuss ten key steps that should, in fact, comprise a sound simulation study.<<ETX>>

Simulation-based optimization

We present an introduction to simulation-based optimization, which is, perhaps, the hottest topic in discrete-event simulation today. We give a precise statement of the problem being addressed and also experimental results for two commercial optimization packages applied to a manufacturing example with seven decision variables.

The Transient Behavior of the M/M/s Queue, with Implications for Steady-State Simulation

Although the transient behavior of a queueing system is often of interest, available analytical results are usually quite restricted or are very complicated. We consider the M/M/s queue with an arbitrary number of customers present at time zero. We obtain probabilities in a relatively simple closed form that can be used to evaluate exactly several measures of system performance, including the expected delay in queue of each arriving customer. A numerical examination is carried out to see how the choice of initial condition affects the nature of convergence of the expected delays to their steady-state values. We also discuss the implications of these results for the initialization of steady-state simulations.

Confidence Intervals for Steady-State Simulations: I. A Survey of Fixed Sample Size Procedures

We consider the problem of constructing a confidence interval for the steady-state mean of a stochastic process by means of simulation, and study the five main methods which have been proposed replication, batch means, autoregressive representation, spectrum analysis, and regeneration cycles for the case when the length of the simulation is fixed in advance. Comparing the performances of these methods on stochastic models with known steady-state means, we find that the simulator should exercise caution in interpreting the results from a simulation of fixed length, and that the length of a simulation adequate for acceptable performance is highly model-dependent. We also investigate possible sources of error for the methods, and conclude that variance estimator bias is more important than point estimator bias in confidence interval coverage degradation.

Feature Article-Statistical Analysis of Simulation Output Data

We present a state-of-the-art survey of statistical analyses for simulation output data of a single simulated system. The various statistical problems associated with output data analyses such as start-up bias and determination of estimator accuracy are described in detail. We then discuss the best available techniques for addressing these problems, as well as topics for future research. The paper concludes with a discussion of how developments in simulation languages, computer graphics, and computer execution speed may affect the future of output analyses.

Statistical analysis of simulation output data: the practical state of the art

One of the most important but neglected aspects of a simulation study is the proper design and analysis of simulation experiments. In this tutorial we give a state-of-the-art presentation of what the practitioner really needs to know to be successful. We will discuss how to choose the simulation run length, the warmup-period duration (if any), and the required number of model replications (each using different random numbers). The talk concludes with a discussion of three critical pitfalls in simulation output-data analysis.

How to conduct a successful simulation study

In this tutorial we give a definitive and comprehensive seven-step approach for conducting a successful simulation study. Topics to be discussed include problem formulation, collection and analysis of data, developing a valid and credible model, modeling sources of system randomness, design and analysis of simulation experiments, and project management.