Stability conjecture for regular polling policies

Let ${\cal P}$ be a regular polling policy, and let $\lambda_1$ and $\lambda_2$ be the intensities of the arrival processes in lanes $1$ and $2$, respectively. Let $s$ be the service time of a vehicle. Stability conjecture. If

$$\lambda_1+\lambda_2<\frac{1}{s},$$

then the coordination algorithm with policy ${\cal P}$ is stable. The preceding theorem shows that the opposite strict inequality is sufficient for instability; this conjecture proposes the corresponding sufficient condition for stability for every regular polling policy.