Lecture D1 (2026-09-17): 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.

Concept Explorers linked from this lecture:

• Concept Explorer: Pseudo-Random Number Generators and AI Watermarking
• Concept Explorer: Monte Carlo Examples for Stochastic Modeling
• Concept Explorer: Input Modeling (fully functional Input Analyzer)
• Concept Explorer: Probability Distributions for Input Modeling and Statistics

Lecture C2 (2026-09-15): Beyond DES Simulation – SDM, ABM, and NetLogo

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 applications in life sciences, social sciences, and engineering (Multi-Agent Systems, MAS)/operations research. 

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).

Concept explorers referenced in this lecture material (particularly for Lab 3 material):

• https://tpavlic.github.io/asu-simulating-stochastic-systems/monte_carlo/mc_explorer.html
• https://tpavlic.github.io/asu-simulating-stochastic-systems/monte_carlo/mc_examples.html
• https://tpavlic.github.io/asu-simulating-stochastic-systems/input_modeling/prob_models.html

Lecture C1 (2026-09-10): 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.

Some parts of this lecture make use of an interactive widget that includes several Monte Carlo method examples for stochastic modeling. It can be found at:

• https://tpavlic.github.io/asu-simulating-stochastic-systems/monte_carlo/mc_examples.html

Lecture B3 (2026-09-08): Discrete-Event Simulation Examples, Part II

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.

If time permits, this lecture slot will be used to pivot to discussing the previous "Lab 2 (Muffin Oven Simulation)", which lets us introduce common random numbers (CRNs), statistical blocking, requirements of 2-sample and paired t-tests, and more sophisticated statistical methods that better characterize PRACTICAL significance (and take into account the multiple comparisons problem). Thus, the post-lab2 reflections are largely a preview of future topics in the course.

As an introduction to next week's lab, this lecture also links to an interactive Monte Carlo method concept explorer for students to engage with offline. It can be found at:

https://tpavlic.github.io/asu-simulating-stochastic-systems/monte_carlo/mc_explorer.html

Lecture B2 (2026-09-03): Discrete-Event Simulation Examples, Part I

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 sense of.

Lecture B1 (2026-09-01): 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 make sense of.

Lecture A2 (2026-08-27): 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."