Managing public bus fleets: A complex systems perspective

We study, through nonlinear dynamic simulations of interacting buses, the effects that different combinations of relevant transport parameters ( e.g. , carrying capacity of buses, bus and passenger fluxes, etc.) have on the overall passenger transport, such as occupancy of the buses, efficiency of travel, and waiting times of the passengers. We study these dynamics in a segregated street with a sequence of traffic lights and bus stops, where passengers arrive stochastically and board buses to be transported to their destination if their carrying capacity allows it. In contrast to more traditional cellular automaton models, our simulations numerically solve Newton’s equations of motion for the position and velocity of each bus, enabling the nonlinear dynamics produced by finite acceleration and braking capabilities, which will couple with a stochastic passenger flux. In this study, we found clear relationships between the mean occupancy of buses, fluxes, travel distances, and city dimensions, gaining insight into how the carrying capacity affects efficiencies in travel and waiting times. This allowed us to obtain equations that constrain the capacity and bus flux to ensure system stability. As such, this work opens the possibility of studying the management of bus fleets in more realistic situations that consider a more complex street network, interaction with cars, as in most cities, unbalanced passenger fluxes, using different-sized buses, among many other possibilities.