M. Hajiahmadi, V.L. Knoop, B. De Schutter, and H. Hellendoorn, "Optimal dynamic route guidance: A model predictive approach using the macroscopic fundamental diagram," Proceedings of the 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013), The Hague, The Netherlands, pp. 1022-1028, Oct. 2013.
Since centralized control of urban networks with detailed modeling approaches is computationally complex and inefficient, hierarchical decentralized methods based on aggregate models are of great importance. In this paper, we use an aggregate modeling approach based on the macroscopic fundamental diagram (MFD), in order to find dynamic optimal routing strategies. An urban area can be divided into homogeneous regions each modeled by a (set of) macroscopic fundamental diagrams. Thus, the problem of route guidance can be solved in a regional fashion by using model predictive control and the novel high-level MFD-based model used for prediction of traffic states in the urban network. The optimal routing advices obtained from the high-level controller can be used as references (to track) for lower-level local controllers installed at the borders of the regions. Hence, the complexity of solving the routing problem will be decreased significantly. The performance of the proposed approach is evaluated using a multi-origin multi-destination grid network. Further, the obtained results show significant performance of the optimal dynamic route guidance over other static routing methods.