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19
The Asymptotic Efficiency Of Simulation Estimators
 Operations Research
, 1992
"... A decisiontheoretic framework is proposed for evaluating the efficiency of simulation estimators. The framework includes the cost of obtaining the estimate as well as the cost of acting based on the estimate. The cost of obtaining the estimate and the estimate itself are represented as realizations ..."
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Cited by 43 (14 self)
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A decisiontheoretic framework is proposed for evaluating the efficiency of simulation estimators. The framework includes the cost of obtaining the estimate as well as the cost of acting based on the estimate. The cost of obtaining the estimate and the estimate itself are represented as realizations of jointly distributed stochastic processes. In this context, the efficiency of a simulation estimator based on a given computational budget is defined as the reciprocal of the risk (the overall expected cost). This framework is appealing philosophically, but it is often difficult to apply in practice (e.g., to compare the efficiency of two different estimators) because only rarely can the efficiency associated with a given computational budget be calculated. However, a useful practical framework emerges in a large sample context when we consider the limiting behavior as the computational budget increases. A limit theorem established for this model supports and extends a fairly well known e...
TwoStage MultipleComparison Procedures for SteadyState Simulations
 Annals of Statistics
, 1999
"... this paper, the results naturally apply to (asymptotically) stationary time series. ..."
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Cited by 13 (5 self)
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this paper, the results naturally apply to (asymptotically) stationary time series.
TwoStage Stopping Procedures Based On Standardized Time Series
 Management Science
, 1994
"... this paper we will consider functions h : C[0; 1) ! ! which are typically not continuous, and we let D(h) denote the set of points x 2 C[0; 1) at which h is not continuous. Let fX ffl : ffl ? 0g be a family of random elements taking values in C[0; 1); i.e., the X ffl correspond to stochastic process ..."
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Cited by 12 (6 self)
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this paper we will consider functions h : C[0; 1) ! ! which are typically not continuous, and we let D(h) denote the set of points x 2 C[0; 1) at which h is not continuous. Let fX ffl : ffl ? 0g be a family of random elements taking values in C[0; 1); i.e., the X ffl correspond to stochastic processes with sample paths in C[0; 1). If X is a random element of C[0; 1), then the X ffl are said to converge weakly to X (written X ffl ) X as ffl ! 0) if
Estimating Customer And Time Averages
, 1993
"... In this paper we establish a joint central limit theorem for customer and time averages by applying a martingale central limit theorem in a Markov framework. The limiting values of the two averages appear in the translation terms. This central limit theorem helps to construct confidence intervals fo ..."
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Cited by 5 (3 self)
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In this paper we establish a joint central limit theorem for customer and time averages by applying a martingale central limit theorem in a Markov framework. The limiting values of the two averages appear in the translation terms. This central limit theorem helps to construct confidence intervals for estimators and perform statistical tests. It thus helps determine which finite average is a more asymptotically efficient estimator of its limit. As a basis for testing for PASTA (Poisson arrivals see time averages), we determine the variance constant associated with the central limit theorem for the difference between the two averages when PASTA holds. OR/MS Subject Classification: Queues, limit theorems: central limit theorems for customer and time averages. Queues, statistical inference: estimating customer and time averages. Statistics, estimation: averages over time and at embedded points. This paper is concerned with estimating limiting time averages, customer (embedded) averages a...
Simulation Run Length Planning
 In Proceedings of the 1989 Winter Simulation Conference
, 1989
"... To design a stochastic simulation experiment, it is helpful to have an estimate of the simulation run lengths required to achieve desired statistical precision. Preliminary estimates of required run lengths can be obtained by approximating the stochastic model of interest by a more elementary Markov ..."
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Cited by 5 (1 self)
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To design a stochastic simulation experiment, it is helpful to have an estimate of the simulation run lengths required to achieve desired statistical precision. Preliminary estimates of required run lengths can be obtained by approximating the stochastic model of interest by a more elementary Markov model that can be analyzed analytically. When steadystate quantities are to be estimated by sample means, we often can estimate required run lengths by calculating the asymptotic variance and the asymptotic bias of the sample mean in the Markov model. 1. INTRODUCTION Simulation experiments are like exploring trips. We usually have initial goals, but the interesting discoveries often come from the unexpected. We typically do not know in advance precisely how we will proceed and we cannot predict all the benefits. In reality, most simulation experiments are sequences of experiments, with new goals being based on successive discoveries; see Albin (1984). Thus, there obviously is a limit to ...
TwoStage Procedures for Multiple Comparisons with the Best in SteadyState Simulations
 In preparation
, 1996
"... Suppose that we have k different stochastic systems, where JJi denotes the steadystate mean of system i. We assume that the system labeled k is a control and want to compare the performance of the other systems, labeled 1,2,...,k 1, relative to this control. This problem is known in the statistica ..."
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Cited by 2 (0 self)
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Suppose that we have k different stochastic systems, where JJi denotes the steadystate mean of system i. We assume that the system labeled k is a control and want to compare the performance of the other systems, labeled 1,2,...,k 1, relative to this control. This problem is known in the statistical literature as multiple comparisons with a control (MCC). Independent steadystate simulations will be performed to compare the systems to the control. Twostage procedures, based on the method of batch means, are presented to construct simultaneous lower onesided confidence intervals for Jli Jl k (i = 1, 2,..., k), each having prespecified (absolute or relative) halfwidth 8. Under the assumption that the stochastic processes representing the evolution of the systems satisfy a functional central limit theorem, it can be shown that asymptotically (as 6+ 0 with the size of the batches proportional to 1/6 2), the joint probability that the confidence intervals simultaneously contain the Jli JJk (i = 1,2,..., k 1) is at least 1 0:, where 0: is prespecified by the user. 1
Extending the FCLT version of L = λW
"... The functional central limit theorem (FCLT) version of Little’s law (L = λW) established by Glynn and Whitt is extended to show that a bivariate FCLT for the number in system and the waiting times implies the joint FCLT for all processes. It is based on a converse to the preservation of convergence ..."
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The functional central limit theorem (FCLT) version of Little’s law (L = λW) established by Glynn and Whitt is extended to show that a bivariate FCLT for the number in system and the waiting times implies the joint FCLT for all processes. It is based on a converse to the preservation of convergence by the composition map with centering on the function space containing the sample paths, exploiting monotonicity. Keywords: Little’s law, L = λW, functional central limit theorem, confidence intervals, continuous mapping theorem, composition with centering 1.
Submitted to Operations Research manuscript (Please, provide the mansucript number!) Statistical Analysis with Little’s Law
, 2012
"... The theory supporting Little’s law (L = λW) is now well developed, applying to both limits of averages and expected values of stationary distributions, but applications of Little’s law with actual system data involve measurements over a finite time interval, which is neither of these. To make infere ..."
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The theory supporting Little’s law (L = λW) is now well developed, applying to both limits of averages and expected values of stationary distributions, but applications of Little’s law with actual system data involve measurements over a finite time interval, which is neither of these. To make inferences from the empirical averages, we advocate taking a statistical approach. We regard the averages as estimates of associated unknown parameters of an underlying stochastic model, which may be nonstationary. Given a single sample path in a stationary setting, we suggest estimating confidence intervals using the method of batch means, as is often done in stochastic simulation output analysis. We also discuss ways to remove bias due to interval edge effects when the system does not begin and end empty, which is especially important in nonstationary settings. We illustrate the methods with data from a call center. Key words: Little’s law; L = λW; measurements; parameter estimation; confidence intervals; confidence intervals with L = λW; edge effects in L = λW; performance analysis; bias.