A Macroscopic Node Model Related to Capacity Drop

Abstract The automobile traffic congestion annually generates an estimated cost of several million euros for such a urban area as a European capital. At the origin of this congestion, the capacity drop is a well-known phenomenon which still remains complex to model [1] , [2] , [3] , [4] . The capacity drop is related to the hysteresis of traffic: for a state of disturbed traffic, the return to the normal of the traffic is delayed when demand decreases [5] . This paper intends to present a macroscopic convergent model to get a better modeling for capacity drop. Considering previous investigations [8] , one considers bounded acceleration for the flow. As the most common case of convergent is the merge of two road lanes, or two motorways, the convergent is modeled as a box with two entry flows and one output flow. A static storage capacity is provided to the box. Vehicles are mainly characterized by their bounded acceleration. The point is to describe the evolution of the convergent considering the number of vehicles stored inside the box. The process is to consider the convergent box as a cell of network regarding the Godunov scheme [6] . The supply function has a classical fundamental diagram shape, but the demand function is modified regarding the bounded acceleration of vehicles [7] . The partial supply functions for the node cell are calculated accordingly to the importance of the converging roads. Then the model is solved using the Godunov scheme, with an update of the number of stored vehicles for every time step. The model is to be tested on Paris ring with 40 seconds data.

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