A mathematical model for headway variance of fixed-route buses

A mathematical model for computing and analysing headway variance of fixed-route buses offering scheduled service is developed. The model assumes a situation where both the passengers' OD pattern and the bus-route structure do not have any particular form but the number of passengers served at any bus station is a stationary Poisson process. Basic probability concepts are mostly used in deriving the model. Innovations in the model are the inclusion of a skip probability at a stop and the correlation factors between successive bus loads at a loading point and between the travel times of successive buses on a link. The model is, therefore, applicable to a wider range of situations than was possible with the earlier models. Results indicate that bus loading conditions and traffic conditions along the route are the major factors responsible for headway variability. The developed model can be used to determine the relative importance of these factors on headway variance at individual stopping station and thereby simplify the task of evolving effective countermeasures in any given situation. A numerical example that illustrates the application of the model is also given.