Characterizing Policies with Optimal Response Time Tailsunder Heavy-Tailed Job Sizes
2020
We consider the tail behavior of the response time distribution in
an M/G/1 queue with heavy-tailed job sizes, specifically those with
intermediately regularly varying tails. In this setting, the response
time tail of many individual policies has been characterized, and
it is known that policies such as Shortest Remaining Processing
Time (SRPT) and Foreground-Background (FB) have response time
tails of the same order as the job size tail, and thus such policies are
tail-optimal. Our goal in this work is to move beyond individual
policies and characterize the set of policies that are tail-optimal.
Toward that end, we use the recently introduced SOAP framework
to derive sufficient conditions on the form of prioritization used
by a scheduling policy that ensure the policy is tail-optimal. These
conditions are general and lead to new results for important policies
that have previously resisted analysis, including the Gittins policy,
which minimizes mean response time among policies that do not
have access to job size information. As a by-product of our analysis,
we derive a general upper bound for fractional moments of M/G/1
busy periods, which is of independent interest.
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