Second best toll and capacity optimisation in network: solution algorithm and policy implications

This paper looks at the first and second-best jointly optimal toll and road capacity investment problems from both policy and technical oriented perspectives. On the technical side, the paper investigates the applicability of the constraint cutting algorithm for solving the second-best problem under elastic demand which is formulated as a bilevel programming problem. The approach is shown to perform well despite several problems encountered by our previous work in Shepherd and Sumalee (2004). The paper then applies the algorithm to a small sized network to investigate the policy implications of the first and second-best cases. This policy analysis demonstrates that the joint first best structure is to invest in the most direct routes while reducing capacities elsewhere. Whilst unrealistic this acts as a useful benchmark. The results also show that certain second best policies can achieve a high proportion of the first best benefits while in general generating a revenue surplus. We also show that unless costs of capacity are known to be low then second best tolls will be affected and so should be analysed in conjunction with investments in the network

A linear model for the continuous network design problem

This article is concerned with the continuous network design problem on traffic networks, assuming system optimum traffic flow conditions and time-dependent demand. A linear programming formulation is introduced based on a dynamic traffic assignment (DTA) model that propagates traffic according to the cell transmission model. The introduced approach is limited to continuous link improvements and does not provide for new link additions. The main contribution of the article is to provide an analytical formulation for network design that accounts for DTA conditions that can be used for further analysis and extensions. The model is tested on a single destination example network, resembling a freeway corridor, for various congestion levels, loading patterns and budget sizes, to demonstrate the simplicity and effectiveness of the approach

Linear Programming Models for the User and System Optimal Dynamic Network Design Problem: Formulations, Comparisons and Extensions

Dynamic traffic assignment, Equilibrium, Linear programming, Network design, Recourse, Stochastic programming, Transportation networks,