About multistage transportation model and sufficient conditions for its potentiality

Multistage modeling of traffic flows began to actively develop since the 70s of the last century. Transportation modeling packages were created, which are based on a set of convex optimization problems, whose sequential solution (with appropriate feedback mechanism) converges to the desired equilibrium distribution. An alternative way is to try to find such a general convex optimization problem, the solution of which would give the desired equilibrium. In this paper, we attempt to find sufficient conditions to guarantee that the alternative path will be successful. In particular, the paper has shown that one of the blocks of a multistage model can use a stable dynamics model (rather than the generally accepted Beckmann model), combined with the possibility to choose different types of users and vehicles.