Introduction

This is a simulation project used for modelling the Braess's paradox meant for traffic modelling. It gives an idea on how resources can be added or removed from an existing network in order to increase the overall efficiency of it.

The basis of the paradox relies on the Nash equilibrium that is established in a network when there is a flow of persons who would operate on a selfish or greedy behaviour. This looks at how allocation of resources can modify or impact the overall states of the network and all the users. This project is a simulation outline of the scenarios possible or encountered when the network is operational and can be modified and extended to cover a greater range of situations where networks may be involved and resources need to be allocated.

Report

The STREAM github repository contains the necessary files and requirements for the tool.

The detailed findings and report of this simulation and analysis is attached below :

Requirements

• Python 3.x
• NetworkX - Python Package
• JSON

pip install networkx

Project Structure

• build_graph.py: Script to build the graph from a JSON file containing edge data.
• update_weights.py: Script to update the weights of the edges based on traffic flow data.
• shortest_path.py: Script to find the shortest path for a new person entering the network.
• analyze_braess.py: Script to analyze Braess's paradox by removing and adding edges.
• main.py: Script to loop through each pair of nodes, perturb each possibility, and analyze Braess's paradox.
• graph_data.json: JSON file containing the graph structure.
• graph_flow.json: JSON file containing the flow state of each edge in the graph.
• braess_analysis_results.json: Output JSON file containing the results of the Braess's paradox analysis.

Files Description

python build_graph.py

python update_weights.py

python shortest_path.py

python analyse_braess.py

python main.py

JSON Files

{
    "edges": [
        {"start": "A", "end": "B", "base_weight": 1, "linear_factor": 1},
        {"start": "B", "end": "D", "base_weight": 1, "linear_factor": 1},
        {"start": "A", "end": "C", "base_weight": 1, "linear_factor": 1},
        {"start": "C", "end": "D", "base_weight": 1, "linear_factor": 1},
        {"start": "B", "end": "C", "base_weight": 1, "linear_factor": 1}
    ]
}

{
    "flows": {
        "('A', 'B')": 10,
        "('B', 'D')": 10,
        "('A', 'C')": 10,
        "('C', 'D')": 10,
        "('B', 'C')": 0
    }
}

Running the Project

1. Ensure you have the required Python packages installed.
2. Ensure your graph_data.json and graph_flow.json files are properly set up.
3. Run main.py to perform a comprehensive analysis of Braess's paradox on your graph:

python main.py

4. The results will be saved to braess_analysis_results.json.

License

This project is licensed under the MIT License.

Credits

This project/tool was created by @SidZRed as a part of a Game Theory reading and analysis project. Any contributions to the above are most welcome!