  Multiserver queueing systems are found at the core of a wide variety of
practical systems. Many important multiserver models have a
previously-unexplained similarity: identical mean response time behavior is
empirically observed in the heavy traffic limit. We explain this similarity for
the first time.
  We do so by introducing the work-conserving finite-skip (WCFS) framework,
which encompasses a broad class of important models. This class includes the
heterogeneous M/G/k, the limited processor sharing policy for the M/G/1, the
threshold parallelism model, and the multiserver-job model under a novel
scheduling algorithm.
  We prove that for all WCFS models, scaled mean response time $E[T](1-\rho)$
converges to the same value, $E[S^2]/(2E[S])$, in the heavy-traffic limit,
which is also the heavy traffic limit for the M/G/1/FCFS. Moreover, we prove
additively tight bounds on mean response time for the WCFS class, which hold
for all load $\rho$. For each of the four models mentioned above, our bounds
are the first known bounds on mean response time.
