Skip to content

Latest commit

 

History

History
64 lines (40 loc) · 2.76 KB

README.md

File metadata and controls

64 lines (40 loc) · 2.76 KB

MAT-350 Project 1: Network Flow Analysis Using Linear Systems

Author: Justin Paul Guida
Course: MAT-350 - Applied Linear Algebra
Date: September 18, 2025

Overview

This project models a computer network flow system using systems of linear equations.
Each router in the network (A, B, C, D, and E) is represented as a node, and data transfer between routers is modeled using equations that balance inflow and outflow rates.

The project demonstrates how to construct a coefficient matrix A, a constant vector b, and solve the system Ax = b using MATLAB.
It also includes validation through LU decomposition, Cramer’s Rule, and determinant analysis.

The project is submitted as a report (.pdf) generated in MATLAB, showing full calculations, code, and annotated results.

Objectives

  1. Develop a linear system of equations for a five-router network.
  2. Represent the system in matrix form (Ax = b).
  3. Solve the system using MATLAB’s built-in tools (rref, lu, inv, det).
  4. Verify the solution using multiple algebraic methods.
  5. Interpret network flow results and identify potential system bottlenecks or upgrade recommendations.

Key MATLAB Concepts Demonstrated

  • Matrix Construction: Defining coefficient matrices and augmented matrices.
  • Row Reduction: Solving systems using rref() for reduced row echelon form.
  • LU Decomposition: Breaking down A into lower (L) and upper (U) matrices.
  • Forward/Backward Substitution: Solving Ly = b and Ux = y.
  • Matrix Inversion: Using inv() to compute the inverse of U.
  • Determinants and Cramer’s Rule: Cross-verifying results using determinant calculations.

Results Summary

  • All routers yield unique flow values with no free variables, confirming a consistent system.
  • The final data flow vector was determined to be:

x = [50; 25; 30; 100; 45] Mbps

  • Determinant of the system matrix A is 2.00, confirming the system’s invertibility.
  • LU and Cramer’s Rule methods both reproduce identical results.
  • Network recommendations include upgrading links nearing capacity to prevent congestion.

File Description

File Description
mat350_project1_network_flow_analysis.pdf Final report with MATLAB code, output, and written explanations.

Tools and Requirements

  • MATLAB R2023a or later
  • No additional toolboxes required

Educational Purpose

This project reinforces the application of linear algebra in network modeling, demonstrating how fundamental matrix operations can represent and analyze real-world data flow systems.
It highlights the practical use of MATLAB for solving and verifying linear systems in engineering and applied mathematics contexts.