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.
IEE 475: Simulating Stochastic Systems
Archived lectures from undergraduate course on stochastic simulation given at Arizona State University by Ted Pavlic
Thursday, October 3, 2024
Tuesday, October 1, 2024
Lecture E2 (2024-10-01): 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 smaller numbers of samples. For independence, we discuss autocorrelation tests and runs test, and then we demonstrate a runs above-and-below-the-mean test. We then shift to discussing inverse-transform sampling for continuous random variates and discrete random variates and how the resulting random-variate generators might be implemented in a tool like Rockwell Automation's Arena.
Thursday, September 26, 2024
Lecture E1 (2024-09-06): Random-Number Generation
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 ability to shift the mean significantly, as in physical leverage). This sets us up to talk about random processes and particular random variables in the next lecture.
Tuesday, September 24, 2024
Lecture D2 (2024-09-24): 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 variables. If we do not have time to do so during this lecture, we will finish the discussion in the next lecture with the Bernoulli-based discrete variables and Poisson processes.
Thursday, September 19, 2024
Lecture D1 (2024-09-19): 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 the ability to shift the mean significantly, as in physical leverage). This sets us up to talk about random processes and particular random variables in the next lecture.
Tuesday, September 17, 2024
Lecture C2 (2024-09-17): Beyond DES – SDM, ABM, and NetLogo
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 ABM describes applications in life sciences, social sciences, and engineering (Multi-Agent Systems, MAS)/operations research. NetLogo is introduced (as part of preparation for Lab 4), and it is used to present examples of running ABM's as well as the code behind them. This lecture is also coupled with notes discussing the Lab 3 (Monte Carlo simulation) results and general experience. These comments focus on interval estimation (which is right 95% of the time, as opposed to point estimation that is right 0% of the time) and the role of non-trivial distributions of random variables (as opposed to just their means).Thursday, September 12, 2024
Lecture C1 (2024-09-12): 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 networks (SAN's). Although we show that spreadsheets can be very powerful for this kind of work, we highlight that this approach is cumbersome for systems with increasing complexity. So this motivates why we would use more sophisticated tools specifically built for simulation (but perhaps not so great for data analysis by themselves), like Arena, FlexSim, Simio, and NetLogo.
This lecture was recorded by Theodore Pavlic as part of IEE 475 (Simulating Stochastic Systems) at Arizona State University.
Popular Posts
-
In this lecture, we (nearly) finish our coverage of Input Modeling, where the focus of this lecture is on parameter estimation and assessing...
-
In this lecture, we introduce the three different simulation methodologies (agent-based modeling, system dynamics modeling, and discrete eve...
-
This lecture covers Variance Reduction Techniques (VRT) for stochastic simulation, covering: Common Random Numbers (CRNs), Control Variates ...
-
In this lecture, we continue to discuss hypothesis testing -- introducing parametric, non-parametric, exact, and non-exact tests and reviewi...
-
In this lecture, we close out our review of DES fundamentals and hand simulation. After going through a hand-simulation example one last tim...
-
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...
-
In this lecture, we go over course policies for the Fall 2022 session of IEE 475.
-
In this lecture, we introduce Industrial and Systems Engineering as a blend of science and engineering that necessitates model building. We ...
-
In this lecture, we review fundamentals of Discrete Event System (DES) simulation (e.g., entities, resources, activities, processes, delays,...
-
In this lecture, we continue our discussion of statistically rigorous methods for input modeling in simulation of stochastic systems. We fir...