Sufficient conditions for multi-stages traffic assignment model to be the convex optimization problem

TL;DR

This paper formulates multi-stage traffic assignment with multiple demand layers and user types as a convex optimization problem, providing conditions for convexity and discussing numerical solution methods.

Contribution

It introduces sufficient conditions under which multi-stage traffic assignment models can be formulated as convex optimization problems, combining demand calculation and traffic assignment stages.

Findings

Reformulation of traffic assignment as a saddle-point problem.

Conditions for convexity of the multi-stage model.

Discussion of numerical solution approaches.

Abstract

In this paper we consider multi-stages traffic assignment with several demand layers, user types and network types. We consider two stages: demand matrix calculation (Entropy Wilson's model) and traffic assignment models (Beckmann or Nesterov--de Palma). For the traffic assignment stage we use dual reformulation and combine these stages as a saddle-point problem (convex-concave). Then we discuss how one can solve this problem numerically.