The instability conjecture for interference queueing networks on grids

Consider an interference queueing network on the $d$-dimensional grid with arrival rate $\lambda$ and interference sequence $(a_i)_{i\in\mathbb{Z}}$. Instability conjecture. For all $d\geq 1$, if

$$\lambda > \frac{1}{\sum_{j \in \mathbb{Z}^d}a_j},$$

then the system is unstable.

The paper proves this conclusion for $d=1$ and monotone interference sequences, and conjectures its extension to all dimensions and arbitrary interference sequences. The general case remains open in the source.