A gradient approximation approach for adjusting temporal origin–destination matrices

The temporal demand matrix is an essential input to both on-line and off-line applications of dynamic traffic assignment (DTA). This paper presents a new method to solve the simultaneous adjustment of a dynamic traffic demand matrix, searching for a reliable solution with acceptable computational times for off-line applications and using as an input traffic counts and speeds, prior O–D matrices and other aggregate demand data (traffic demand productions by zone). The proposed solving procedure is a modification of the basic Simultaneous Perturbation Stochastic Approximation (SPSA) path search optimization method; it can find a good solution when the starting point (the seed matrix) is assumed to be “near” the optimal one, working with a gradient approximation based on a simultaneous perturbation of each demand variable.