1. Basic MC/Defn/Short Answer/Application Cumulative
Bring a basic calculator
Will be given references like Distribution PDF/CDF, and T Table, Chi-Square Table, KS Table
Course Outcomes (last 4 definitely represented in long answers)

2. Last 4 Course Outcomes
Explain the difference between transient and steady state behavior of a system and how to estimate the steady-state performance parameters such as mean and variance.
Compute confidence intervals for a given sample of data and interpret the meaning of the computed confidence intervals.
Conduct a goodness-of-fit test using Chi-square hypothesis testing to decide if a given distribution fits a sample of data.
Analyze the performance of a single queue or a queuing network using basic queuing theory results

3. Types of Questions Observations
Know properties/definitions so you can compare and contrast them within categories (distributions, similar terminology)
Are they similar? What makes them different?
Understand process of application. Steps of creating a sim./model. (How was that done in assignments, class example, or new area) How to determine an event probability from a sample space (card games)?
More variety of solving questions. Finding mean/variance, determining a distribution, goodness of fit, confidence intervals, Markov chains and queueing theory questions.

4. Modeling (Midterm) What is a model? Limitations?
Approaches? Experimental/Simulation/Analytical. Why choose one for a problem?
Model Taxonomy : deterministic, stochastic, static, dynamic, continuous, discrete
Terminology: entity, attribute, state, event
When not to simulate, Mistakes that can be made
Monte Carlo, time-stepped, trace-driven, discrete-event simulation
Steps 1,2,3,4,5,6 (goals, conceptual (high level design), specification (details, math, input, pseudocode), computational, verify (model right), validate(right model))

5. Probability/Random Variables/Distributions (Midterm)
Definitions: Random, sample space, probability, independence, exclusive, complementary
Continuous random variable: Probability density function PDF
Discrete random variable: Probability mass function PMF
Cumulative Distribution Function CDF
Mean/Variance/Standard Deviation/Coefficient of Variation/Covariance
Correlation vs Autocorrelation
Discrete vs continuous, infinite vs finite
Geometric (events until first succ), Exponential (time between events in Poisson process), Uniform, Poisson (k events in given time)
Memoryless property

6. RNG/PRNG (Midterm) What does pseudo-RNG change? What are definitions?
What are desirable mathematical properties? Additional properties for simulation/engineering system?
Uniform(0,1)?
Statistical testing to show uniformity and independence?
Linear Congruential Generator?
How does it work? Important features? Period (always full?) Seed Selection, Streams, Mistaken assumptions (complex, unpredictable, seed dangers, system/language specifications effect on accuracy)

7. Random Variate Generation (Midterm)
For discrete (inverse method)
Bernoulli trials, uniform, geometric
For continuous (inverse method)
uniform, exponential
Using convolution
Geometric, binomial, Poisson
Empirical
Common Random Variables
Discrete -> Uniform, Bernoulli, geometric, binomial, Poisson
Continuous -> Uniform, Exponential, Normal

8. Processes (Midterm)
Stochastic Process (collection of random variables indexed over time)
Counting Process (stochastic process for total # of events in time interval [0,t])
Poisson Process (counting process with a rate lambda)
Arrivals vs Inter-arrivals
Arrival counts (poisson distribution generated)
Inter-arrival times (exponential distribution generated)
Pooling property, splitting property
Poisson point process (space, not time)

9. Discrete-Event Simulation (Midterm/New)
Concepts
activity (defined) vs delay (result of system conditions on run)
Components
Time-stepping vs Event Scheduling
Examples: how to pull out state, entities, events, activities, delays to do design process of modelling
Queueing systems
Single/multi server, finite/infinite population, tandem queue (blocking), closed network model
Service type (FCFS, LCFS, RR, SJF, SRPT)
Measures
Event List management
Array/Linked List/Multiple Linked List/Binary Tree/Heap/Calendar Queue
Properties (speed, robustness, adaptability)
Choice of data structure

10. Simulation Output Analysis
Transient and Steady State Analysis (Course Outcome)
Transient state -> not in steady state (common from initial start of simulation)
Steady State -> independent of time and initial start, behaviour over long-run
How to collect steady state data while minimizing transient state data
Measured variable Y can examine
distribution (CDF)
statistics like mean and variance
Confidence interval of the mean (which is related to the variance)
Confidence Intervals and Measuring Error (Course Outcome)

11. Performance Evaluation
Factors – components varied in experiment to see impact on system
Levels – settings of the factors
Metrics – measurements of the system
Experimental Design – Structure of study (method to approach)
Vary one factor through levels
Vary two factors to see combinations
Vary all factors in their levels to explore everything (may not be feasible)
Data analysis and presentation

12. Statistical Inference
When you begin from a controlled pRNG seed(s) your single simulation run is in effect a sample path -> results are probabilistic answers to performance evaluation questions -> we can use statistical approaches and methods
Chi-Square Testing vs Kolmogorov-Smirnov Testing (Course outcome)
Big/Discrete/Buckets vs Small/Continuous/CDF
Simulation length – sweet spot of long enough to be reasonable time but results not too influenced by startup transient effects
Confidence in results often based around repeated simulations and examination of statistical properties of the results
Want consistency/unbiased
ANOVA method – analysis of variance (rather than means) to determine what factors most impact the system

13. Simulation Input Analysis
Input drives output of model (garbage in -> garbage out)
Desirable to take empirical measurements and reproduce via input model (Such as distribution)
Data can be pre-processed but leaving out edge cases can miss realistic biases in input model
Checklist (amount, discrete/continuous, range, central tendency, shape, outliers/gaps/anomalies, time series data, correlation, other phenomena)
Both questions and visualization or mathematical methods of examining
Question for exam? (sample data, what kind of distribution is it?)
Once we have a possible solution you can check the properties of the created model against measured data to see if its properties fit as desired (ex QQ plot and goodness of fit tests -> Chi-Square/KS tests (Course Outcome))

14. Queueing Theory Kendall Notation Queuing Systems
Read notation to get properties or create notation based on properties described
Defaults
Markovian/Deterministic/General
Queuing Systems
Calling population, system capacity, queue behaviour vs discipline
Stability 𝜆<𝑚𝜇, Utilization 𝜌= 𝜆 𝑚 𝜇 and other fundamental rules
Little’s Law (mean in system = arrival rate * mean response time)

15. Queueing Theory Markov Models Markov Process
Birth-Death Process, 𝑀/𝑀/1, 𝑀/𝑀/1/𝐾, 𝑀/𝑀/𝑐/𝑐, M/M/∞
Performance (Course Outcome)
Markov Chain -> Set of Linear Equations -> State probabilities