Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2412.18560

Adapting Priority Riemann Solver for GSOM on road networks

Caterina Balzotti·Roberta Bianchini·Maya Briani·Benedetto Piccoli
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we present an extension of the Generic Second Order Models (GSOM) for traffic flow on road networks. We define a Riemann solver at the junction based on a priority rule and provide an iterative algorithm to construct solutions at junctions with n incoming and m outgoing roads. The logic underlying our solver is as follows: the flow is maximized while respecting the priority rule, which can be adjusted if the supply of an outgoing road exceeds the demand of a higher-priority incoming road. Approximate solutions for Cauchy problems are constructed using wave-front tracking. We establish bounds on the total variation of waves interacting with the junction and present explicit calculations for junctions with two incoming and two outgoing roads. A key novelty of this work is the detailed analysis of returning waves - waves generated at the junction that return to the junction after interacting along the roads - which, in contrast to first-order models such as LWR, can increase flux variation.

Explore related subjects

math.AP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Caterina Balzotti, Roberta Bianchini, Maya Briani, Benedetto Piccoli. 2024-12-24. Adapting Priority Riemann Solver for GSOM on road networks. https://arxiv.org/abs/2412.18560

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A linear test approach to global controllability of third- and fifth-order nonlinear dispersive equations

We investigate third- and fifth-order nonlinear dispersive equations of KdV type on the torus and establishes approximate controllability by a fixed four-dimensional control; rather than relying solely on the saturation machinery, the analysis exploits the finite-dimensional controllability of the inviscid Burgers equation linearized around a carefully constructed return trajectory, with the trajectory itself obtained from an observable family. This ``linear test" strategy, yields more information about the structure of the control than the standard approach. In particular, the constructed control is shown to depend continuously on the initial and target states, a property that is by no means automatic in nonlinear control problems, and to decompose as a bounded linear operator applied to the data plus a fixed remainder, with the operator part interestingly independent of the order of dispersion.

math.AP↗
arXiv2026

A conditional Lagrangian clock barrier at the $C^{1,\frac{1}{3}}$ threshold for axisymmetric Euler without swirl

We consider axisymmetric no-swirl solutions to the three-dimensional incompressible Euler equations, with initial velocity in $C^{1,α}\cap L^2$, where $α\in\left[\frac{1}{3},1\right)$. In a major breakthrough, Shkoller introduced a clock-and-driver framework that he used in order to prove finite-time type I blow-up below the $C^{1,\frac{1}{3}}$ threshold in this setting. Motivated by this, we define Lagrangian classes of coherent conditional solutions for which the same mechanism yields a supercritical-critical barrier to blow-up when $α\geq\frac{1}{3}$. When $α>\frac{1}{3}$, the aforementioned barrier is genuinely depleted, whereas at the critical endpoint $α=\frac{1}{3}$, we obtain an exponential bound preventing blow-up. In the general case, we formulate a matrix-clock criterion in terms of the smallest singular value of the deformation gradient and show that, under transverse cusp-tail, longitudinal, off-clock, Dini, and suitable geometric coherence hypotheses, this singular value cannot collapse in finite time. In particular, we also show that the class of such coherent solutions includes the smooth ones locally in time. In the on-axis case, the criterion reduces to the scalar clock inequality $\displaystyle \dot{J}(t)\gtrsim -B(t)J(t)-CJ(t)^{3α}$, which rules out Shkoller-type clock collapse for $α\geq\frac{1}{3}$. These results do not enlarge the known Lorentz-space global regularity classes. Rather, they in particular identify the supercritical Lagrangian obstruction dual to Shkoller's subcritical blow-up mechanism in the case $α>\frac{1}{3}$.

math.AP↗