2 problems

Gaussian-tail conjecture. (a) $N_{n}(\infty)$ exists for each $n$; (b) the sequence $\{\tilde{N}_{n}(\infty):n\in\mathbb{N}\}$ weakly converges to $\check{N}(\infty)$; and (c)

Tail-dependence conjecture. The limiting tail behavior of $\tilde{N}_{n}(\infty)$ depends on the service time distribution only through its first two moments, and on the patience t…