Noisy demand and mode choice

Mode choice under stochastically varying demand is studied via a dynamic mathematical model which describes the behavioural interactions between population groups. The model is developed by assuming competing attractivity functions for automobile and public transit which motivate their use subject to an overall demand for transportation. When this demand is allowed to vary stochastically, a set of stochastic differential equations describing the model are obtained. These are solved for their steady-state values. It is found that noisy demand can structure the system qualitatively differently than when the demand is fixed. The noise is found to generally reduce the level of public transit ridership, but it also changes the values of the threshold at which new regimes occur and, most interestingly, it induces new steady-state solutions for ridership at critical values of the variance of demand. In the latter case, noise becomes a source of new possibilities in the system by triggering a steady-state solution not present in the noise-free environment.