This paper develops a comprehensive framework for analysing and calculating user equilibrium,
system optimum, and externalities in time-dependent road networks. Under dynamic user
equilibrium, traffic is assigned such that for each origin-destination pair in the network, the
individual travel costs experienced by each traveller, no matter which combination of travel route
and departure time he/she chooses, are equal and minimal. The system optimal flow is
determined by solving a state-dependent optimal control problem, which assigns traffic such that
the total system cost of the network system is minimized. The externalities are derived by using a
novel sensitivity analysis. The analyses developed in this paper can work with general travel cost
functions. Numerical examples are provided for illustration and discussion. Finally, some
concluding remarks are given
