Common Bus Lines

In large cities operating an important public mass transit network, we are faced with the problem of ‘common bus lines’: some routes share common sections and the passenger must select the buses he will probably use. While most computer packages code the section as a unique link and disregard the precise assignment of passengers on the distinct routes, we give a solution to this operational assignment based on the “perceived” travel time. Formulated as an optimization problem within a probabilistic context, the optimal subset of routes “to be selected” is obtained. A more detailed treatment on uniform and exponential cases for the time of the first vehicle to arrive on a route concludes the paper.