Sensitivity of output performance measures to input distributions in queueing simulation modeling
01 Dec 1997-Vol. 1, pp 296-302
TL;DR: Investigation of the sensitivity of output performance measures in two types of queueing networks, namely two versions of a two-node call center, to see if network mixing might reduce the sensitivity effect.
Abstract: In Gross and Juttijudata (1997) a single node, G/G/1 queue was investigated as to the sensitivity of output performance measures, such as the mean queue wait, to the shape of the interarrival and service distributions selected. Gamma, Weibull, lognormal and Pearson type 5 distributions with identical first and second moments were investigated. Significant differences in output measures were noted for low to moderate traffic intensities (offered load, /spl rho/), in some cases, even as high as 0.8. We continue this type of investigation for two types of queueing networks, namely two versions of a two-node call center, to see if network mixing might reduce the sensitivity effect.
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TL;DR: The central idea is to transform a Gaussian vector autoregressive process into the desired multivariate time-series input process that the authors presume as having a VARTA (Vector-Autoregressive-To-Anything) distribution.
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.
131 citations
TL;DR: An automated and statistically valid algorithm is presented to fit autoregressive-to-anything (ARTA) processes with marginal distributions from the Johnson translation system to stationary univariate time-series data.
Abstract: Providing accurate and automated input-modeling support is one of the challenging problems in the application of computer simulation of stochastic systems. The models incorporated in current input-modeling software packages often fall short because they assume independent and identically distributed processes, even though dependent time-series input processes occur naturally in the simulation of many real-life systems. Therefore, this paper introduces a statistical methodology for fitting stochastic models to dependent time-series input processes. Specifically, an automated and statistically valid algorithm is presented to fit autoregressive-to-anything (ARTA) processes with marginal distributions from the Johnson translation system to stationary univariate time-series data. ARTA processes are particularly well suited to driving stochastic simulations. The use of this algorithm is illustrated with examples.
68 citations
Cites background from "Sensitivity of output performance m..."
...…system might seem restrictive, it is less so than it first appears: In many applications, simulation output performance measures are insensitive to the specific input distribution chosen, provided that enough moments of the distribution are correct (see, for instance, Gross and Juttijudata 1997)....
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TL;DR: This work explores the use of Bayesian statistics for verification and validation of simulation models and for simulation output analysis, in both cases using priors on the performance measures of interest.
Abstract: The standard approach to analyzing the results of probabilistic simulation rests on the use of classical statistics. In this paper, we explore the use of Bayesian statistics as an alternative. This makes it possible to incorporate prior information into the analysis of simulation results in a formal and rigorous manner, through the use of prior distributions. The Bayesian approach will typically yield improved analyses, by better taking into account what is actually known and what is not known about the system to be simulated (assuming that the prior distributions themselves adequately represent this knowledge). We briefly review Bayesian methods for readers who are not familiar with this type of analysis and suggest ways in which these methods can be applied to simulation. Specifically, we explore the use of Bayesian statistics for verification and validation of simulation models and for simulation output analysis, in both cases using priors on the performance measures of interest. We then study the use of prior distributions on the input parameters to the simulation, as a way to quantify the effects of input uncertainties on both the mean and the uncertainty of the performance measures of interest, and discuss Bayesian and related methods for choosing input distributions. Finally, we briefly consider the use of a joint prior on both the input parameters and the resulting performance measures. Bayesian methods are particularly appropriate for use in practice when simulations are costly, or when input uncertainties are large. Our work provides guidance on the use of Bayesian methods for simulation analysis. We hope that it will stimulate readers to learn more about this important subject, and also encourage further research in this area.
40 citations
TL;DR: Reading this paper provides readers the foundational knowledge needed to develop intuition and insights on the complexities of stochastic simple serial lines, and serves as a guide to better understand and manage the effects of variability and design factors related to improving serial production line performance.
Abstract: Many Queueing Theory and Production Management studies have investigated specific effects of variability on the performance of serial lines since variability has a significant impact on performance. To date, there has been no single summary source of the most relevant research results concerned with variability, particularly as they relate to the need to better understand the ‘Law of Variability’. This paper fills this gap and provides readers the foundational knowledge needed to develop intuition and insights on the complexities of stochastic simple serial lines, and serves as a guide to better understand and manage the effects of variability and design factors related to improving serial production line performance, i.e. throughput, inter-departure time and flow time, under random variation.
32 citations
01 Dec 2001
TL;DR: The authors present a general-purpose input-modeling tool for representing, fitting, and generating random variates from multivariate input processes to drive computer simulations.
Abstract: Providing accurate and automated input modeling support is one of the challenging problems in the application of computer simulation. The authors present a general-purpose input-modeling tool for representing, fitting, and generating random variates from multivariate input processes to drive computer simulations. We explain the theory underlying the suggested data fitting and data generation techniques, and demonstrate that our framework fits models accurately to both univariate and multivariate input processes.
26 citations
References
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TL;DR: These algorithms are used to approximate an interarrival-time distribution for a queueing model, and the accuracy of associated performance-measure approximations is then used to evaluate the moment-matching algorithms.
Abstract: Algorithms for matching moments to phase-type distributions are evaluated on the basis of their performance in their intended application, queueing models. The moment-matching algorithms under consideration match two moments to a hyperexponential distribution with balanced means and three moments to a mixture of two Erlang distributions of common order. These algorithms are used to approximate an interarrival-time distribution for a queueing model, and the accuracy of associated performance-measure approximations is then used to evaluate the moment-matching algorithms. Three performance measures are considered, and attention is focussed on the steady-state mean queue length (number in system) of theGI/M/1 queue. Performance-measure approximations are compared to three-moment bounds and performance-measure values arising from hypothetical approximated distributions.
65 citations
TL;DR: A graphical, interactive technique for modeling univariate simulation input processes by using a family of probability distributions based on Bezier curves that has an open-ended parameterization and is capable of accurately representing an unlimited variety of distributional shapes.
Abstract: We describe a graphical, interactive technique for modeling univariate simulation input processes by using a family of probability distributions based on Bezier curves. This family has an open-ende...
61 citations
TL;DR: Two related methods for deriving probability distribution estimates using approximate rational Laplace transform representations are proposed, addressing the question of the number of terms, or the order, involved in a generalized hyperexponential, phase-type, or Coxian distribution, a problem not adequately treated by existing methods.
Abstract: We propose two related methods for deriving probability distribution estimates using approximate rational Laplace transform representations Whatever method is used, the result is a Coxian estimate for an arbitrary distribution form or plain sample data, with the algebra of the Coxian often simplifying to a generalized hyperexponentia l or phase-type The transform (or, alternatively, the moment-generating function) is used to facilitate the computations and leads to an attractive algorithm For method one, the first 2N - 1 derivatives of the transform are matched with those of an approximate rational function; for the second method, a like number of values of the transform are matched with those of the approximation The numerical process in both cases begins with an empirical Laplace transform or truncation of the actual transform, and then requires only the solution of a relatively small system of linear equations, followed by root finding for a low-degree polynomial Besides the computationally attractive features of the overall procedure, it addresses the question of the number of terms, or the order, involved in a generalized hyperexponential, phase-type, or Coxian distribution, a problem not adequately treated by existing methods Coxian distributions are commonly used in the modeling of single-stage and network queueing problems, inventory theory, and reliability analyses They are particularly handy in the development of large-scale model approximations
44 citations
"Sensitivity of output performance m..." refers background in this paper
...…that have more than two parameters (e.g., Johnson translation distributions, phase-type distributions, Coxian distributions, generalized hyper exponential distributions), fitting can be a formidable task (see, for example, Johnson and Taffe, 1991, Johnson, 1993, and Harris and Marchal, 1997)....
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TL;DR: In this article, the GI/PH/1 model is used to explore the behavior of phase-type (PH) approximations of interarrival- and service-time distributions.
Abstract: The GI/PH/1 model (single-server queue with general independent interarrival times and phase-type service times) is used to explore the behavior of phase-type (PH) approximations of interarrival- and service-time distributions. Various PH approximating distributions are considered for five non-PH interarrival-time distributions and two PH service-time distributions. Simple two- and three-moment-matching approximations and, in some cases, approximations obtained by also considering distribution shape are compared. Each approximating distribution is evaluated on the basis of the quality of the corresponding approximations of steady-state measures of the congestion seen by an arriving customer. The traffic intensity and the variability of the distribution (interarrival-or service-time) that is not approximated are shown to have a substantial effect on the accuracy of the queueing approximations. Rules for selecting approximating distributions for queueing applications are suggested
32 citations
"Sensitivity of output performance m..." refers background in this paper
...…that have more than two parameters (e.g., Johnson translation distributions, phase-type distributions, Coxian distributions, generalized hyper exponential distributions), fitting can be a formidable task (see, for example, Johnson and Taffe, 1991, Johnson, 1993, and Harris and Marchal, 1997)....
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