Before revision:  We then use insights from the Gittins' Index policy to construct a simple heuristic, Size Estimate Hedging (SEH), that only uses jobs' estimated processing times for scheduling while exhibiting near-optimal performance .
After revision:  We then use insights from the Gittins' Index policy to construct a simple heuristic, Size Estimate Hedging (SEH), that only uses jobs' 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 when estimation errors are not unreasonably large .