4 problems

Let $V$ be a set of $v$ servers, and let a data placement be a family of $b$ blocks, each of size $k$, on $V$. For a placement $(V,\mathcal{F})$, let … where $v_j$ is the number of…

Consider the partial fork-join systems studied in the paper, with replication and random server slowdowns, and let asymptotic optimality refer to achieving the minimum asymptotic d…

Let $n$ be the number of servers and let $r$ be the number of replicated tasks in an $(n,r,1)$ partial-fork-join system, where a job is forked to $r$ of the $n$ servers and the sys…

Let $n$ be the number of servers, let $\bar{F}_X$ be the survival function of a task's service time, and let $\rX$ denote the service-time distribution. For a fork-join system, let…