A network model for capped link-based tolls

Toll road operators and other toll facility stakeholders require analysis tools to estimate the ridership and projected income for an increasing variety of tolling schemes. Some tolling schemes commonly considered include link-based tolls as well as derived schemes, such as charging both a minimum and a maximum toll (or cap) for the use of the facility. In addition, different entry ramps may incur different tolls, which may be added to a link-based toll and subject the total toll to a toll cap value. Network equilibrium models that consider such tolls result in non-additive costs on the modeled network due to the capping. To obtain a more tractable equivalent model, a network transformation is used. The model uses the addition of a set of temporary links to the network, which inherit the delays and tolls of the original links. It considers the toll cost per link, as well as minimum and a maximum value of the tolls paid. It is shown that the modified and the original network formulations are equivalent. To solve the resulting multi-class network equilibrium model, a multi-threaded bi-conjugate variant of the linear approximation method has been adapted for the particular network model used. The method is illustrated with a small example as well as an instance of capped link-based toll modeling on a network originating from practice that employs the toll structure considered.