A Model for the Bus System in Cuernevaca (Mexico)

The bus transportation system in Cuernevaca, Mexico, has certain distinguished, innovative features and has been the subject of an intriguing, recent study by M. Krbalek and P. Seba. Krbalek and Seba analyzed the statistics of bus arrivals on Line 4 close to the city center. They studied, in particular, the bus spacing distribution and also the bus number variance measuring the fluctuations of the total number of buses arriving at a fixed location during a time interval T. Quite remarkably, it was found that these two statistics are well modeled by the Gaussian Unitary Ensemble (GUE) of random matrix theory. Our goal in this paper is to provide a plausible explanation of these observations, and to this end we introduce a microscopic model for the bus line that leads simply and directly to GUE.