Modelling and Simulation Concepts Module 1

Study Notes

Module 1: MODELLING AND SIMULATION CONCEPTS

This module is divided into six units.
The module covers basics of modelling and simulation, random numbers, random number generation, Monte Carlo methods, statistical distribution functions, and common probability distributions.

Unit 1: Basics of Modelling and Simulation

Introduction: The ability to define future outcomes and choose alternatives is crucial in contemporary society.
Intended learning outcomes (ILOs): Define model and modelling, explain when and why we use models, describe the modelling process and types of models. .
Main Content:
- Definitions: Modelling is the process of creating abstract, conceptual, graphical, and/or mathematical models to represent real-world phenomena.
- What is modelling and simulation? A tool supporting decision-analysis and optimization by evaluating alternatives, dealing with uncertainty and complex interactions across disciplines.
- Types of models: Physical, mathematical, analog, simulation, heuristic, stochastic, and deterministic.
- Advantages of Using Models: Safer, less expensive, easier to control compared to real world systems.

Unit 2: Random Numbers

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Unit 3: Random Number Generation

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Unit 4: Monte Carlo Method

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Unit 5: Statistical Distribution Functions

Introduction: Simulation often involves uncertainty, requiring statistical analysis of system parameters.
Intended Learning Outcomes (ILOs): Define statistics, explain statistical distributions, calculate measures of central tendency, and explain variations in statistical distributions.
Main Content:
- What is Statistics? The collection, description, and interpretation of data.
- What is a Statistical Distribution? Describes the frequency of different possible outcomes. .
- Measures of Central Tendency: Mean, median, and mode.
- Measures of Variation: Range and standard deviation.
- Showing Data Distribution in Graphs: Bar graphs, double bar graphs, histograms, and pie charts.
- Difference between Continuous and Discrete Distributions: Continuous distributions describe infinite possible values; discrete distributions have a finite number of possible values.
- Normal Distribution: A bell-shaped continuous probability distribution; important for describing many real-world phenomena.
- Standard Normal Distribution: A special case of the normal distribution with a mean of zero and standard deviation of one; used to standardize normal distributions for easier calculations.
- Skewed Distributions: Distributions that are not symmetrical, have longer tails on either side of the center.
- Percentile: The proportion of data values below a particular value.
- Probability and the Normal Curve: Total area under the normal curve equals 1; probabilities for different areas under the curve are calculated using statistical tables or calculators.