mfd_scaling: Hierarchical Scaling and Variogram-based Imputation

This repository contains the Python notebooks and code used in the paper: "Maiti, N., Seppecher, M., & Leclercq, L. Scaling Methods for Estimating Macroscopic Fundamental Diagrams in Urban Networks with Sparse Stationary Sensor Coverage, Transportation Research Part C: Emerging Technologies (2025)" PDF.

The repository provides two main components:

• Hierarchical Scaling: A method for scaling traffic variables from an LD-equipped subnetwork to non-equipped links using road hierarchy information.
• Variogram-based Imputation: A geostatistical approach for estimating missing traffic states based on spatial dependencies captured by empirical variograms.

Contents

• hierarchical_scaling.ipynb: Jupyter Notebook demonstrating the hierarchical scaling methodology, including:

  • Link hierarchy classification
  • Scaling factor estimation
  • Network-wide traffic state extrapolation

• variogram.ipynb: Jupyter Notebook implementing the variogram-based imputation approach, including:

  • Empirical variogram estimation
  • Model fitting and parameter calibration
  • Kriging interpolation for traffic state imputation

Requirements

The notebooks are written in Python 3 and require the following packages:

• numpy
• pandas
• matplotlib
• scikit-learn
• scikit-gstat
• networkx (for graph-based distance calculations)
• geopandas (optional, for visualizing spatial data)

Install dependencies via:

pip install -r requirements.txt