Paper Published: Why Does Public Transport Not Arrive on Time? The Pervasiveness of Equal Headway Instability

Gershenson C, Pineda LA (2009) Why Does Public Transport Not Arrive on Time? The Pervasiveness of Equal Headway Instability. PLoS ONE 4(10): e7292. doi:10.1371/journal.pone.0007292



The equal headway instability phenomenon is pervasive in public transport systems. This instability is characterized by an aggregation of vehicles that causes inefficient service. While equal headway instability is common, it has not been studied independently of a particular scenario. However, the phenomenon is apparent in many transport systems and can be modeled and rectified in abstraction.


We present a multi-agent simulation where a default method with no restrictions always leads to unstable headways. We discuss two methods that attempt to achieve equal headways, called minimum and maximum. Since one parameter of the methods depends on the passenger density, adaptive versions—where the relevant parameter is adjusted automatically—are also put forward. Our results show that the adaptive maximum method improves significantly over the default method. The model and simulation give insights of the interplay between transport design and passenger behavior. Finally, we provide technological and social suggestions for engineers and passengers to help achieve equal headways and thus reduce delays.


The equal headway instability phenomenon can be avoided with the suggested technological and social measures.

Full paper at: http://dx.plos.org/10.1371/journal.pone.0007292


Fractal Projections:Tetrahedra

Fractal Projections:Tetrahedra by ~hawmkoonstormbringer on deviantART

I was a few weeks ago in Budapest for a conference on artificial life. I went to the Vasarely museum, and I liked a lot his perspective games, e.g. a sphere projected on a plane and cubes projected on the sphere. I thought that you could do this recursively, so you can project tetrahedra on the faces of tetrahedra, and this is the result...

This work is dedicated to the 30th birthday of my hopeful wife Nadya...