[Nov 25] Michael Florian: A model and method for distance-based tolls modelling

Some feasibility studies for current toll road projects require the ability to model distance-based tolls, which is the way that some toll road operators establish the fees for usage in order to predict expected flow patterns and toll revenues. In practice, different variants of distance-based tolls are experimented with, such as capped maximum toll, minimum toll and different fees per entry ramp. In static multi-class assignment problems, all these toll variants can be modelled by a method referred to as “ramp-to-ramp tolls”, with the condition that there are no alternative tolled roads between an entry-exit ramp pair. Also, the ramp-to-ramp method requires the user of the software to prepare the toll value for all the possible combinations of entry/exit ramps ahead of time. In order to overcome these limitations a new algorithm for distance-based toll modelling was developed which directly uses the toll cost per link instead of the cost of entry-exit ramp pairs. Similar to the ramp-to-ramp method, the algorithm is based on the construction of temporary links, which span the toll road with the significant difference that the original links are kept as well and are used during the equilibration process. In order to solve the static traffic assignment problem on this augmented network a parallel version of the bi-conjugate linear approximation method has been adapted for the particular toll structure considered. The new method is illustrated with an example of capped distance-based toll modelling on a real-world network, along with other results.