  This study investigates dynamic system-optimal (DSO) and dynamic user
equilibrium (DUE) traffic assignment of departure/arrival-time choices in a
corridor network. The morning commute problems with a many-to-one pattern of
origin-destination demand and the evening commute problems with a one-to-many
pattern are considered. Specifically, a novel approach to derive closed-form
solutions for both DSO and DUE problems is developed. We first derive a
closed-form solution to the DSO problem based on the regularities of the cost
and flow variables at an optimal state. By utilizing this solution, we prove
that the queuing delay at a bottleneck in a DUE solution is equal to an optimal
toll that eliminates the queue in a DSO solution under certain conditions of a
schedule delay function. This enables us to derive a closed-form DUE solution
by using the DSO solution. We also show the theoretical relationship between
the DSO and DUE assignment. Numerical examples are provided to illustrate and
verify the analytical results.
