In this lecture, we review topics from the first half of the semester that will be tested over in the upcoming midterm. Most of the class involves working examples on the whiteboard.
Whiteboard notes captured for this session can be found at: https://www.dropbox.com/s/pih0wt3abwbatbb/IEE475-LectureF-2021-09-30-Midterm_Review-Whiteboard_Notes.pdf?dl=0
In this lecture, we finish covering tests of uniformity (Chi-squared and Kolmogorov–Smirnov) and independence (autocorrelation and runs (above and below) tests) for pseudo-random number generators (PRNGs). We then move on to discussing the details of inverse-transform sampling for random-variate generation. We cover how to derive a CDF from a piecewise PDF and how to invert a CDF to produce a quantile function fit for random-variate generation. We also discuss the discrete inverse-transform case.
We start the lecture covering some discrete random variables that we did not get to during Lecture D2. We also introduce the Poisson process and how it relates to the Poisson and exponential random variables. We then pivot to discussing pseudo-random number generators (PRNGs), including their required as well as desired properties and statistical tests to test for independence and uniformity. We will continue the discussion of statistical tests for independence at the start of next lecture (Lecture E2).
In this lecture, we review basic probability space concepts from the previous lecture. We then go on to discuss the common probabilistic models that we will use in stochastic simulation (e.g., uniform, triangular, normal, exponential, Weibull, Erlang, Poisson, etc.). Basic background on the structure of each distribution is given as well as practical reasons why one distribution might be picked over another.
In this lecture, we use motivation from stochastic modeling (i.e., incorporating randomness into models in order to capture realistic variation without having to specify a great many details) to formally introduce random variables and probability spaces (as a subset of measure theory). We heavily lean on the analogy between probability and mass as we introduce the sample space, probability measure, random variable, probability mass function (pmf), probability density function (pdf), cumulative distribution function (cdf), and moments (including expectation and central moments as in variance).
In this lecture, we review results from the Monte Carlo simulation lab (Lab 3) and setup motivation for the agent-based modeling/NetLogo lab (Lab 4). For the MC-lab review, we cover the estimation of pi by drawing random coordinates in the unit cube. We also discuss the possibly counter-intuitive results from estimating the length of a 3-path stochastic activity network. To prepare for Lab 4, we review the three different types of simulation methodologies (ABM/IBM, DES, and SDM) and then give a brief introduction to NetLogo. A more detailed/tutorial introduction to NetLogo will take place during Lab 4.
In this lecture, we discuss more sophisticated dynamical simulation models that can be implemented within spreadsheets. We start with a review of the M/M/1 single-channel, single-server queueing node and then show how more explicit state variables can be introduced in an M/M/2 version (i.e., with two servers). We then discuss two different popular inventory management models (implemented within a spreadsheet) -- the "Order-up-to (M,N)" model as well as the "newsvendor (single-period/perishable) model". We close with some discussion of Monte Carlo methods -- which apply simulation techniques as numerical methods to solve mathematical problems that might otherwise be intractable analytically. Despite all of these examples of the power of spreadsheets, we end with a hint that much more is possible in terms of simulation of complex systems if we use specialized simulation tools. We will introduce some of those more specialized tools starting in the next lecture.
In this lecture, we review hand-simulation/DES simulation basics. We then introduce how to simulate discrete event system simulations (which are dynamic simulation models built around the idea of "state") in declarative programming frameworks like spreadsheets (which have no "state"). We work through the relationships necessary to encode in a spreadsheet to simulate a single-channel, single-server queue. We then pivot to covering comments from Lab 2, which was a hand simulation of a system with partial batching. This allows for motivating why we use multiple replications when we do empirical work with stochastic simulations, and how tools such as common random numbers can reduce variance but require special statistical tools (such as the paired-difference t-test). We then discuss the multiple comparisons problem, some ways to solve it, and how linear models extend what we can say from empirical studies -- so we can go from statistically significant to practically significant. (i.e., we can better characterize the "effect size" of a variable we have control over).
In this lecture, we carry forward our high-level description of the event-scheduling world view to specific hand-simulation examples of a single-channel, single-server queueing network node.
