Buses of Cuernavaca - an agent-based model for universal random matrix behavior minimizing mutual information

TL;DR

This paper models the random matrix behavior of bus arrival times in Cuernavaca using an agent-based approach, showing that a specific parameter minimizes mutual information and reproduces observed statistical distributions.

Contribution

It introduces a novel agent-based model that captures the universal random matrix statistics of bus arrival times and links the model parameter to information-theoretic optimality.

Findings

The model reproduces the Wigner surmise distribution for bus arrival fluctuations.

A specific parameter value minimizes pairwise mutual information.

Numerical evidence supports the link between the model parameter and information minimization.

Abstract

The public transportation system of Cuernavaca, Mexico, exhibits random matrix theory statistics [1]. In particular, the fluctuation of times between the arrival of buses on a given bus stop, follows the Wigner surmise for the Gaussian Unitary Ensemble. To model this, we propose an agent-based approach in which each bus driver tries to optimize his arrival time to the next stop with respect to an estimated arrival time of his predecessor. We choose a particular form of the associated utility function and recover the appropriate distribution in numerical experiments for a certain value of the only parameter of the model. We then investigate whether this value of the parameter is otherwise distinguished within an information theoretic approach and give numerical evidence that indeed it is associated with a minimum of averaged pairwise mutual information.