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IEE 475: Simulating Stochastic Systems

Theodore P. Pavlic

Archived lectures from undergraduate course on stochastic simulation given at Arizona State University by Ted Pavlic

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Lecture B1 (2024-09-03): Fundamental Concepts of...

IEE 475: Simulating Stochastic Systems ·

2024/09/03

In this lecture, we cover fundamentals of discrete-event system (DES) simulation (DESS). This involves reviewing basic simulation concepts (entities, resources, attributes, events, activities, delays) and introducing the event-scheduling world view, which provides a causality framework on which an automatic simulation of a DES system can be built. We also discuss briefly how the stochastic modeling inherent to DESS means that outputs will be variable and thus will require rigorous statistics to make

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Lecture A2 (2024-08-29): Introduction to Simulation...

IEE 475: Simulating Stochastic Systems ·

2024/08/30

In this lecture, we introduce the three different simulation methodologies (agent-based modeling, system dynamics modeling, and discrete event system simulation) and then focus on how stochastic modeling is used within discrete-event system simulation. In particular, we define terms such as system, dynamic system, state, state variable, activity, delay, resource, entity, and the notion of "input modeling."

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Lecture A1 (2024-08-27): Introduction to Modeling

IEE 475: Simulating Stochastic Systems ·

2024/08/27

This lecture introduces the topic of modeling with particular focus on the role of quantitative modeling in industrial engineering and operations research. This is an introduction to a course on stochastic simulation.

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Lecture 0 (2024-08-22): Introduction to the Course...

IEE 475: Simulating Stochastic Systems ·

2024/08/22

In this lecture, we outline the structure and purpose of IEE 475 (Simulating Stochastic Systems) for the Fall 2024 semester at Arizona State University. We go over topics covered in the syllabus and on the course learning management system website.

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Lecture M (2022-11-29): Final Exam Review

IEE 475: Simulating Stochastic Systems ·

2022/11/29

In this lecture, we prepare for the final exam and give a brief review of all topics from the course.

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Lecture L (2022-11-22): Course Wrap Up

IEE 475: Simulating Stochastic Systems ·

2022/11/23

In this lecture, we wrap up the course content in IEE 475. We first do a quick overview of the four variance reduction techniques (VRT's) covered in the previous unit. That is, we cover: common random numbers (CRN's), antithetic variates (AV's), importance sampling, and control variates. We then remember some general comments about the goal of modeling and commonalities seen across simulation platforms (as well as the different types of simulation platforms in general).

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Lecture K1 (2022-11-15): Variance Reduction...

IEE 475: Simulating Stochastic Systems ·

2022/11/16

In this lecture, we start by reviewing approaches for absolute and relative performance estimation in stochastic simulation. This begins with a reminder of the use of confidence intervals for estimation of performance for a single simulation model. We then move to different ways to use confidence intervals on mean DIFFERENCES to compare two different simulation models. We then move to the ranking and selection problem for three or more different simulation models, which allows us to talk about

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Lecture J4 (2022-11-10): Estimation of Relative...

IEE 475: Simulating Stochastic Systems ·

2022/11/10

In this lecture, we review what we have learned about one-sample confidence intervals (i.e., how to use them as graphical versions of one-sample t-tests) for absolute performance estimation in order to motivate the problem of relative performance estimation. We introduce two-sample confidence intervals (i.e., confidence intervals on DIFFERENCES based on different two-sample t-tests) that are tested against a null hypothesis of 0. This means covering confidence interval half widths for the

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Lecture J3 (2022-11-08): Estimation of Absolute...

IEE 475: Simulating Stochastic Systems ·

2022/11/08

In this lecture, we start by further reviewing confidence intervals (where they come from and what they mean) and prediction intervals and then use them to motivate a simpler way to determine how many replications are needed in a simulation study (focusing first on transient simulations of terminating systems). We then shift our attention to steady-state simulations of non-terminating systems and the issue of initialization bias. We discuss different methods of "warming up" a steady-state simulation

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Lecture J2 (2022-11-03): Estimation of Absolute...

IEE 475: Simulating Stochastic Systems ·

2022/11/04

In this lecture, we review estimating absolute performance from simulation, with focus on choosing the number of necessary replications of transient simulations of terminating systems. The lecture starts by overviewing point estimation, bias, and different types of point estimators. This includes an overview of quantile estimation and how to use quantile estimation to use simulations as null-hypothesis-prediction generators. We the introduce interval estimation with confidence intervals and

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Lecture J1 (2022-11-01): Estimation of Absolute...

IEE 475: Simulating Stochastic Systems ·

2022/11/02

In this lecture, we introduce the estimation of absolute performance measures in simulation – effectively shifting our focus from validating input models to validating and making inferences about simulation outputs. Most of this lecture is a review of statistics and reasons for the assumptions for various parametric and non-exact non-parametric methods. We also introduce a few more advanced statistical topics, such as non-parametric methods and special high-power tests for normality. We then switch

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Lecture I (2022-10-27): Statistical Reflections...

IEE 475: Simulating Stochastic Systems ·

2022/10/28

In this lecture, we review statistical fundamentals – such as the origins of the t-test, the meaning of type-I and type-II error (and alternative terminology for both, such as false positive rate and false negative rate) and the connection to statistical power (sensitivity). We review the Receiver Operating Characteristic (ROC) curve and give a qualitative description of where it gets its shape in a hypothesis test. We close with a validation example (from the previous lecture) where we use a power

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Lecture H (2022-10-25): Verification, Validation, and...

IEE 475: Simulating Stochastic Systems ·

2022/10/25

In this lecture, we mostly cover slides from Lecture G3 (on goodness of fit) that were missed during the previous lecture. In particular, we review hypothesis testing fundamentals (type-I error, type-II error, statistical power, sensitivity, false positive rate, true negative rate, receiver operating characteristic, ROC, alpha, beta) and then go into examples of using Chi-squared and Kolmogorov–Smirnov tests for goodness of fit for arbitrary distributions. We also introduce Anderson–Darling (for

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Lecture G3 (2022-10-20): Input Modeling, Part 3...

IEE 475: Simulating Stochastic Systems ·

2022/10/20

In this lecture, we (nearly) finish our coverage of Input Modeling, where the focus of this lecture is on parameter estimation and assessing goodness of fit. We review input modeling in general and then briefly review fundamentals of hypothesis testing. We discuss type-I error, p-values, type-II error, effect sizes, and statistical power. We discuss the dangers of using p-values at very large sample sizes (where small p-values are not meaningful) and at very small sample sizes (where large p-values

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Lecture G2 (2022-10-18): Input Modeling, Part 2...

IEE 475: Simulating Stochastic Systems ·

2022/10/18

In this lecture, we continue discussing the choice of input models in stochastic simulation. Here, we pivot from talking about data collection to selection of the broad family of probabilistic distributions that may be a good fit for data. We start with an example where a histogram leads us to introduce additional input models into a flow chart. The rest of the lecture is about choosing models based on physical intuition and the shape of the sampled data (e.g., the shape of histograms). We close

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Lecture G1 (2022-10-13): Input Modeling, Part 1 (Data...

IEE 475: Simulating Stochastic Systems ·

2022/10/14

In this lecture, we introduce the detailed process of input modeling. Input models are probabilistic models that introduce variation in simulation models of systems. Those input models must be chosen to match statistical distributions in data. Over this unit, we cover collection of data for this process, choice of probabilistic families to fit to these data, and then optimized parameter choice within those families and evaluation of fit with goodness of fit. In this lecture, we discuss issues

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Lecture F (2022-09-29): Midterm Review

IEE 475: Simulating Stochastic Systems ·

2022/09/30

Midterm review session for ASU IEE 475 for Fall 2022.Whiteboard notes for this lecture can be found at:https://www.dropbox.com/s/ljc61rarhns41u2/2022-Fall-Midterm_Review_Notes.pdf?dl=0

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Lecture E2 (2022-09-27): Random-Variate Generation

IEE 475: Simulating Stochastic Systems ·

2022/09/28

In this lecture, we review pseudo-random number generation and then introduce random-variate generation by way of inverse-transform sampling. In particular, we start with a review of the two most important properties of a pseudo-random number generator (PRNG), uniformity and independence, and discuss statistically rigorous methods for testing for these two properties. For uniformity, we focus on a Chi-square/Chi-squared test for larger numbers of samples and a Kolmogorov–Smirnov (KS) test for

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Lecture E1 (2022-09-22): Random-Number Generation

IEE 475: Simulating Stochastic Systems ·

2022/09/22

In this lecture, we first cover some discrete distributions (and the Poisson process) that we ran out of time for during the previous lecture. We then launch into a discussion of how to generate pseudo-random numbers distributed uniformly between 0 and 1 (which are necessary for us to easily generate random variates of any distribution). We talk about the two most important properties of a pseudo-random number generator (PRNG), uniformity and independence. We then talk about desirable properties

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Lecture D2 (2022-09-20): Probabilistic Models

IEE 475: Simulating Stochastic Systems ·

2022/09/20

In this lecture, we review basic probability fundamentals (measure spaces, probability measures, random variables, probability density functions, probability mass functions, cumulative distribution functions, moments, mean/expected value/center of mass, standard deviation, variance), and then we start to build a vocabulary of different probabilistic models that are used in different modeling contexts. These include uniform, triangular, normal, exponential, Erlang-k, Weibull, and Poisson variables

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IEE 475: Simulating Stochastic Systems

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