IEE 475: Simulating Stochastic Systems

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

  1. AUG 28

    Lecture A2 (2025-08-28): Introduction to Simulation Modeling

    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."

  2. AUG 26

    Lecture A1 (2025-08-26): Introduction to Modeling

    In this lecture, we introduce Industrial and Systems Engineering as a blend of science and engineering that necessitates model building. We then define model (as something that answers a "What If" question) and different types of models. This gives us an opportunity to discuss how modeling is less about describing reality and more about generating tools to do useful things/make useful predictions. We end with a comparison of mental and quantitative models, as well as a comparison of different types of quantitative models (including simulation modeling).

  3. AUG 21

    Lecture 0 (2025-08-21): Course Introduction

    This lecture introduces students to IEE 475 (Simulating Stochastic Systems), a required course for Industrial Engineering majors that covers the design and analysis of simulation models of real-world engineered systems. The lecture covers contents of the syllabus as well as where students can find more information in the Canvas Learning Management System site for the course.

  4. 12/04/2024

    Lecture M (2024-12-03): Final Exam Review

    In this lecture, we prepare for the final exam and give a brief review of all topics from the course. Students are encouraged to bring their own questions so that the focus of the class is on the topics that students feel they need the most help with.

  5. 11/27/2024

    Lecture L (2024-11-26) Course Wrap-Up

    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 Unit K. 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).

  6. 11/22/2024

    Lecture K2 (2024-11-21): Variance Reduction Techniques, Part 2 (AVs and Importance Sampling)

    In this lecture, we review four different Variance Reduction Techniques (VRT's). Namely, we discuss common random numbers (CRNs), control variates, antithetic variates (AVs), and importance sampling. Each one of these is a different approach to reducing the variance in the estimation of relative or absolute performance of a simulation model. Variance reduction is an alternative way to increase the power of a simulation that is hopefully less costly than increasing the number of replications.

  7. 11/20/2024

    Lecture K1 (2024-11-19): Variance Reduction Techniques, Part 1 (CRNs and Control Variates)

    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 analysis of variance (ANOVA) and post hoc tests (like the Tukey HSD or Fisher's LSD). After that review, we move on to introducing variance reduction techniques (VRTs) which reduce the size of confidence intervals by experimentally controlling/accounting for alternative sources of variance (and thus reducing the observed variance in response variables). We discuss Common Random Numbers (CRNs), which use a paired/blocked design to reduce the variance caused by different random-number streams. We start to discuss control variates (CVs), but that discussion will be picked up at the start of the next lecture.

  8. 11/15/2024

    Lecture J4 (2024-11-14): Estimation of Relative Performance

    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 paired-difference t-test, the equal-variance (pooled) t-test, and Welch's unequal variance t-test. Each of these different experimental conditions sets up a different standard error of the mean formula and formula for degrees of freedom that are used to define the actual confidence interval half widths (centered on the difference in sample means in the pairwise comparison of systems). We then generalize to the case of more than 2 systems, particularly for "ranking and selection (R&S)." This lets us review the multiple-comparisons problem (and Bonferroni correction) and how post hoc tests (after an ANOVA) are more statistically powerful ways to do comparisons.

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

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