Abstract. This paper develops a graph-theoretic framework for large scale bi-dimensional transport networks and provides new insight into the dynamic traffic assignment. Reactive dynamic assignment are deployed to handle the traffic contingencies, traffic uncertainties and traffic congestion. New shortest paths problem in large networks is defined and routes cost calculation is provided. Since mathematical modelling of traffic flow is a keystone in the theory of traffic flow management, and then in the traffic assignment, it is convenient to elaborate a good model of assignment for large scale networks relying on an appropriate model of flow related to very large networks. That is the zone-based optimization of traffic flow model on networks developed by [8], completed and improved by [9].

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This chapter provides Lagrangian dynamic fluid model of the traffic of personal rapid maglev transporters or personal rapid transit (PRT). The transport system using these maglev transporters -named sky-cars or sky-podcars -operate in the style of demand-responsive system. The dynamical evolution of sky-podcar travelers' demand is modelled and the problem of relocation of podcars is addressed. In a multimodal transport mobility, we describe assignment in such transit system, and its spatial interactions with other common transportation systems.

We present in this paper a model of vehicular traffic flow for a multimodal transportation road network. We introduce the notion of class of vehicles to refer to vehicles of different transport modes. Our model describes the traffic on highways (which may contain several lanes) and network transit for pubic transportation. The model is drafted with Eulerian and Lagrangian coordinates and uses a Logit model to describe the traffic assignment of our multiclass vehicular flow description on shared roads. The paper also discusses traffic streams on dedicated lanes for specific class of vehicles with event-based traffic laws. An Euler-Lagrangian-remap scheme is introduced to numerically approximate the model's flow equations.