Multimodal Transportation Network Modeling Based on the Generic Second Order Modeling Approach

The generic second order modeling (GSOM) approach to vehicular traffic flow combines the traditional kinematic description of traffic with dynamic equations for vehicle attributes. The GSOM model provides a unifying framework for many models in the literature. This framework includes tools such as local supply and demand, discretization, variational formulation, and generic intersection models.The object of the paper is to extend this approach to multimodal modeling of transportation networks. I n multimodal networks two connected but distinct flows co-exist: vehicular and passenger flow. The main idea of the paper is to express the passenger flow as the flow of a specific attribute: the passenger load of vehicles, the unit of which is expressed in passengers per vehicle. Supplementary attributes pertaining to passengers can be added: destinations, activity plans, information availability, passenger category, and so forth. Intermodal poles, stations (bus, taxi, train), and intersections are modeled as nodes. It is shown that the stock variables associated to vehicles and passengers satisfy a system of conservation equations (on links) coupled with a system of ordinary differential equations (in nodes). Boundary conditions and numerical methods are proposed for the resolution of the model. Some examples are given, notably a method for managing a major incident on an automatic train line. The method uses most elements of the model in order to define the control strategy: passenger and train dynamics, station models, and local traffic supply and demand analysis.