A decomposition approach to the static traffic assignment problem

- A spatial parallelization scheme for the static traffic assignment problem is proposed.
- The properties of the proposed parallelization scheme are investigated.
- It is proved that the algorithm converges to the equilibrium solution on the full network.
- The correctness and benefits of the algorithm is studied using the Austin network.

This paper describes a spatial parallelization scheme for the static traffic assignment problem. In this scheme, which we term a decomposition approach to the static traffic assignment problem (DSTAP), the network is divided into smaller networks, and the algorithm alternates between equilibrating these networks as subproblems, and master iterations using a simplified version of the full network. The simplified network used for the master iterations is based on linearizations to the equilibrium solution for each subnetwork obtained using sensitivity analysis techniques. We prove that the DSTAP method converges to the equilibrium solution on the full network, and demonstrate computational savings of 35-70% on the Austin network. Natural applications of this method are statewide or national assignment problems, or cities with rivers or other geographic features where subnetworks can be easily defined.