Lecture M (2025-12-02): Final Exam Review
In this lecture, we prepare for the final exam and give a brief review of all topics from the course.
Dec 02, 2025
IEE 475: Simulating Stochastic Systems
Archived lectures from undergraduate course on stochastic simulation given at Arizona State University by Ted Pavlic
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Episodes
Lecture K2 (2025-11-25): Variance Reduction Techniques, Part 2 (Antithetic Variates 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. We ...
Nov 25, 2025
Lecture K1 (2025-11-20): 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 a...
Nov 21, 2025
Lecture J4 (2025-11-19): 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...
Nov 19, 2025
Lecture J3 (2025-11-13): Estimation of Absolute Performance, Part III (Non-Terminating Systems/Steady-State Simulations)
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 simula...
Nov 13, 2025
Lecture J2 (2025-11-06): Estimation of Absolute Performance, Part II (Terminating Systems/Transient Simulations)
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 pred...
Nov 07, 2025
Lecture J1 (2025-11-04): Estimation of Absolute Performance, Part I (Introduction to Point and Interval Estimation)
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 swi...
Nov 04, 2025
Lecture I (2025-10-30): Statistical Reflections
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 Lecture H) where we use a power analysi...
Oct 30, 2025
Lecture H (2025-10-28): Verification, Validation, and Calibration of Simulation Models
At the start of this lecture, we review statistical topics and fitting techniques from Unit G (particularly Lecture G3, on goodness of fit). 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 And...
Oct 29, 2025
Lecture G3 (2025-10-23) Input Modeling, Part 3 (Parameter Estimation and Goodness of Fit)
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-val...
Oct 23, 2025
IEE 475: Lecture G2 (2025-10-21): Input Modeling, Part 2 (Selection of Model Structure)
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...
Oct 22, 2025
Lecture G1 (2025-10-16): Input Modeling, Part 1 (Data Collection)
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 re...
Oct 16, 2025
Lecture F (2025-10-02): Midterm Review for IEE 475 (Simulating Stochastic Systems)
During this lecture, we review the topics covered up to this point in the course as preparation for the upcoming midterm exam. Students are encouraged to bring their own questions to class so that we can focus on the topics that students feel like they need the most help with.
Oct 03, 2025
Lecture E2 (2025-09-30): Random-Variate Generation
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 sm...
Oct 01, 2025
Lecture E1 (2025-09-25): Random-Number Generation
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...
Sep 25, 2025
Lecture D2 (2025-09-23): Probabilistic Models
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 variable...
Sep 23, 2025
Lecture D1 (2025-09-18): Probability and Random Variables
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 th...
Sep 18, 2025
Lecture C2 (2025-09-16): Beyond DES Simulation – SDM, ABM, and NetLogo (and pre-lab discussion for Lab 4 and post-lab discussion for Lab 3)
This lecture 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 ABM describes appli...
Sep 16, 2025
Lecture C1 (2025-09-11): Basic Simulation Tools and Techniques
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 netwo...
Sep 11, 2025
Lecture B3 (2025-09-09): DES Examples, Part II (and post-lab discussion for Lab 2)
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. At the end of the lecture, we pivot to d...
Sep 09, 2025
Lecture B2 (2025-09-04): DES Examples, Part I
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.
Sep 04, 2025
Lecture B1 (2025-09-02): Fundamental Concepts of Discrete-Event Simulation
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 ...
Sep 02, 2025
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."
Aug 28, 2025
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 ty...
Aug 26, 2025
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.
Aug 21, 2025
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