Chaos and headway distribution of shuttle buses that pass each other freely

We study the dynamical behavior of a few shuttle buses that pass each other freely on a cyclic route. We present a discrete dynamical model of the shuttle buses to take into account the interactions among buses and passengers. It is found that the bus exhibits a chaotic motion by the free passing. The chaotic motion depends on loading parameter, bus speed, and bus number. The time-headway between buses takes irregular values with varying time. The time headway has an extended distribution for high value of loading parameter, while the distribution exhibits two localized peaks for low value of loading parameter. The dependence of the time-headway distribution on the parameters is shown. With increasing loading parameter, the maximum value of time headway increases and diverges at the critical value which increases with the number of buses.