System optimal traffic assignment with departure time choice

This thesis investigates analytical dynamic system optimal assignment with departure time choice in a rigorous and original way. Dynamic system optimal assignment is formulated here as a state-dependent optimal control problem. A fixed volume of traffic is assigned to departure times and routes such that the total system travel cost is minimized. Although the system optimal assignment is not a realistic representation of traffic, it provides a bound on performance and shows how the transport planner or engineer can make the best use of the road system, and as such it is a useful benchmark for evaluating various transport policy measures. The analysis shows that to operate the transport system optimally, each traveller in the system should consider the dynamic externality that he or she imposes on the system from the time of his or her entry. To capture this dynamic externality, we develop a novel sensitivity analysis of travel cost. Solution algorithms are developed to calculate the dynamic externality and traffic assignments based on the analyses. We also investigate alternative solution strategies and the effect of time discretization on the quality of calculated assignments. Numerical examples are given and the characteristics of the results are discussed. Calculating dynamic system optimal assignment and the associated optimal toll could be too difficult for practical implementation. We therefore consider some practical tolling strategies for dynamic management of network traffic. The tolling strategies considered in this thesis include both uniform and congestion-based tolling strategies, which are compared with the dynamic system optimal toll so that their performance can be evaluated. In deriving the tolling strategies, it is assumed that we have an exact model for the underlying traffic behaviour. In reality, we do not have such information so that the robustness of a toll calculation method is an important issue to be investigated in practice. It is found that the tolls calculated by using divided linear traffic models can perform well over a wide range of scenarios. The divided linear travel time models thus should receive more attention in the future research on robust dynamic traffic control strategies design. In conclusion, this thesis contributes to the literature on dynamic traffic modelling and management, and to support further analysis and model development in this area