System optimal traffic assignment with departure time choice

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