  This study presents a distributed gradient-based approach to solve system
optimal dynamic traffic assignment (SODTA) formulated based on the cell
transmission model. The algorithm distributes SODTA into local sub-problems,
who find optimal values for their decision variables within an intersection.
Each sub-problem communicates with its immediate neighbors to reach a consensus
on the values of common decision variables. A sub-problem receives proposed
values for common decision variables from all adjacent sub-problems and
incorporates them into its own offered values by weighted averaging and
enforcing a gradient step to minimize its objective function. Then, the updated
values are projected onto the feasible region of the sub-problems. The
algorithm finds high quality solutions in all tested scenarios with a finite
number of iterations. The algorithm is tested on a case study network under
different demand levels and finds solutions with at most a 5% optimality gap.
