Queue Simulation Using Stochastic Models

View Full Report (PDF)

This project demonstrates a simulation of an M/G/1 queueing system using stochastic models. It combines theoretical analysis via the Pollaczek–Khinchine formula with Monte Carlo simulation in R to analyze performance metrics like average wait time, system time, and queue length.

The simulation is based on real-life customer service scenarios where interarrival times follow an exponential distribution and service times follow a general distribution (gamma in our case).

Key Concepts

• M/G/1 Queueing Model
• Pollaczek–Khinchine Formula
• Monte Carlo Simulation in R
• Little's Law for validation
• Gamma-distributed service times

Repository Contents

File Name	Description
final project stochastic models.pdf	Full written report (theory, results, conclusions)
stochastic models final project only code (2).Rmd	RMarkdown script with full simulation code
Pollaczek–Khinchine formula (2).xlsx	Excel sheet calculating queueing metrics
install_packages.R	R script to install required packages

Tools Used

• R with base packages for simulation
• Excel for analytical comparison
• Theoretical derivations for queueing metrics

Summary

The project evaluates a single-server system where arrivals are Poisson and service time is gamma-distributed. We simulate the system to empirically validate theoretical results, specifically the expected waiting time using the Pollaczek–Khinchine formula, and compare it with simulation outputs.