For a single server system, Shortest Remaining Processing Time (SRPT) is a size-based policy that is optimal in the sense that, regardless of the job size distribution, it minimizes the number of jobs in the system at each point in time. However, one reason that size-based policies such as SRPT are rarely deployed in practice is that the exact processing times of jobs are usually not known to the scheduler. In this paper, we will discuss scheduling a single-server system when accurate 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. When the estimation error distribution is known, the Gittins' Index policy is known to be optimal in minimizing the mean sojourn time in an M/G/1 queue. For a multiplicative error model, we first characterize the Gittins' Index policy for any estimation error distribution. 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 .
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 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 .
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that is optimal in the sense that, regardless of the job size distribution, it minimizes the number of jobs in the system at each point in time. However, one reason that size-based policies such as SRPT are rarely deployed in practice is that the exact processing times of jobs are usually not known to the scheduler.
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When the estimation error distribution is known, the Gittins' Index policy is known to be optimal in minimizing the mean sojourn time in an M/G/1 queue. For a multiplicative error model, we first characterize the Gittins' Index policy for any estimation error distribution. We then use insights from the Gittins' Index policy to construct
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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