Multiserver-job Response Time under Multilevel Scaling

Abstract: We study the multiserver-job setting in the load-focused multilevel scaling limit, where system load approaches capacity much faster than the growth of the number of servers $n$. We specifically consider the ``1 and $n$'' system, where each job requires either one server or all $n$ servers. Within the multilevel scaling limit, we examine three regimes: load dominated by $n$-server jobs, 1-server jobs, or balanced. In each regime, we characterize the asymptotic growth rate of the boundary of the stability region and the scaled mean queue length. We numerically verify our asymptotic results against exact formulae.