Analysis of dynamic traffic models and assignments

This paper develops a comprehensive framework for analysing and solving traffic models and \nassignments in dynamic setting. Traffic models capture the time-varying travel times and flows on a \nroad network and traffic assignments represent the corresponding responses of travellers. There \nare two different kinds of traffic assignments: dynamic user equilibrium and dynamic system \noptimum. Under dynamic user equilibrium, traffic is assigned such that for each origin-destination \npair in the network, the individual travel costs experienced by each traveller, no matter which \ncombination of travel route and departure time he/she chooses, are equal and minimal. The system \noptimum assigns traffic such that the total system cost of the network system is minimized. The \nsystem optimal traffic pattern provides a useful benchmark for evaluating various transport policy \nmeasures such as implementing dynamic road tolls. This system optimal assignment is formulated \nas a state-dependent optimal control problem. The analysis developed in this paper is novel and it \ncan work with general travel cost functions. Numerical examples are provided for illustration and \ndiscussion. Finally, some concluding remarks are given.