Different Policy Objectives of the Road Authority in the Optimal Toll Design Problem

Different Policy Objectives of the Road Authority in the Optimal Toll Design Problem


Dusica Joksimovic, Technical University of Delft, NL and Michiel Bliemer, ARS Transport & Technology, NL


By introducing different tolling strategies, road authority's policy objective may be optimized. In this paper, the effect of different tolling schemes will be analyzed with regards to different policy objectives of the road authority.


Problem definition
In the road-pricing problem the road authority aims to introduce the best tolling scheme depending on their goals. A tolling scheme is defined as a package in which a set of links and time intervals is chosen to toll, together with the toll levels corresponding to certain time-varying tolling patterns. Depending on the goal, the road authority has to select the best tolling scheme.
In this paper the dynamic optimal design problem is formulated as an optimization problem in which the upper level describes the policy objectives with chosen toll levels while the lower level describes the behavior of travelers including user-specific route and departure time choice.

Formulation of different objectives of the road authority
Road pricing
For our experiments three different objectives are chosen. 1) The total revenues on the network are a product of the inflows into tolled links and the corresponding toll levels at the link. Maximum toll levels to be charged are given. 2) Instead of maximizing total toll revenues, the road authority may be more interested in minimizing total travel time (e.g. as a proxy for minimizing congestion or pollution). This objective function of the road authority can be formulated as a product of the link inflows and link travel times on the network. 3) The combination between two previous mentioned objective functions can be expressed as the objective of maximizing social welfare for the road authority and travelers.

Travel behavior
Generalized travel cost function is modeled by a linear combination and extended to capture (not only route travel time) but also value of time of travelers, route toll costs, and penalties for scheduling delays. Value of time is the only class specific parameter in the generalized travel cost function. Based on experienced generalized travel costs, each traveler is assumed to simultaneously choose the route and departure time that he or she perceives to have the least travel costs (yielding a stochastic user equilibrium (SUE) assignment). The joint probability of choosing a specific route and departure time are given by multinomial logit (MNL) model.

Results and discussion
In case studies on a simple hypothetical network the different policy objectives under different tolling schemes is analyzed. The aim is to investigate which tolling scheme will give the best result with regard to a specific road authority?s policy objective to be reached. For the objective of maximizing revenues, three different tolling regimes (uniform, quasi-uniform and variable tolls) will be considered (see Figure 1).

Figure 1. Total revenue (Z) for different tolling schemes (uniform, quasi-uniform, and variable) and toll levels ( )

It is shown in the case that the toll level is zero, there are clearly no revenues. For very high toll levels, all travelers will choose to travel on the untolled route, resulting in zero revenues as well. As can be observed from Figure 1, uniform tolling (with toll value of 3.11) yields the highest revenues. In this experiment, the variable tolling scheme is not able to provide high revenues due to the small number of tolled time periods. Results of other policy objectives where different tolling schemes are applied can be analyzed and the best tolling scheme can be proposed.


The aim of this research is to investigate different policy objectives of the road authority and different tolling schemes. In the case studies in the paper is shown that policy objectives can indeed be optimized by imposing tolls, and that different policy objectives lead to different optimal tolling schemes and toll levels.

Reference list
Joksimovic D, M.C.J Bliemer and P.H.L. Bovy (2005). Optimal toll design problem in dynamic traffic networks- with joint route and departure time choice. Accepted for publication in Transportation Research Record journal.


Association for European Transport