Bottleneck model in METROPOLIS2

This repository contains Python scripts to simulate the Bottleneck model with the METROPOLIS2 transport simulator. The model replicated is the one from de Palma, Ben-Akiva, Lefevre and Litinas (1983). The results from these scripts are presented in Javaudin and de Palma (2024).

de Palma, A., Ben-Akiva, M., Lefevre, C., & Litinas, N. (1983). Stochastic equilibrium model of peak period traffic congestion. Transportation Science, 17(4), 430-453.

Javaudin, L., & de Palma, A. (2024). METROPOLIS2: A Multi-Modal Agent-Based Transport Simulator. THEMA Working Paper.

How to run

The location to the METROPOLIS2 executable is defined in the Python file python/functions.py (variable METROSIM_EXEC). Version 0.8.0 of METROPOLIS2 was used in the companion paper, Javaudin and de Palma (2024).

The graphs are stored in the graph/ directory. The runs input and output data are stored in the runs/ directory.

The list of Python packages required to run the code are listed in requirements.txt.

The Python code is located in the python/ directory. Configuration variables are defined as global variables at the beginning of the scripts.

Library files:

• functions.py: Functions used to generate the input data for METROPOLIS2, many variables can be configured there.
• mpl_utils.py: Functions used to plot graphs with matplotlib.

Script files:

• main_simulation.py: Run the standard simulation and plot the results.
• different_epsilons.py: Run simulations with different random seeds.
• uniform_epsilons.py: Run the standard simulation with systematic sampling.
• distributed_tstars.py: Run a simulation where desired arrival times are distributed among agents.
• convergence_learning_model.py: Run simulations with different values for the smoothing factor, $\lambda$.
• impact_breakpoint_interval.py: Run simulations with different values for the length between two breakpoints, $\delta$.
• impact_mu.py: Run simulations with different values for the scale of utility's random component, $\mu$.
• impact_nb_agents.py: Run simulations with different values for the number of agents, $N$.
• theoretical_solution.py: Functions to compute the analytical solution of the model, also plot graphs of the solution.
• deterministic_solution.py: Compute and plot the analytical solution of the deterministic model.
• bottleneck_example.py: Plot a graph to illustrate a travel-time function in METROPOLIS2.
• mu_interpretation.py: Compute values and plot graph to interpret the scale of utility's random component, $\mu$.