It is shown how gradient projection algorithms can effectively be applied also to sequential local choices at nodes for users directed toward a given destination.

It is proved that, in the case of deterministic route choices, the Dynamic User Equilibrium based on arc conditional probabilities formulated as a Variational Inequality problem is equivalent to that based on path probabilities.

The flow propagation of demand flows travelling towards a given destination based on given travel times and arc conditional probabilities is formulated and solved as a sequence of square linear systems, one for each temporal layer, without introducing bushes of efficient arcs.

In the proposed framework, it is also possible to consider large time interval of several minutes, which is an extremely relevant feature if computing times are an issue, like in operation.

Convergence measured by the relative gap is reached in an acceptable number of iterations (e.g. 100) to a good level (e.g. 10⁻⁴) for moderate congestion (without spillback) and to a fair level (e.g. 10⁻²) for high congestion (with spillback).