## Optimal Tolls for Multiple User Classes

### Authors

J Holguín-Veras, J Jiang, Rensselaer Polytechnic Institute, US; M Cetin, University of South Carolina, US

### Description

This paper focuses on the computation of optimal tolls using a multi-class formulation to compute optimal tolls. The formulation is comprised of two major modules: an optimization component and performance models to estimate the externalities.

### Abstract

An important question of relevance to road pricing projects is related to the estimation of the tolls for the different user classes (i.e., passenger cars, small trucks, large trucks, buses). Estimating optimal tolls for the user classes using the facility is no straightforward task as the different user classes have different values of time, produce different amount of externalities, have different demand functions and willingness to pay, and?equally important?have different levels of political power. The latter aspect leads many decision makers towards the path of attempting to mitigate congestion, or generate revenues, by disproportionally raising tolls for freight vehicles. This indicates that the innate preference of the decision makers is to extract as much toll revenues as possible from truck traffic, to reduce the charges on passenger car users (Holguín-Veras et al. 2006a).

This is far from an isolated case. In a recent paper, Holguín-Veras et al. (2006a) conducted a comparative analysis of toll policy in the United States. Using data collected a sample of toll agencies across the US, they estimated econometric models that capture the statistical patterns of toll policy in the country (Holguín-Veras et al. 2006a). One of the chief conclusions is that the commercial vehicle tolls seem to be disproportionally higher with respect to the externalities produced by these vehicles. However, since proxy variables were used to measure the externalities, and no optimal tolls were calculated, the conjecture went unproven. This flies in the face of economic intuition that suggests that since the value of time of freight vehicles is many times higher than the one for passenger cars, it may be economically advantageous to assign scarce road space to freight traffic, meaning the that toll policies that favor passenger car are far from optimal.

This paper attempts to shed light into this complex problem with the assistance of multi-class formulation to compute optimal tolls. The formulation is comprised of two major modules. The first one is an optimization component aimed at computing optimal tolls assuming a Stackelberg game in which the toll agency sets the tolls, and the equilibrating traffic plays the role of the followers. The optimization component is supported by a set of performance models that estimate the externalities as a function of a multivariate vector of traffic flows. These models were estimated using Taylor series expansions of the output obtained from traffic simulations of a hypothetical test case. The formulation presented in the paper is then applied to a variety of scenarios to gain insight into the optimality of current toll policies.

In order to generate the data needed for estimating the cost functions, a micro-simulation of a stretch of a hypothetical highway was developed using state of the practice traffic simulation software. The network consists of a three-lane freeway segment that leads to a one-mile-long bridge that imposes a capacity constraint on the freeway. The free-flow speed on both facilities is 65 mph, and the total length of both facilities is 20 miles. In this simple network, there is only one origin zone at one end of the highway where the traffic demand is generated. Three vehicle classes are considered: passenger cars, small trucks (2 axles), and heavy trucks (5-axle semi-trailers). The different vehicle types were characterized using the standard parameters for physical and operational characteristics: length, width, and height), weight, top speed, and acceleration and deceleration rates. In order to obtain a set of continuous and differentiable cost functions capturing the amount of externalities produced by a given traffic, a set of regression models were estimated with the amount of externality as the dependent variable, and the vector of traffic levels as the independent variables. To account for non-linearities, second order Taylor series were used to provide the basic formulation of the models. Using the simulation data, these cost functions are estimated by ordinary least squares regression.

In the final section of the paper, the authors compare the optimal tolls computed against the observed values of tolls in the US. The comparison is based on welfare impacts, traffic impacts, and equity.

#### Publisher

Association for European Transport