We study the steady‐state behavior of multiserver queues with general job size distributions under size interval task assignment (SITA) policies. Assuming Poisson arrivals and the existence of the αth moment of the job size distribution for some α > 1, we show that if the job arrival rate and the number of servers increase to infinity with the traffic intensity held fixed, the SITA policy parameterized by α minimizes in a large deviation sense the steady‐state probability that the total number of jobs in the system is greater than or equal to the number of servers. The optimal large deviation decay rate can be arbitrarily close to the one for the corresponding probability in an infinite‐server queue, which only depends on the system traffic intensity but not on any higher moments of the job size distribution. This supports in a many‐server asymptotic framework the common wisdom that separating large jobs from small jobs protects system performance against job size variability.
