Representation of capacity drop at a road merge via point constraints in a first order traffic model

Abstract

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 Haut et al. (Proceedings 16th IFAC World Congress. Prague, Czech Republic 229 (2005) TuM01TP/3), 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.

Coherence and chattering of a one‐way valve

“…On the one hand, the coherence of a Riemann solver is a desirable property for a numerical scheme. Indeed, a numerical time‐stepping scheme based on a Riemann solver that fails to be consistent may not produce the expected solution of a Riemann problem, see for instance []. On the other hand, the lack of coherence has a physical counterpart, which is typical when dealing with real valves: it can induce commuting.…”

Car path tracking in traffic flow networks with bounded buffers at junctions

“…Remark1 Note that different flux functions f e satisfying the assumptions from above could be also applied. As a consequence, following the ideas in Dal Santo et al, the coupling conditions have to be defined more carefully. Therefore, to improve readability, we stick to the same flux function on every edge e .…”

“…We remark that flux maximization is not the only possibility to uniquely determine the flux at junctions. Alternatively, capacity drop assumptions might be used, see, eg, Dal Santo et al and Haut et al…”

“…The demand d( e (b e , t)) gives the maximum flux that can come from a road e ∈  at time t whereas the supply s( e (a e , t)) denotes the maximum flux that can enter road e. We remark that flux maximization is not the only possibility to uniquely determine the flux at junctions. Alternatively, capacity drop assumptions might be used, see, eg, Dal Santo et al and Haut et al 15,16 We only consider networks consisting of dispersing and merging junctions, see Figure 1. To model the flow at a junction v, we also introduce demand and supply functions for the buffer.…”

On the implementation of a finite volumes scheme with monotone transmission conditions for scalar conservation laws on a star-shaped network

“…Moreover, we show the consistency of the scheme with respect to the case of a network with no discontinuity at the junction, namely taking the same flux on each arc, and finally a convergence analysis is also performed. These results are used in the validation of the finite volumes scheme with point constraints at the junction introduced in [9].…”