Environmentally Sustainable Toll Design for Congested Road Networks with Uncertain Demand

ABSTRACT

This article proposes a new road toll–design model for congested road networks with uncertain demand that can be used to create a sustainable urban transportation system. For policy assessment and strategic planning purposes, the proposed model extends traditional congestion pricing models to simultaneously consider congestion and environmental externalities due to vehicular use. Based on analyses of physical and environmental capacity constraints, the boundary conditions under which a road user on a link should pay either a congestion toll or an extra environmental tax are identified. The sustainable toll design model is formulated as a two-stage robust optimization problem. The first-stage problem before the realization of the future travel demand aims to minimize a risk-averse objective by determining the optimal toll. The second stage after the uncertain travel demand has been determined is a scenario-based route choice equilibrium formulation with physical and environmental capacity constraints. A heuristic algorithm that combines the sample average approximation approach and a sensitivity analysis-based method is developed to solve the proposed model. The upper and lower bounds of the model solution are also estimated. Two numerical examples are given to show the properties of the proposed model and solution algorithm and to investigate the effects of demand variation and the importance of including risk and environmental taxation in toll design formulations.

Key Words:

• sample average approximation
• sustainable toll design
• two-stage optimization
• uncertain demand

ACKNOWLEDGMENTS

The work that is described in this article was jointly supported by grants from the Research Committee of the Hong Kong Polytechnic University (Project nos. G-YX1 V and 1-ZV4 T), the National Natural Science Foundation of China (70971045), the Research Foundation for the Author of National Excellent Doctoral Dissertation (China) (200963), the Program for New Century Excellent Talents in University (China) (NCET-10-0385), and the University Research Committee and HKU SPACE Research Fund of the University of Hong Kong (201007176059).

Notes

Note. The bolded row implies that the environmental capacity is less than the associated physical capacity.

Note. SD = standard deviation; conf. int. = confidence interval.

Note. The bolded rows imply that the environmental capacity is less than the associated physical capacity.