Discrete Event Simulation

Summary

This repository contains a series of Jupyter Notebooks that explore different simulation and statistical analysis problems using Python. Each notebook is built from scratch without relying on external simulation packages, making them ideal for educational purposes and foundational understanding.

inverse-transform_sampling.ipynb

1. Reviews the Cumulative Distribution Function (CDF) for the Uniform Distribution.
2. Explains the theoretical foundation behind the uniform distribution and how the CDF is derived.
3. Includes Python examples demonstrating:

• Generating uniform random variables
• Visualizing the PDF and CDF
• Calculating probabilities using the CDF

confidence_interval_simulation.ipynb

1. Shows how to construct a confidence interval for the mean of simulated data using the Student’s t-distribution.
2. Uses an example of 10 simulation runs to estimate the mean number in a system.
3. Includes code for:

• Computing sample mean and standard deviation
• Calculating confidence intervals
• Evaluating whether the margin of error is within 5% or 10% of the true mean

discrete_event_simulation_three_servers.ipynb

1. Implements a Discrete Event Simulation (DES) of a system with three FCFS (First-Come-First-Served) servers.
2. Models routing behavior where jobs are probabilistically sent to one of two entry servers (Node 1 or 2), and then all go to Node 3.
3. Estimates the average number of jobs at Node 3 over time.