Lecture G2 (2020-10-20): Input Modeling, Part 2

This is the second part in a unit on input modeling for simulating stochastic systems (stochastic simulation). In the this part, we describe how to start making sense of data collected from real-world systems. We start with an example that builds a model of a single-server, single-channel queue based on summary statistics alone and demonstrate that the resulting model is a poor fit for a realistic system. We then use a histogram to reveal insights into how the system can be re-structured to be more realistic while also requiring simpler input models. This leads into a discussion on building histograms to be maximally insightful.

Lecture F2 (2020-10-13): Review Before Midterm Retake

In this lecture period, we discuss student-generated questions as a means of reviewing for the upcoming midterm retake. Most of the discussion centers around the solution set from the first midterm.

Lecture G1 (2020-10-08): Input Modeling, Part 1

In this lecture, we re-motivate the topic of Input Modeling in stochastic simulation. Input modeling is the process of choosing probabilistic models to represent realistic variation that is statistically similar to measured data even though the probabilistic models leave out the real-world details underlying that variation. This lecture focus primarily on issues relating to collecting data (when to use old data, issues related to data censoring, issues related to correlated variables, issues related to multi-modal distributions, etc.).

Lecture F (2020-10-01): Midterm Review

Midterm review lecture for Fall 2020. Starts with an introduction to inverse-transform sampling for discrete random variables (including sampling from empirical CDF's).

Lecture E2 (2020-09-29): Random-Variate Generation

In this lecture, we review random-number generation and tests of uniformity and independence. We then focus on random-variate generation (for stochastic simulation) using inverse-transform sampling.

Lecture E1 (2020-09-24): Random Number Generation

This lecture surrounds random number generation. The topic is motivated by the need for generating samples from arbitrary random variables, which can be accomplished through transforming random numbers uniformly distributed between 0 and 1. We describe the key properties of a good pseudo-random number generator (uniformity and independence), discuss some historical random number generators, and then a more modern pseudo-random number generator. We close with descriptions of tests for uniformity (Chi-square and Kolmogorov-Smirnov) and independence (autocorrelation and runs tests).

Lecture D2 (2020-09-22): Probabilistic Models

In this lecture, we review the motivations for stochastic modeling in discrete event system simulation. We also review the basics of probability theory (specifically probability spaces, random variables, probability density functions, probability mass functions, cumulative distribution functions, and moments including expected value (first moment/mean) and variance). We then describe several popular continuous and discrete random variables used in input modeling for stochastic simulation.