8 problems

Asymptotic velocity conjecture. For every $j$, the limit

Let $X=\delta+Z$ be a CU service time, where $\delta\ge 0$ is constant and the support of the random variable $Z$ includes $0$. Under server-dependent scaling, consider the expecte…

Let $\operatorname{Bi-Modal}(B,\epsilon)$ be the service-time distribution with straggling magnitude $B$, and let $Y_{k:n}$ denote the job completion time for $k$ useful responses…

Let $n$ be the number of workers, let $Y_{k:n}$ denote the job completion time when the diversity/parallelism parameter is $k$, and consider a general CU service time under additiv…

Message-rate conjecture. Access to incoming job sizes should permit a policy with vanishing queueing delay even when its message rate is strictly less than the arrival rate…

The proposed proximity-aware two choices scheme redirects requests using nearby servers' cache contents and the queue lengths of two randomly chosen servers within a neighborhood o…

Common-left-eigenvector convergence conjecture. If the matrices $C(t_k)$, $k\geq 0$, have a common left eigenvector corresponding to the eigenvalue one, then the state of system co…

The paper considers a large-scale heterogeneous system with multiple independent routers and the PULL-2 load-distribution algorithm, which uses pull-messages and occasional pull-re…