Modeling and Solving Network Traffic Flow with Systems of Linear Equations

Overview

This project focuses on understanding and solving network traffic flow using simple step-by-step methods.
We begin with small examples of networks — starting with very simple ones and gradually moving to more complex ones — showing exactly how to figure out how much data moves across each link.

Once we understand the smaller cases, we apply the same approach to bigger networks and use a Python program to calculate the results automatically. This helps demonstrate how mathematics can be applied to real-world computer network problems such as routing, congestion detection, and planning for network capacity.

Suitable For

• BS Computer Science – computer networks, programming projects

• BS Electrical Engineering – data communication and systems modeling

• BS Mathematics – practical applications of algebra

• BS Data Science – modeling and analyzing network data

Technologies Used

• Programming Language: Python

• Libraries: NumPy (for calculations), Matplotlib (for visualizations)

• Techniques:

  • Step-by-step problem solving for small networks

  • Automated solution for larger networks

  • Simple tables and diagrams to show results

Features

• Explains the idea of traffic entering and leaving each network node

• Uses clear step-by-step examples for small networks (2-node, 3-node, etc.)

• Shows how to calculate data flow across each connection

• Builds a simple Python program that can handle bigger, real-world networks

• Creates tables and diagrams showing results and identifying potential slow points in the network

Deliverables

• Complete Python code for solving traffic flow

• Well-structured documentation with theory, examples, and results

• Diagrams of sample networks

• Tables showing calculated data flow

• Optional interactive notebook for trying out new network setups

Benefits for Students

• Learn how to apply problem-solving techniques to network flow

• Gain hands-on experience with Python for real-world projects

• Understand how data moves in a network and where bottlenecks can form

• Build a strong, portfolio-ready project that connects programming, networking, and logical thinking