MSA algorithms for solving the combined assignment-control problem

In this paper we focus on the combined assignment-control problem that arises when signal control parameters of an urban road network are locally optimised and they have to be consistent with equilibrium traffic flows. This problem can be formulated as an (asymmetric) equilibrium assignment problem. In this paper we compare some solution algorithms for solving the combined assignment-control problem, based on the MSA (Method of Successive Averages) framework; some algorithms, proposed in the literature for solving the (symmetric) assignment problem, are adapted to the combined assignment-control problem. All the algorithms are tested on a real-scale network. Numerical results show that these algorithms are able to reduce computing times significantly, respect the classic MSA algorithm, in order to solve the asymmetric assignment problem.