  The shortest-remaining-processing-time (SRPT) scheduling policy has been
extensively studied, for more than 50 years, in single-server queues with
infinitely patient jobs. Yet, much less is known about its performance in
multiserver queues. In this paper, we present the first theoretical analysis of
SRPT in multiserver queues with abandonment. In particular, we consider the
M/GI/s+GI queue and demonstrate that, in the many-sever overloaded regime,
performance in the SRPT queue is equivalent, asymptotically in steady state, to
a preemptive two-class priority queue where customers with short service times
(below a threshold) are served without wait, and customers with long service
times (above a threshold) eventually abandon without service. We prove that the
SRPT discipline maximizes, asymptotically, the system throughput, among all
scheduling disciplines. We also compare the performance of the SRPT policy to
blind policies and study the effects of the patience-time and service-time
distributions.
