  Multiserver jobs, which are jobs that occupy multiple servers simultaneously
during service, are prevalent in today's computing clusters. But little is
known about the delay performance of systems with multiserver jobs. We consider
queueing models for multiserver jobs in scaling regimes where the system load
becomes heavy and meanwhile the total number of servers in the system and the
number of servers that a job needs become large. Prior work has derived upper
bounds on the queueing probability in this scaling regime. However, without
proper lower bounds, the existing results cannot be used to differentiate
between policies. In this paper, we study the delay performance by establishing
sharp bounds on the mean waiting time of multiserver jobs, where the waiting
time of a job is the time spent in queueing rather than in service. We first
characterize the exact order of the mean waiting time under the
First-Come-First-Serve (FCFS) policy. Then we prove a lower bound on the mean
waiting time of all policies, which has an order gap with the mean waiting time
under FCFS. Finally, we show that the lower bound is achievable under a
priority policy that we call Smallest-Need-First (SNF).
