Representation of capacity drop at a road merge via point constraints in a first order traffic model. (English) Zbl 1420.35156
Summary: We reproduce the capacity drop phenomenon at a road merge by implementing a non-local point constraint at the junction in a first order traffic model. We call capacity drop the situation in which the outflow through the junction is lower than the receiving capacity of the outgoing road, as too many vehicles trying to access the junction from the incoming roads hinder each other. In this paper, we first construct an enhanced version of the locally constrained model introduced by B. Haut, G. Bastin and Y. Chitour [“A macroscopic traffic model for road networks with a representation of the capacity drop phenomenon at the junctions”, IFAC Proc. Vols. 38, No. 1, 114–119 (2005; doi:10.3182/20050703-6-CZ-1902.02042)], then we propose its counterpart featuring a non-local constraint and finally we compare numerically the two models by constructing an adapted finite volumes scheme.
MSC:
| 35L65 | Hyperbolic conservation laws |
| 35R02 | PDEs on graphs and networks (ramified or polygonal spaces) |
| 90B20 | Traffic problems in operations research |
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 35A35 | Theoretical approximation in context of PDEs |
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