A supply model for public transit services

Assume that a bus network is given, i.e. we are given a network of streets on which certain bus lines have been set up. Let the total number of buses be given. Assume furthermore that the total demand for bus transportation is given in the form of the marginal totals of an origin-destination matrix, i.e. the total demand for travel from certain origins as well as the total demand for travel to certain destinations is given. Problem: Determine the complete travel pattern and decide which bus frequencies to use on the various lines. The problem is formulated as a non-linear programming problem in the form of a compound minimization problem. The most interesting features are that the model explicitly takes into account capacity constraints on the buses, and that the distribution of trips between different zone is influenced by the frequencies of the bus lines. An iterative algorithm to solve this problem is developed. The algorithm converges to stationary points. This scheme employs as a component an algorithm for the combined distribution- assignment problem in traffic planning which is developed by using decomposition. The model has been tested on the bus network in the town of Linköping (80,000 inhabitants). The model suggests certain actions which are in agreement with the actions actually taken by the bus operator.