20 problems

Robustness conjecture. The same effects should be present in more realistic simulations and even in monotonicity-violating real traffic systems.

Greedy approximation conjecture. A greedy approximation algorithm similar to the algorithm in Hoffmann's Proposition 2.17 should also be designable.

Let two jamitons collide, and denote their lengths before collision by $L$ and $L_{\mathrm{test}}$, and the length of the resulting jamiton by $L_{\mathrm{col}}$. Jamiton-length ad…

Let $\tau$ be the relaxation time, and consider the jamiton produced by a collision. Denote its length by $L$. Length-dependence conjecture. The length of the jamiton resulting fro…

Let $\tau$ be the relaxation time, and consider the jamiton produced by a collision. Denote its amplitude by $A$ and its downstream density by $\rho_+$. Amplitude and downstream-de…

Let $\tau$ be the relaxation time in the second-order macroscopic traffic model, and consider the jamiton produced by a collision. Sonic-velocity invariance conjecture. The sonic v…

Let $Q_{\mathrm{jam}}$ be a jamiton with sonic density $\rho_s$. Let $\{Q_{\mathrm{jam}}(\rho_s^{ \mathrm{jam}})\}$ be a corresponding non-empty set of compatible jamitons parametr…

Let two compatible jamitons be given, with their parameters describing their densities, velocities, and lengths. Unique post-collision jamiton conjecture. The collision of two comp…

Singular-limit conjecture. The local model is the singular limit of the non-local model as $\mu\to\delta_{0^{+}}$.

In the simulation of circular roads approximated by regular polygons with $50$ edges, the theoretical and simulated maximum-flow values $z^{\text{max}}$ show a small mismatch. Poly…

Let $\rho^{n,m}$ be the discrete densities generated by the particle scheme, and suppose that, under the stated assumptions, a subsequence converges almost everywhere and in…

The scheme approximates a density $\rho$ for a vehicular-flow initial-boundary value problem, with entropy solutions understood through the boundary trace condition associated with…

The model with buffer has constant initial traffic densities on each incoming and outgoing road, together with drivers' turning preferences and initial queue lengths inside the buf…

Let $e(t)=\left\lVert f(t)-f^\infty\right\rVert_2$ denote the distance from the stable equilibrium $f^\infty$ at time $t$, and let $r=\Delta v/\delta v$ be the ratio of the velocit…

Homogeneous-demand conjecture. To reach $J_{max}$ around $\rho=0.25$ and $\rho=0.75$, it is necessary to have a homogeneous demand on all streets, so as to prevent “idling” of some…

A fundamental diagram is a flow-density relation for a traffic link, and an active bottleneck is a bottleneck at which capacity drop occurs. Capacity-drop conjecture. Discontinuous…

An active bottleneck is a traffic bottleneck whose flow has stabilized, and a capacity drop is the reduction in the maximum discharging flow after congestion forms. Driver-accelera…

Uniform boundedness and compact-support conjecture. In a globally optimal solution, all departure rates $\bar u_{k,p}$ are uniformly bounded and have compact support.

Consider the macroscopic traffic model associated with the cellular automaton, and let the density denote the macroscopic car density. Density-dependence conjecture. The effect by…

In the mesoscopic cellular-automaton traffic model, let $\beta$ denote the look-ahead parameter and let cross-correlations refer to correlations between spatial neighbors in the un…