Course Description This course covers modeling of discrete-event dynamic systems and introduces simulation- based methods for using these models to solve engineering design and analysis problems.
Prerequisites You will be expected to come in knowing a bit of basic calculus, probability, and statistics. But don’t worry too much – we’ll provide bootcamps on that material so as to make the class pretty much self-contained. In addition, this course will involve extensive computer programming, so it would be nice to have at least a little experience in something like Excel, just to bring back the programming memories.
Course Goals
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Learn how to develop simulation models and conduct simulation studies. Become familiar with the organization of simulation languages. In particular, we will do a great deal of modeling with Arena, a comprehensive simulation package with animation capabilities. Review statistical aspects including input analysis, random variate generation, output analysis, and variance reduction techniques.
Grading Policies
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There will be two midterms and a final exam. Test questions are typically multiple choice or T/F. There will be 11 Homework assignments (not as bad as it sounds). There will be a bunch of bonus questions spread throughout the semester, which you can do to earn a few extra points. HWs that are late will suffer a 10x% deduction, where x is the number of days late, with x = 3 being the upper bound on the allowed lateness. So plan ahead!
 We will have a project, which you can select from among several theory- and applications-oriented topics. You will be allowed to work in small groups.  You must achieve an overall weighted average of 60% to pass the course.  Work hard and you will be rewarded – Grading is usually pretty generous.
 Grading Disputes:
o Let’s be winners, not whiners. We are happy to discuss grades, but please make
reasonable requests.
o To this end, we will generously provide various bonus point opportunities
throughout the course; but because of this lovely act of kindness, we will not accept any test grade whining for matters involving up to 4 points. (Makes great sense, eh?!)
Mother Teresa: “Wow, that’s something nice that I would do!”
o If you really, really want to request a regrade (for matters involving more than 4
points), simply fill out the convenient form that can be found at http://www.isye.gatech.edu/%7Esman/courses/gradegrovel.pdf.
o Here is some sage advice on whining: https://www.youtube.com/watch?
v=Ow0lr63y4Mw.
 Grading Breakdown
Homework Project Midterm Exam 1 Midterm Exam 2 Final Exam Bonus Opportunities TOTAL
10% 10% 25% 25% 30% 2.5% 102.5%
Timing Policy
The Modules follow a logical sequence, so they (mostly) need to be done in order.
You will have access to the course content for the scheduled duration of the course.
Exam Policy
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For Quiz x (x = 1,2,3), you are allowed to use x sheets of paper, either 8.5”x11” or A4, with handwritten or printed notes (both sides of the sheet, 2x sides total). For all quizzes, you are allowed a blank sheet of paper for scratch work. (All OMS Analytics and OMS CS students will be proctored; you will have to show the front and back of the blank sheet while you are being proctored.) You are also allowed to bring any reasonable calculator.
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You will not be allowed to use packages such as Excel, Arena, R, etc. during the exams.
Attendance Policy
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This is a fully online course. Login on a regular basis to complete your work, so that you do not have to spend a lot of time reviewing and refreshing yourself regarding the content.
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Student Honor Code All GT students should abide by the Georgia Tech Student Honor Code.
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Review the Georgia Tech Student Honor Code: https://osi.gatech.edu/content/honor-code You are responsible for completing your own work.
  Any GT student suspected of behavior in violation of the Georgia Tech Honor Code will
be referred to Georgia Tech’s Office of Student Integrity.
Communication
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 Always be courteous and nice (see Netiquette below). 
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Netiquette
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Netiquette refers to etiquette that is used when communicating on the Internet. Review the Core Rules of Netiquette. When you are communicating via email, discussion forums or synchronously (in real-time), please use correct spelling, punctuation, and grammar consistent with the academic environment and scholarship1.
We expect all participants in Georgia Tech’s MS in Analytics program, (learners,
faculty, teaching assistants, staff) to interact respectfully. You must always play nice
1Conner, P. (2006–2014). Ground Rules for Online Discussions, Retrieved 8/14/2020 from https://tilt.colostate.edu/TipsAndGuides/Tip/128
Course Materials
 All content and course materials can be accessed online. 
There is no required textbook for this course, though students are encouraged to find copies of the following references:
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Law, A. M., Simulation Modeling and Analysis, 5th edition, McGraw-Hill Education, New York, 2015. [This textbook is most for the “theory” aspects of the course.] Kelton, W. D., Sadowski, R. P., and Zupick, N. B., Simulation with Arena, 6th edition, McGraw-Hill, New York, 2015. [This book covers the Arena simulation language.] If you want to review probability and statistics, you can get a free pdf version of my book A First Course in Probability and Statistics here. You can also buy an el cheapo softbound version here. We’ve heard that this makes the perfect Independence Day gift!
Technology/Software Requirements
Internet connection (DSL, LAN, or cable connection desirable) R statistical software (free download; see cran.r-project.org)
   Arena simulation software
 Arena is free! Get it here (but make sure to click the “Student” option on the
“Job Type” menu)!
 Arena requires a Windows operating system to run on your computer. If you don’t have Windows, you can run Arena thru ISyE’s Virtual Lab.   Arena (and our corresponding lecture material) is currently transitioning to a
new version, so the latest Arena version doesn’t perfectly match what’s in the notes. The good news is that everything still works.
 Adobe Acrobat PDF reader (free download; see https://get.adobe.com/reader/)
Disabilities and Special Circumstances
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COVID-19 Related Precautions
Student Illness or Exposure to COVID-19
Course Topics and Pacing Schedule
Weeks
Course Topics
Module 1: Whirlwind Tour of Simulation
Lesson 1: Getting to Know You Lesson 2: Syllabus Lesson 3: Whirlwind Tour Lesson 4: Whirlwind Tour – History Lesson 5: What Can We Do for You Lesson 6: Some Baby Examples Lesson 7: More Baby Examples Lesson 8: Generating Randomness Lesson 9 [OPTIONAL]: Simulation Output Analysis
Week 1 Homework
Homework 1
Module 2: Bootcamps
Lesson 1 [OPTIONAL]: Calculus Primer Lesson 2 [OPTIONAL]: Saved By Zero! Solving Equations Lesson 3 [OPTIONAL]: Integration Lesson 4 [OPTIONAL]: Integration Computer Exercises Lesson 5: Probability Basics Lesson 6: Simulating Random Variables
Release Dates (all times EASTERN)
Weeks
Course Topics
Release Dates (all times EASTERN)
Lesson 7: Great Expectations Lesson 8: Functions of a Random Variable Lesson 9: Jointly Distributed Random Variables Lesson 10 [OPTIONAL]: Conditional Expectation Lesson 11: Covariance and Correlation Lesson 12: Probability Distributions Lesson 13: Limit Theorems Lesson 14 [OPTIONAL]: Introduction to Estimation Lesson 15 [OPTIONAL]: Maximum Likelihood Estimation Lesson 16 [OPTIONAL]: Confidence Intervals
Week 2 Homework
Homework 2
Module 3: Hand Simulations
Lesson 1: Stepping Through Differential Equation Lesson 2: Monte Carlo Integration Lesson 3: Monte Carlo Integration Demo Lesson 4: Making Some Pi Lesson 5: A Single-Server Queue Lesson 6: An (s,S) Inventory System Lesson 7: An (s,S) Inventory System Demo Lesson 8: Simulating Random Variables Lesson 9: Simulating Random Variables Demo Lesson 10: Spreadsheet Simulation
Module 4: General Simulation Principles Lesson 1: Steps in a Simulation Study Lesson 2: Some Useful Definitions Lesson 3: Time-Advance Mechanisms Lesson 4: Two Modeling Approaches Lesson 5: Simulation Languages
Project Milestone 1
Project Topics Announced
Week 3 Homework
Homework 3
Release Dates (all times EASTERN)
Weeks
Course Topics
Module 5: The Arena Simulation Language
Lesson 1: Introduction Lesson 2: Process-interaction Lesson 3: Let’s Meet Arena! Lesson 4: The Arena Basic Template Lesson 5: Create-Process-Dispose Modules Lesson 6: The Process Module Lesson 7: Resource, Schedule, and Queue Spreadsheets Lesson 8: The Decide Module Lesson 9: The Assign Module Lesson 10: Attribute, Variable, and Entity Spreadsheets Lesson 11: Arena Internal Variables Lesson 12: Displaying Stuff Lesson 13: Batch, Separate, and Control Lesson 14: Run Setup and Control
Week 4 Homework
Homework 4
Midterm Exam 1
Midterm Exam 1 [Covers everything up to and including Lesson 9 of Module 5 from Week 4. See Topics Attachment.]
Module 5 (cont.): More Arena
Lesson 15: Two-Channel Manufacturing Example Lesson 16: Fake Customers Lesson 17: The Advanced Process Template Lesson 18: Resource Failures + Maintenance Lesson 19: The Blocks Template Lesson 20: The Joy of Sets Lesson 21: Description of Call Center Lesson 22: Call Center Demo Lesson 23: An Inventory Model Lesson 24: One Line vs Two Lines? Lesson 25 [OPTIONAL]: A Re-entrant Queue Lesson 26 [OPTIONAL]: SMARTS Files and Rockwell Demos Lesson 27: A Manufacturing System Demo
NOT OPTIONAL
(in spite of what the
Release Dates (all times EASTERN)
Weeks
Course Topics
Lesson 31: Mfg System Details: Model Walk-Through Lesson 32: Mfg System Details: Transporters and Conveyors
Week 5 Homework
Homework 5
Module 6: Random Number Generation
Lesson 1: Introduction Lesson 2: Some Lousy Generators Lesson 3: Linear Congruential Generators Lesson 4: Tausworthe Generators Lesson 5: Generalization of LCGs Lesson 6: Choosing a Good Generator – Some Theory Lesson 7: Choosing a Good Generator – Statistics Tests, Intro Lesson 8: Choosing a Good Generator – Goodness-of-Fit Tests Lesson 9: Choosing a Good Generator – Independence Tests I Lesson 10: [OPTIONAL]: Independence Tests II
Week 6 Homework
Homework 6
Module 7: Random Variate Generation
Lesson 1: Introduction Lesson 2: Inverse Transform Method Lesson 3.1: ITM – Continuous Examples Lesson 3.2: ITM – Continuous Examples DEMO 1 Lesson 3.3: ITM – Continuous Examples DEMO 2 Lesson 4: Inverse Transform Method – Discrete Examples Lesson 5 [OPTIONAL]: ITM – Empirical Distributions Lesson 6.1: Convolution Method Lesson 6.2: Convolution Method DEMO Lesson 7: Acceptance-Rejection Method Lesson 8 [OPTIONAL]: Proof of the A-R Method Lesson 9.1: A-R Method – Continuous Examples Lesson 9.2: A-R Method – Continuous Examples DEMO Lesson 10: A-R Method – Poisson Distribution
Project Milestone 2
Project Progress Report (nice and simple; rubric TBA)
Week 7
Homework 7
Weeks
Course Topics
Module 7 (cont.): More RV Generation
Lesson 11: Composition Lesson 12: Box-Muller Normal RVs Lesson 13: Order Statistics Other Stuff Lesson 14: Multivariate Normal Distribution Lesson 15: Baby Stochastic Processes Lesson 16.1: Nonhomogeneous Poisson Processes Lesson 16.2: Nonhomogeneous Poisson Processes DEMO Lesson 17.1: Time Series Lesson 17.2: Time Series DEMO Lesson 18: Queueing Lesson 19.1: Brownian Motion Lesson 19.2: Brownian Motion DEMO
Week 8 Homework
Homework 8
Release Dates (all times EASTERN)
11:59 p.m.
Midterm Exam 2
Midterm Exam 2 [Covers everything up to and including Lesson 13 of Module 7 from Week 8, with emphasis on more-recent stuff. See Topics Attachment.]
Module 8: Input Analysis Lesson 1: Introduction Lesson 2: Identifying Distributions Lesson 3: Unbiased Point Estimation Lesson 4: Mean Squared Error Lesson 5: Maximum Likelihood Estimators Lesson 6: MLE Examples Lesson 7: Invariance Property of MLEs Lesson 8 [OPTIONAL]: The Method of Moments Lesson 9: Goodness-of-Fit Tests Lesson 10: Exponential Example Lesson 11: Weibull Example Lesson 12: Still More Goodness-of-Fit Tests Lesson 13: Problem Children Lesson 14: Demo Time
Week 9 Homework
Homework 9
Weeks
Course Topics
Week 10 Homework
Module 9: Output Analysis Lesson 1: Introduction Lesson 2 [OPTIONAL]: Mathematical Interlude Lesson 3: Finite-Horizon Analysis Lesson 4: Finite- Horizon Extensions Lesson 5: Simulation Initialization Issues Lesson 6: Steady-State Analysis Lesson 7: Properties of Batch Means Lesson 8: Other Steady-State Methods
Module 10: Comparing Systems
Lesson 1: Introduction Lesson 2: Confidence Interval for the Mean Lesson 3: CIs for the Difference in Two Means Lesson 4: Paired CI for the Difference in Two Means Lesson 5: CIs for the Mean Difference in Simulations Lesson 6: Common Random Numbers Lesson 7: Antithetic Random Numbers Lesson 8 [OPTIONAL]: Control Variates
Homework 10
Module 10 (cont.): More Comparing Systems Lesson 9: Ranking and Selection Methods Lesson 10: Normal Means Selection Lesson 11: Single-Stage Normal Means Procedure Lesson 12: Normal Means Extensions Lesson 13: Bernoulli Probability Selection Lesson 14: Bernoulli Extensions Lesson 15: Multinomial Cell Selection Lesson 16: Multinomial Procedure + Extensions Lesson 17: Summary
Release Dates (all times EASTERN)
Project Milestone 3
Week 11 Homework
No HW (though some sample problems will be handed out)
Weeks
Course Topics
Final Exam
Final Exam [Covers everything, with emphasis on more-recent stuff. See Topics Attachment below. ]
Release Dates (all times EASTERN)
Test Topix for ISyE 6644, Summer 2022
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 As GT students, you are expected to formulate problems and solution strategies which are more than mere rote regurgitation of material you learned in class. Thus, you shouldn’t be surprised if some questions cover natural extensions of material from class. I’ll supply all necessary tables, e.g., N(0,1), t, and χ2, but you can feel free to use your own.
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TEST 1 TOPIX
1.
Intro Material a. Definition of simulation b. Advantages and disadvantages of simulation c. History of simulation d. Typical questions and applications
2. Calculus, Probability, and Statistics Review
a. Calculus [not really responsible for this material, except I might make you search
for a zero]
i. Basic definitions ii. Derivatives iii. Solving for zeros Integration iv. v. Numerical integration
b. Probability Preliminaries
i. Conditional probability ii. Independent events iii. Definition of random variable iv. Discrete RV’s and probability mass function v. Continuous RV’s and probability density function vi. Cumulative distribution function
c. Simulating RV’s (first pass)
i. Discrete uniform distribution ii. General discrete distribution iii. iv. Exponential (and other) continuous distributions via IVT. v. Generating U(0,1)’s via desert island algorithm, including walk-through of
Inverse Transform Theorem for continuous RV’s
pseudo-code.
d. Expected Values i. Definition ii. Discrete and continuous examples of expected value iii. Law of the Unconscious Statistician iv. Moments, central moments, variance, standard deviation v. Discrete and continuous examples of LOTUS vi. Moment generating function vii. Examples and properties of mgf’s
e. Functions of a RV
i. Discrete examples ii. Continuous examples iii. iv. Relationship with LOTUS
IVT methods (again) with examples
f.
Jointly distributed RV’s
Joint and marginal pmf’s Joint and marginal pdf’s
i. Definition of joint cdf ii. Marginal cdf’s iii. iv. v. Examples for discrete and continuous cases vi. vii. Conditional pmf’s and pdf’s viii. Conditional expectation [this won’t be on the test] ix. Double expectation E(E(Y|X)) = EY, including examples [this won’t be on the
Independent RV’s
test]
g. Covariance and correlation
i. Definitions ii. Relationship between independence and correlation iii. Examples iv. Miscellaneous properties (e.g., Var(X+Y), bounds on correlation, etc.)
h. Probability distributions
i. Discrete distributions 1. Bernoulli 2. Binomial 3. Geometric 4. Poisson (including discussion on Poisson processes)
ii. Continuous distributions
1. Uniform 2. Exponential (including memoryless property) 3. Erlang, Gamma distributions 4. Triangular 5. Normal (including Standard Normal)
6. Other sampling distributions (including chi-square, t, F, and various
relationships with each other)
i.
Limit theorems
i.
ii. iii. iv. v.
Linear combinations of independent normal (including distribution of sample mean) Convergence in distribution Law of Large Numbers Central Limit Theorem for independent and identically distributed data. Examples
j.
Statistics Tidbits [this material will eventually be covered in modules 8, 9, 10, so it’s in fair territory to have it on the Final!  ]
i. ii.
Properties of sample mean and sample variance Confidence intervals for the mean and variance
3. Hand Simulations
a. “Simulating” a differential equation b. Monte Carlo integration c. Determining π via simulation (dart tossing on a circle and sphere) d. Single- server queue (including FIFO and LIFO service disciplines) e. f. g. Spreadsheet simulation (e.g., stock portfolio in Excel)
(s,S) inventory system Simulating RV’s (repeats some material from the Prob/Stats review)
4. General Simulation Principles a. Steps in a simulation study b. List of various simulation definitions (e.g., event, system state, simulation clock, etc.) c. Event-Scheduling vs. Process Interaction modeling approaches d. How are events processed? e. Future events list + extended example f.
Simulation languages – what to look for
Plus, the first few Arena mini-topix below…
5. Arena
a. Layout of Arena screen (panels, modules, etc.) b. Basic Process template: CREATE-PROCESS-DISPOSE modules c. SEIZE-DELAY-RELEASE inside of the PROCESS module. d. Resource, Schedule, Queue, Entity, and other spreadsheets e. DECIDE module – probabilistic and conditional routing f. ASSIGN module
Everything from Test 1 + the following (with less emphasis placed on the Test 1 material)…
TEST 2 TOPIX
g. Simple examples, e.g. (partial list),
i. Single-server queue ii. Parallel servers iii. Schedules for servers iv. Multiple arrival streams
h. Displays, graphics, etc. i. BATCH and SEPARATE modules j. Run set-up and control k. More-sophisticated queueing networks (e.g., two-channel manufacturing example,
call center example)
i. Advanced Process modules (e.g., SEIZE, DELAY, RELEASE modules) ii. Some primitive blocks (e.g., QUEUE) iii. Use of “pretend” customers iv. Nonhomogeneous Poisson arrivals v. Use of resource sets, including how to prioritize servers vi. Use of submodels
Inventory processes
l. m. Crazy examples such as re-entrant queues n. SMARTS files and other Rockwell examples o. Manufacturing systems
i. Advanced Transfer modules (e.g., ROUTE, ENTER, LEAVE) ii. Sequences of customer visitation locations iii. Advanced sets of sequences iv. Transporters and conveyors
6. Uniform Random Number Generation
a. Overview – desirable properties of a pseudo-random number generator b. Some generators we won’t use, e.g.,
i. PRN’s from tables ii. Midsquare
c. Linear congruential generators
i. Cycling ii. 16807 desert island generator (again) iii. RANDU (a bad generator)
d. Tausworthe generator e. Combined generators
i. L’Ecuyer’s generator of cycle length 2191 ii. Mersenne Twister
Some theoretical considerations, e.g., from Knuth’s book
f. g. Statistical tests for randomness
i. Goodness-of-fit test – Chi-squared i. Runs tests for independence 1. Runs up and down 2. Runs above and below the mean 3. Autocorrelation test [this won’t be on the test]
7. Random Variate Generation
a.
Inverse Transform Theorem (yet again)
i. Proof ii. Discrete example adaptations iii. Continuous examples
1. East ones such as Exponential, Weibull, etc. 2. Slightly harder examples such as Triangle distribution 3. Normal distribution, both exact and approximate methods
iv. Special case methods, e.g., Geometric v. Empirical distributions [this won’t be on the test]
b. Convolution method i. Binomial ii. Triangle iii. Erlang iv. CLT
1. Desert island sum of Uniforms to generate Normal 2. Normal approximation to Poisson (including continuity correction)
v. Cauchy
1. Cauchy’s add up to another Cauchy 2. 3. Ratio of two Normals c. Acceptance-Rejection methods
IVT method
i. Trivial Uniform example ii. Some discussion on general method iii. Proof of the general method [don’t expect to see this on the test, unless I’m
in a really bad mood!]
iv. Examples involving polynomial and half-normal p.d.f.’s v. Poisson distribution
d. Composition e. Special-case techniques
i. Box-Muller method for Normal distribution
ii. Extensions of B-M, e.g., Cauchy, Chi-squared. iii. Generating min’s and max’s of iid RV’s, e.g., min of iid Exponentials.
TEST 3 (FINAL) TOPIX
Everything in the freaking course, including the following new stuff (with less emphasis placed on the Tests 1 and 2 material)…
f. Multivariate Normal
i. Definition in 2 and then >2 dimensions ii. Cholesky decomposition method for generating realizations (exact expression
in 2 dimensions, algorithm for >2 dimensions)
g. Stochastic processes i. Markov chains ii. Poisson processes iii. Nonhomogeneous Poisson processes (via thinning method) iv. Time series 1. MA(1) 2. AR(1) 3. EAR(1) 4. ARTOP
v. M/M/1 queue waiting times vi. Brownian motion
1. Definition and history 2. Elementary properties, including covariance structure 3. General CLT 4. How to generate 5. Geometric BM and financial applications
8.
Input Analysis
a. General discussion
i. Careful about GIGO with respect to simulation input ii. What makes a good distribution iii.
Identification of obvious distributions
b. Estimation review
i. Unbiased estimators
1. Definition 2. Sample mean 3. Sample variance 4. Other examples such as Unif(0,θ)
ii. Mean squared error iii. Maximum likelihood estimators
1. Definition 2. Examples such as Exponential 3. Two-dimensional examples such as Normal with unknown mean
and variance
4. Other tougher examples such as Unif(0,θ) and Gamma 5.
Invariance Property + examples
iv. Method of Moments [this won’t be on the test (sorry, MoM!)]
c. Goodness-of-fit tests for input distributions i. Chi-squared for Exponential ii. Chi-squared for Weibull, including search techniques such as bisection
and Newton
iii. Kolmogorov-Smirnov iv. More goodness-of-fit tests
d. Problem Children
i. Little or no data ii. Data from an unusual distribution iii. Nonstationary data iv. Multivariate / correlated data
e. Arena Input Analyzer demo
9. Output Analysis
a.
Introduction
i. The need for output analysis in a proper statistical study ii. Simulation data isn’t iid normal, and this is a problem iii. Types of output analysis – finite-horizon (terminating) and steady-state
b. A mathematical interlude related to the fact that the variance of the sample mean isn’t Var(Xi)/n, and its consequences [I might ask you to calculate the variance of the sample mean for a specific process, but nothing else.]
c. Finite-horizon (terminating) simulations
i. Examples ii. Confidence intervals for mean performance via the method of
Independent Replications
Initialization problems
d. e. Steady-state analysis for a single system
i. Examples ii. Confidence intervals for the steady-state mean via the method of Batch
Means
iii. Properties of Batch Means [The more-mathematical aspects of this topic
this won’t be on the test.]
iv. Overlapping Batch Means v. Other methods
10. Comparing Systems
a. Classical confidence interval for the mean of one normal population b. Classical confidence interval to compare the means of two normal systems
i. Variance completely unknown ii. Paired-t CI iii. Use in simulation scenarios
c. Variance reduction techniques
i. Common random numbers ii. Antithetic random numbers [no theory related to this will be on the test] iii. Control variates [this won’t be on the test]
d. Ranking and selection methods to compare means of >2 systems
i. Definition of problem ii. Relevance to simulation Indifference-zone approach iii. iv. Normal means selection problem
 Bechhofer’s single-stage procedure 
Extensions
v. Bernoulli parameter selection problem
 
Sobel and Huyett single-stage procedure Extensions
vi. Multinomial cell selection problem
 Multinomial review and motivation  Bechhofer, Elmaghraby, and Morse single-stage procedure 
Extensions