A diagonalization algorithm for solving the dynamic network user equilibrium traffic assignment model

We develop a numerical method to solve the user equilibrium simultaneous departure time and route choice problem on congested general traffic networks. This method is based on the diagonalization algorithm which has been used to solve general variational inequalities. The diagonalized problem is solved using the Frank–Wolfe method. Computational results are presented for a test network with 76 arcs, 24 nodes and 528 origin–destination pairs over the time interval of 120 periods. The improved accuracy of the diagonalization algorithm is demonstrated through numerical comparisons to an approximate solution obtained by the heuristic algorithm. The CPU time spent by each algorithm is also compared to demonstrate that the diagonalization algorithm converges to a more accurate equilibrium solution signigficantly faster than the heuristic algorithm.