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Traffic gridlock on a honeycomb city.

L E Olmos¹, J D Muñoz¹

¹Simulation of Physical Systems Group, Physics Department, National University of Colombia, Bogotá, Colombia.

Physical Review. E

|April 19, 2017

Summary

The Biham-Middleton-Levine (BML) model on honeycomb streets shows a single traffic flow transition, unlike square grids. Simple changes improve performance, suggesting honeycomb as a better urban planning model.

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Area of Science:

Complex Systems
Urban Planning
Traffic Flow Dynamics

Background:

The Biham-Middleton-Levine (BML) model is a standard for traffic flow phase transition studies.
Traditional BML models are often studied on square lattice networks.
Urban planning typically utilizes grid-like street designs.

Purpose of the Study:

To investigate the behavior of the BML model on a honeycomb street network.
To compare traffic flow transitions on honeycomb versus square lattices.
To explore potential urban planning advantages of honeycomb topology.

Main Methods:

Simulation of the Biham-Middleton-Levine (BML) model on a hypothetical city with a honeycomb street network.
Analysis of phase transitions between free and congested traffic flow.
Comparison with BML model behavior on a square lattice.
Inclusion of simple modifications such as random car stops and traffic light period adjustments.

Main Results:

The BML model on a honeycomb lattice exhibits a single, continuous phase transition, lacking anisotropy and intermediate states seen in square lattices.
This transition is fully characterizable using classical percolation theory.
The transition occurs at a lower density compared to the conventional BML model.
Simple modifications (random stops, longer traffic light periods) enhance model performance on honeycomb lattices.

Conclusions:

Honeycomb street networks facilitate a simpler, continuous traffic flow transition compared to square grids.
The findings challenge the universal applicability of square grid urban designs.
Honeycomb topology emerges as a promising alternative for urban planning, especially when considering real-world traffic complexities like traffic lights and disruptions.

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