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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 E1 (2024-09-06): Random-Number Generation

IEE 475: Simulating Stochastic Systems ·

2024/09/26

In this lecture, we introduce the measure-theoretic concept of a random variable (which is neither random nor a variable) and related terms, such as outcomes, events, probability measures, moments, means, etc. Throughout the lecture, we use the metaphor of probability as mass (and thus probability density as mass density, and a mean as a center of mass). This allows us to discuss the "statistical leverage" of outliers in a distribution (i.e., although they happen infrequently, they still have the

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Lecture D2 (2024-09-24): Probabilistic Models

IEE 475: Simulating Stochastic Systems ·

2024/09/24

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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Lecture D1 (2024-09-19): Probability and Random...

IEE 475: Simulating Stochastic Systems ·

2024/09/19

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Lecture C2 (2024-09-17): Beyond DES – SDM, ABM, and...

IEE 475: Simulating Stochastic Systems ·

2024/09/17

This lecture (slides embedded below) provides some historical background and motivation for System Dynamics Modeling (SDM) and Agent-Based Modeling (ABM), two other simulation modeling approaches that contrast with Discrete Event System (DES) simulation.In particular, in this lecture, we briefly introduce System Dynamics Modeling (SDM) and Agent-Based/Individual-Based Modeling (ABM/IBM) as the two ends of the simulation modeling spectrum (from low resolution to high resolution). The introduction of

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Lecture C1 (2024-09-12): Basic Simulation Tools and...

IEE 475: Simulating Stochastic Systems ·

2024/09/12

This lecture covers content related to implementing simulations with spreadsheets and the motivations for the use of special-purpose Discrete Event System Simulation tools. In particular, we discuss different approaches to implementing Discrete Event System (DES) simulations (DESS) with simple spreadsheets (e.g., Microsoft Excel, Google Sheets, Apple Numbers, etc.). We cover inventory management problems (such as the newsvendor model) as well as Monte Carlo sampling and stochastic activity networks

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Lecture B3 (2024-09-10): Discrete-Event Simulation...

IEE 475: Simulating Stochastic Systems ·

2024/09/11

In this lecture, we close out our review of DES fundamentals and hand simulation. After going through a hand-simulation example one last time, we show how to implement a Discrete Event System (DES) simulation using a spreadsheet tool like Microsoft Excel without any "macros" (VBA, etc.). This involves defining relationships ACROSS TIME that allow the spreadsheet to (in a declarative fashion) reconstruct the trajectory that is the output of the simulation.We then pivot to discussing the previous "Lab

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Lecture B2 (2024-09-05): Discrete-Event Simulation...

IEE 475: Simulating Stochastic Systems ·

2024/09/05

In this lecture, we review fundamentals of Discrete Event System (DES) simulation (e.g., entities, resources, activities, processes, delays, attributes) and we run through a number of DES modeling examples. These examples show how different research/operations questions can lead to different choices of entities/resources/etc. We close with a hand-simulation example of a single-channel, single-server queue with provided interarrival times and service times.

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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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IEE 475: Simulating Stochastic Systems

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