3 problems

Transient mean-field convergence conjecture. The stochastic process $\bar y^n(t)$ converges to $\bar y(t)$ defined above as $n\to\infty$. The assertion concerns the transient, rath…

For each $n$, let $\pi^n$ be the invariant distribution of the system with $n$ servers, and let $\pi$ be the unique distribution satisfying the mean-field fixed-point equation. Inv…

Let $d$ be the degree of parallelism and let the mean-field equations describe the limiting occupancy process of a tagged server. Let $\bar y$ denote the corresponding mean-field o…