5 problems

MJSQ–JSQ efficiency conjecture. Based on preliminary calculations, MJSQ and JSQ should deliver comparable efficiency at the level of the $k$ shortest queues for any fixed $k$.

JSQ steady-state scaling conjecture. It has been conjectured that both the minimum and the average steady-state queuelengths scale like

Consider a system with $N$ servers operating under the Join-the-Shortest-Queue policy in the super-Halfin–Whitt regime, where … for some $\varepsilon\in(0,0.5)$, and let…

Let $T>0$, let $j\geq 2$, and let $c\in(0,1)$. The event that, at some time $t\in[0,T]$, some servers have queues of length $j$ while the remaining servers have queues of length…

Let $T>0$, let $j\geq 2$, and let $c\in(0,1)$. The event that some servers have queues of length $j$ while the remaining servers are idle is … This corresponds to $nc$ queues of le…