An Overview Of Tes Processes And Modeling Methodology
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paper_title: Generation of a random sequence having a jointly specified marginal distribution and autocovariance

paper_content:

We consider the problem of generating a random sequence with a specified marginal distribution and autocovariance. The proposed scheme for generating such a sequence consists of a white Gaussian noise source input to a linear digital filter followed by a zero-memory nonlinearity (ZMNL). The ZMNL is chosen so that the desired distribution is exactly realized and the digital filter is designed so that the desired autocovariance is closely approximated. Both analytic results and examples are included. The proposed scheme should prove useful in simulations involving non-Gaussian processes.
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paper_title: Minification processes and their transformations

paper_content:

It is shown that the stationary, autoregressive, Markovian minification processes introduced by Tavares and Sim can be extended to give processes with marginal distributions other than the exponential and Weibull distributions. Necessary and sufficient conditions on the hazard rate of the marginal distributions are given for a minification process to exist. Results are given for the derivation of the autocorrelation function; these correct the expression for the Weibull given by Sim. Mopotonic transformations of the minification processes are also discussed and generate a whole new class of autoregressive processes with fixed marginal distributions. Stationary processes generated by a maximum operation are also introduced and a comparison of three different Markovian processes with uniform marginal distributions is given.
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paper_title: TES: A Class of Methods for Generating Autocorrelated Uniform Variates

paper_content:

This paper introduces a class of methods called TES (Transform-Expand-Sample) for generating autocorrelated variates with uniform marginals and Markovian structure. TES methods are readily implemented on a computer and have generation complexity comparable to that of the i.i.d. uniform sequence which they transform to an autocorrelated uniform sequence. For any prescribed correlation coefficient ρ, there is a TES method generating a uniform sequence with the 1-lag autocorrelation ρ, and the resultant autocorrelation is monotonic quadratic in two structural TES parameters. A simulation study reveals that TES methods give rise to autocorrelation functions with monotone decreasing as well as oscillating magnitude, bounded by monotone envelopes. The structural parameters were found to control the “amplitude” and “frequency” of the resultant autocorrelation function. A third parameter can be used to transform a TES sequence into more continuous-looking versions and to control the skewness of sample path cycles. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
---
paper_title: Spectral Analysis of Basic TES Processes

paper_content:

This paper studies the spectral properties of a class of stochastic sequences generated by basic TES (Transform-Expand-Sample) methods, as well as transformed TES sequences. A TES sequence is obtained as a marginally uniform process from an autoregressive scheme with modulo-1 reduction, followed by additional transformations. We derive formulas for the spectral density function and the spectral distribution function which are suitable for efficient numerical computation. A set of examples is calculated and exhibited for TES processes with uniform and exponential marginals. The results contribute to the understanding of TES sequences as models of autocorrelated sequences, particularly in a Monte Carlo simulation context. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
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paper_title: The Winner s Curse

paper_content:

Economics is distinguished from other social sciences by the belief that most (all?) behavior can be explained by assuming that agents have stable, well-defined preferences and make rational choices consistent with those preferences in markets that (eventually) clear. An empirical result qualifies as an anomaly if it is difficult to "rationalize," or if implausible assumptions are necessary to explain it within the paradigm. This coluimn will present a series of such anomalies. Of course, "difficult" and "implausible" are judgments, and others might disagree with my assessment. Therefore, I invite readers to submit brief explanations (within the paradigm or otherwise) for any of the anomalies I report. To be considered for publication, however, proposed explanations must be falsifiable, at least in principle. Future topics for this column will come from as many fields of empirical economics as possible. Readers are invited to suggest topics by sending a note with some references to (or better yet copies of) the relevant research. My address is: Richard Thaler, c/o Journal
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paper_title: Dependence in packet queues

paper_content:

The burstiness of the total arrival process has been previously characterized in packet network performance models by the dependence among successive interarrival times. It is shown that associated dependence among successive service times and between service times and interarrival times also can be important for packet queues involving variable packet lengths. These dependence effects are demonstrated analytically by considering a multiclass single-server queue with batch-Poisson arrival processes. For this model and more realistic models of packet queues, insight is gained from heavy-traffic limit theorems. This study indicates that all three kinds of dependence should be considered in the analysis and measurement of packet queues involving variables packet lengths. Specific measurements are proposed for real systems and simulations. This study also indicates how to predict expected packet delays under heavy loads. Finally, this study is important for understanding the limitations of procedures such as the queuing network analyzer (QNA) for approximately describing the performance of queuing networks using the techniques of aggregation and decomposition. >
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paper_title: The Impact of Autocorrelation on Queuing Systems

paper_content:

The performance of single-server queues with independent interarrival intervals and service demands is well understood, and often analytically tractable. In particular, the M/M/1 queue has been thoroughly studied, due to its analytical tractability. Little is known, though, when autocorrelation is introduced into interarrival times or service demands, resulting in loss of analytical tractability. Even the simple case of an M/M/1 queue with autocorrelations does not appear to be well understood. Such autocorrelations do, in fact, abound in real-life systems, and worse, simplifying independence assumptions can lead to very poor estimates of performance measures. This paper reports the results of a simulation study of the impact of autocorrelation on performance in an FIFO queue. The study used two computer methods for generating autocorrelated random sequences, with different autocorrelation characteristics. The simulation results show that the injection of autocorrelation into interarrival times, and to a lesser extent into service demands, can have a dramatic impact on performance measures. From a performance viewpoint, these effects are generally deleterious, and their magnitude depends on the method used to generate the autocorrelated process. The paper discusses these empirical results and makes some recommendations to practitioners of performance analysis of queuing systems.
---
paper_title: Generation of a random sequence having a jointly specified marginal distribution and autocovariance

paper_content:

We consider the problem of generating a random sequence with a specified marginal distribution and autocovariance. The proposed scheme for generating such a sequence consists of a white Gaussian noise source input to a linear digital filter followed by a zero-memory nonlinearity (ZMNL). The ZMNL is chosen so that the desired distribution is exactly realized and the digital filter is designed so that the desired autocovariance is closely approximated. Both analytic results and examples are included. The proposed scheme should prove useful in simulations involving non-Gaussian processes.
---
paper_title: Minification processes and their transformations

paper_content:

It is shown that the stationary, autoregressive, Markovian minification processes introduced by Tavares and Sim can be extended to give processes with marginal distributions other than the exponential and Weibull distributions. Necessary and sufficient conditions on the hazard rate of the marginal distributions are given for a minification process to exist. Results are given for the derivation of the autocorrelation function; these correct the expression for the Weibull given by Sim. Mopotonic transformations of the minification processes are also discussed and generate a whole new class of autoregressive processes with fixed marginal distributions. Stationary processes generated by a maximum operation are also introduced and a comparison of three different Markovian processes with uniform marginal distributions is given.
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paper_title: The statistical analysis of series of events

paper_content:

Observations in the form of point events occurring in a continuum, space or time, arise in many fields of study. In writing this monograph on statistical techniques for dealing with such data, we have three objectives. First, we have tried to give a simple description, with numerical examples, of the main methods that have been proposed. We hope that by concentrating on the examples the applied statistician with a limited inclination for theory will find something of practical value in the monograph. Second, the monograph is intended as a survey, necessarily incomplete, of some of the problems in theoretical statistics that stem from this sort of data. A number of specialized subjects have, however, been dealt with only briefly, the main emphasis being placed on the problem of examining the structure of a series of events. Finally, we hope that the monograph will be of use to teachers and students of statistics, as illustrating applications of a range of tech niques in theoretical statistics. We are extremely grateful to the International Business Machines Corporation for providing programming assistance and a large amount of computer time. We wish to thank particularly Mr A."
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paper_title: TEStool: an environment for visual interactive modeling of autocorrelated traffic

paper_content:

The authors describe a software environment, called TEStool, for modeling autocorrelated traffic processes using a class of models called TES (Transform-Expand-Sample). TEStool makes heavy use of visualization to provide a pleasant interactive environment supporting modeling of dependent time series. TEStool supports a heuristic search approach to capture simultaneously the marginal distribution and autocorrelation function of empirical traffic data. It casts the search into a process of intuitively modifying a visual representation in small incremental steps, similar to an arcade game. Preliminary experience has confirmed that TEStool speeds up the modeling process and alleviates the tedium of repetitive search. >
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paper_title: TEStool: an environment for visual interactive modeling of autocorrelated traffic

paper_content:

The authors describe a software environment, called TEStool, for modeling autocorrelated traffic processes using a class of models called TES (Transform-Expand-Sample). TEStool makes heavy use of visualization to provide a pleasant interactive environment supporting modeling of dependent time series. TEStool supports a heuristic search approach to capture simultaneously the marginal distribution and autocorrelation function of empirical traffic data. It casts the search into a process of intuitively modifying a visual representation in small incremental steps, similar to an arcade game. Preliminary experience has confirmed that TEStool speeds up the modeling process and alleviates the tedium of repetitive search. >
---
paper_title: TES: A Class of Methods for Generating Autocorrelated Uniform Variates

paper_content:

This paper introduces a class of methods called TES (Transform-Expand-Sample) for generating autocorrelated variates with uniform marginals and Markovian structure. TES methods are readily implemented on a computer and have generation complexity comparable to that of the i.i.d. uniform sequence which they transform to an autocorrelated uniform sequence. For any prescribed correlation coefficient ρ, there is a TES method generating a uniform sequence with the 1-lag autocorrelation ρ, and the resultant autocorrelation is monotonic quadratic in two structural TES parameters. A simulation study reveals that TES methods give rise to autocorrelation functions with monotone decreasing as well as oscillating magnitude, bounded by monotone envelopes. The structural parameters were found to control the “amplitude” and “frequency” of the resultant autocorrelation function. A third parameter can be used to transform a TES sequence into more continuous-looking versions and to control the skewness of sample path cycles. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
---
paper_title: TES: A Class of Methods for Generating Autocorrelated Uniform Variates

paper_content:

This paper introduces a class of methods called TES (Transform-Expand-Sample) for generating autocorrelated variates with uniform marginals and Markovian structure. TES methods are readily implemented on a computer and have generation complexity comparable to that of the i.i.d. uniform sequence which they transform to an autocorrelated uniform sequence. For any prescribed correlation coefficient ρ, there is a TES method generating a uniform sequence with the 1-lag autocorrelation ρ, and the resultant autocorrelation is monotonic quadratic in two structural TES parameters. A simulation study reveals that TES methods give rise to autocorrelation functions with monotone decreasing as well as oscillating magnitude, bounded by monotone envelopes. The structural parameters were found to control the “amplitude” and “frequency” of the resultant autocorrelation function. A third parameter can be used to transform a TES sequence into more continuous-looking versions and to control the skewness of sample path cycles. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
---
paper_title: Spectral Analysis of Basic TES Processes

paper_content:

This paper studies the spectral properties of a class of stochastic sequences generated by basic TES (Transform-Expand-Sample) methods, as well as transformed TES sequences. A TES sequence is obtained as a marginally uniform process from an autoregressive scheme with modulo-1 reduction, followed by additional transformations. We derive formulas for the spectral density function and the spectral distribution function which are suitable for efficient numerical computation. A set of examples is calculated and exhibited for TES processes with uniform and exponential marginals. The results contribute to the understanding of TES sequences as models of autocorrelated sequences, particularly in a Monte Carlo simulation context. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
---
paper_title: TEStool: an environment for visual interactive modeling of autocorrelated traffic

paper_content:

The authors describe a software environment, called TEStool, for modeling autocorrelated traffic processes using a class of models called TES (Transform-Expand-Sample). TEStool makes heavy use of visualization to provide a pleasant interactive environment supporting modeling of dependent time series. TEStool supports a heuristic search approach to capture simultaneously the marginal distribution and autocorrelation function of empirical traffic data. It casts the search into a process of intuitively modifying a visual representation in small incremental steps, similar to an arcade game. Preliminary experience has confirmed that TEStool speeds up the modeling process and alleviates the tedium of repetitive search. >
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paper_title: Tes Modeling of Video Traffic

paper_content:

Video service is slated to be a major application of emerging high-speed communications networks of the future. In particular, full-motion video is designed to take advantage of the high bandwidths that will become affordably available with the advent of B-ISDN. A salient feature of compressed video sources is that they give rise to autocorrelated traffic streams, which are difficult to model with traditional modeling techniques. In this paper, we describe a new methodology, called TES (TransformExpand-Sample), for modeling general autocorrelated time series, and we apply it to traffic modeling of compressed video. The main characteristic of this methodology is that it can model an arbitrary marginal distributionand approximate the autocorrelation structure of an empirical sample such as traffic measurements. Furthermore, the empirical marginal (histogram) and leading autocorrelations are captured simultaneously. Practical TES modeling is computationally intensive and is effectively carried out with software support. A computerized modeling environment, called TEStool, is briefly reviewed. TEStool supports a heuristic search approach for fitting a TES model to empirical time series. Finally, we exemplify our approach by two examples of TES video source models, constructed from empirical codec bitrate measurements: one at the frame level and the other at the group-of-block level. The examples demonstrate the efficacy of the TES modeling methodology and the TEStool modeling environment.
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paper_title: DCT-based embedded coding for packet video☆

paper_content:

Abstract We present an image compression algorithm that is useful for transmitting video over packet networks. The algorithm modifies those in references [4–6, 8, 10] by incorporating motion-compensated prediction. The low and high priority images can be computed in parallel, and the algorithm provides improved motion-compensated prediction of low-frequency discrete cosine transform (DCT) coefficients.
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paper_title: TEStool: an environment for visual interactive modeling of autocorrelated traffic

paper_content:

The authors describe a software environment, called TEStool, for modeling autocorrelated traffic processes using a class of models called TES (Transform-Expand-Sample). TEStool makes heavy use of visualization to provide a pleasant interactive environment supporting modeling of dependent time series. TEStool supports a heuristic search approach to capture simultaneously the marginal distribution and autocorrelation function of empirical traffic data. It casts the search into a process of intuitively modifying a visual representation in small incremental steps, similar to an arcade game. Preliminary experience has confirmed that TEStool speeds up the modeling process and alleviates the tedium of repetitive search. >
---
paper_title: Tes Modeling of Video Traffic

paper_content:

Video service is slated to be a major application of emerging high-speed communications networks of the future. In particular, full-motion video is designed to take advantage of the high bandwidths that will become affordably available with the advent of B-ISDN. A salient feature of compressed video sources is that they give rise to autocorrelated traffic streams, which are difficult to model with traditional modeling techniques. In this paper, we describe a new methodology, called TES (TransformExpand-Sample), for modeling general autocorrelated time series, and we apply it to traffic modeling of compressed video. The main characteristic of this methodology is that it can model an arbitrary marginal distributionand approximate the autocorrelation structure of an empirical sample such as traffic measurements. Furthermore, the empirical marginal (histogram) and leading autocorrelations are captured simultaneously. Practical TES modeling is computationally intensive and is effectively carried out with software support. A computerized modeling environment, called TEStool, is briefly reviewed. TEStool supports a heuristic search approach for fitting a TES model to empirical time series. Finally, we exemplify our approach by two examples of TES video source models, constructed from empirical codec bitrate measurements: one at the frame level and the other at the group-of-block level. The examples demonstrate the efficacy of the TES modeling methodology and the TEStool modeling environment.
---
paper_title: TES: A Class of Methods for Generating Autocorrelated Uniform Variates

paper_content:

This paper introduces a class of methods called TES (Transform-Expand-Sample) for generating autocorrelated variates with uniform marginals and Markovian structure. TES methods are readily implemented on a computer and have generation complexity comparable to that of the i.i.d. uniform sequence which they transform to an autocorrelated uniform sequence. For any prescribed correlation coefficient ρ, there is a TES method generating a uniform sequence with the 1-lag autocorrelation ρ, and the resultant autocorrelation is monotonic quadratic in two structural TES parameters. A simulation study reveals that TES methods give rise to autocorrelation functions with monotone decreasing as well as oscillating magnitude, bounded by monotone envelopes. The structural parameters were found to control the “amplitude” and “frequency” of the resultant autocorrelation function. A third parameter can be used to transform a TES sequence into more continuous-looking versions and to control the skewness of sample path cycles. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
---
paper_title: Spectral Analysis of Basic TES Processes

paper_content:

This paper studies the spectral properties of a class of stochastic sequences generated by basic TES (Transform-Expand-Sample) methods, as well as transformed TES sequences. A TES sequence is obtained as a marginally uniform process from an autoregressive scheme with modulo-1 reduction, followed by additional transformations. We derive formulas for the spectral density function and the spectral distribution function which are suitable for efficient numerical computation. A set of examples is calculated and exhibited for TES processes with uniform and exponential marginals. The results contribute to the understanding of TES sequences as models of autocorrelated sequences, particularly in a Monte Carlo simulation context. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.
---
paper_title: The Impact of Autocorrelation on Queuing Systems

paper_content:

The performance of single-server queues with independent interarrival intervals and service demands is well understood, and often analytically tractable. In particular, the M/M/1 queue has been thoroughly studied, due to its analytical tractability. Little is known, though, when autocorrelation is introduced into interarrival times or service demands, resulting in loss of analytical tractability. Even the simple case of an M/M/1 queue with autocorrelations does not appear to be well understood. Such autocorrelations do, in fact, abound in real-life systems, and worse, simplifying independence assumptions can lead to very poor estimates of performance measures. This paper reports the results of a simulation study of the impact of autocorrelation on performance in an FIFO queue. The study used two computer methods for generating autocorrelated random sequences, with different autocorrelation characteristics. The simulation results show that the injection of autocorrelation into interarrival times, and to a lesser extent into service demands, can have a dramatic impact on performance measures. From a performance viewpoint, these effects are generally deleterious, and their magnitude depends on the method used to generate the autocorrelated process. The paper discusses these empirical results and makes some recommendations to practitioners of performance analysis of queuing systems.
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Title: An Overview Of TES Processes And Modeling Methodology

Section 1: INTRODUCTION
Description 1: Introduce the TES approach to modeling stationary time series, highlighting its non-parametric nature, broad modeling scope, and its main applications in creating source models for Monte Carlo simulations. Discuss the key features of TES, such as the simultaneous fitting of marginal distributions and autocorrelations.

Section 2: Temporal Dependence and Autocorrelations
Description 2: Explain the concept of temporal dependence and its importance. Discuss the role of autocorrelation as a measure of linear temporal dependence in stochastic processes, and provide the mathematical formulation of the autocorrelation function.

Section 3: The Importance of Modeling Temporal Dependence
Description 3: Highlight the significance of modeling temporal dependence in practical systems, particularly in simulation and analytical models. Discuss the risks associated with failing to capture temporal dependence, using queueing systems as an illustrative example.

Section 4: Goodness Criteria for Modeling Empirical Time Series
Description 4: Outline the requirements and criteria for judging the goodness of a TES model. Detail the quantitative and qualitative benchmarks that a candidate time series model should meet based on empirical sample paths.

Section 5: The Merits of the TES Modeling Methodology
Description 5: Summarize the advantages of the TES modeling approach, including its ability to fit arbitrary marginals, approximate empirical autocorrelations, and generate a diverse range of sample paths. Discuss the computational advantages and the role of the TEStool modeling software.

Section 6: TECHNICAL PRELIMINARIES
Description 6: Provide intuitive explanations of key technical concepts essential to understanding TES processes and modeling methodology, such as the inversion method, histogram inversions, modulo-1 arithmetic, iterated uniformity, step-function innovation densities, and stitching transformations.

Section 7: The TES Modeling Approach
Description 7: Present the main elements and steps involved in the TES modeling approach. Describe the process of creating stationary sequences with arbitrary marginal distributions and how TES sequences meet the requirements for fitting both marginal distributions and autocorrelations.

Section 8: OVERVIEW OF TES SEQUENCES
Description 8: Provide an overview of basic and general TES background sequences, their construction, and associated parameters. Discuss the behavior modes and autocorrelation functions of TES sequences, and how these properties are utilized in empirical modeling.

Section 9: TES MODELING AND SOFTWARE SUPPORT
Description 9: Discuss the TES modeling methodology as implemented in TEStool, focusing on practical applications and the use of empirical sample paths. Explain the heuristic search process for selecting TES process parameters and the role of TEStool in facilitating this search.

Section 10: Example: A TES Model of Compressed Video Traffic
Description 10: Provide a concrete example of TES modeling using real-world data, specifically compressed video traffic. Illustrate how the requirements for a good TES model are met using TEStool and discuss the resulting model's effectiveness.

Section 11: CONCLUSION
Description 11: Conclude with a summary of the TES models, methodology, and the supportive role of the TEStool software. Highlight the advantages of TES in providing accurate models for empirical time series and its potential applications in forecasting and simulations.