Network Traffic Flow Analysis in a Four-Node, Five-Link System Using Linear Models, Delays, and Queueing

This project studies a four-node, five-link network with supply, demand, and transit nodes. Using flow optimization and M/M/1 queueing approximation, it evaluates link utilization, service rates, and end-to-end delays. The analysis confirms that the network remains stable, with negligible queueing delays due to low traffic loads.

Suitable For

• BS Mathematics – optimization, applied probability

• BS Computer Science – algorithms, network modeling, simulation

• BS Data Science – computational modeling, numerical evaluation, visualization

• BS Electrical Engineering – communication networks, performance analysis

Technologies Used

• Programming Language: Python

• Libraries: NumPy, Matplotlib

• Techniques: Linear optimization, queueing theory, performance evaluation

• Visualization: Flow diagrams, capacity vs. load plots, delay charts

Features

• Models a directed network with supply, demand, and transit nodes

• Maps link capacities to service rates and flows to arrival rates

• Evaluates stability via M/M/1 queueing

• Computes sojourn times for each link

• Provides numerical tables and visual plots for interpretation

Deliverables

• Python code for flow and queueing evaluation

• LaTeX documentation (theory, steps, results, interpretations)

• Figures: network diagram, utilization plots, delay analysis

Benefits for Students

• Practical understanding of network flow and queueing theory

• Experience with numerical computation and simulation

• Skills in Python-based modeling and visualization

• Portfolio-ready project bridging math, computer science, and networks