  For a single server system, Shortest Remaining Processing Time (SRPT) is an
optimal size-based policy. In this paper, we discuss scheduling a single-server
system when exact information about the jobs' processing times is not
available. When the SRPT policy uses estimated processing times, the
underestimation of large jobs can significantly degrade performance. We propose
a simple heuristic, Size Estimate Hedging (SEH), that only uses estimated
processing times for scheduling decisions. A job's priority is increased
dynamically according to an SRPT rule until it is determined that it is
underestimated, at which time the priority is frozen. Numerical results suggest
that SEH has desirable performance for estimation error variance that is
consistent with what is seen in practice.
