Simulation and Random Number Analysis

This project simulates a queuing system, generates random numbers, and analyzes their distribution using statistical tests and visualizations. I did it as my simulation course on 2019

Script: simulation_and_analysis.R

Description

1. Queuing System Simulation:

   • Simulates a single-server queuing system using a Linear Congruential Generator (LCG) for random number generation.
   • Exports simulation results to Excel files (table2-8.xlsx, table2-9.xlsx, table2-10.xlsx).

2. Random Number Analysis:

   • Generates random numbers from a normal distribution and standardizes them.
   • Computes descriptive statistics and visualizes the data using boxplots and histograms.

3. Uniform Random Number Analysis:

   • Generates uniform random numbers using an LCG and tests their uniformity using the Kolmogorov-Smirnov (KS) test.
   • Transforms uniform random numbers into integers between 8 and 24 and visualizes their distribution.

Usage

1. Clone the repository.
2. Open the R script simulation_and_analysis.R in RStudio or any R environment.
3. Run the script to perform the simulation, generate random numbers, and create visualizations.

Output

• Excel Files:
  • table2-8.xlsx: Random numbers and time between arrivals.
  • table2-9.xlsx: Random numbers and service times.
  • table2-10.xlsx: Full simulation results.
• Plots:
  • boxplot_x.png, histogram_x.png: Boxplot and histogram of normal random numbers.
  • boxplot_rnd.png, histogram_rnd.png: Boxplot and histogram of LCG random numbers.
  • boxplot_transformed.png, histogram_transformed.png: Boxplot and histogram of transformed uniform random numbers.

Dependencies

• R (version 4.0 or higher)
• openxlsx package (for exporting data to Excel)

Author

Your Name

License

This project is licensed under the MIT License. See the LICENSE file for details.