Abstract
Connections between microscopic follow-the-leader and macroscopic fluid-dynamics traffic flow models are already well understood in the case of vehicles moving on a single road. Analogous connections in the case of road networks are instead lacking. This is probably due to the fact that macroscopic traffic models on networks are in general ill-posed, since the conservation of the mass is not sufficient alone to characterize a unique solution at junctions. This ambiguity makes more difficult to find the right limit of the microscopic model, which, in turn, can be defined in different ways near the junctions.In this paper we show that a natural extension of the first-order follow-the-leader model on networks corresponds, as the number of vehicles tends to infinity, to the LWR-based multi-path model introduced in [4,5].
Highlights
Traffic flow can be described at different scales, depending on the level of details one wants to observe
Analogous connections in the case of road networks are instead lacking. This is probably due to the fact that macroscopic traffic models on networks are in general ill-posed, since the conservation of the mass is not sufficient alone to characterize a unique solution at junctions
In this paper we propose a very natural extension of a first-order followthe-leader model on road networks and we prove that its solution tends to the solution of the LWR-based multi-path model introduced in [4, 5] in the limit, i.e. as the number of vehicles tends to infinity while their total length is kept constant
Summary
Traffic flow can be described at different scales, depending on the level of details one wants to observe. Connections between microscopic follow-the-leader and macroscopic fluid-dynamics traffic flow models are already well understood in the case of vehicles moving on a single road. In this paper we propose a very natural extension of a first-order followthe-leader model on road networks and we prove that its solution tends to the solution of the LWR-based multi-path model introduced in [4, 5] in the limit, i.e. as the number of vehicles tends to infinity while their total length is kept constant.
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