• DOI:10.4230/LIPIcs.ITCS.2022.41
• Corpus ID: 238259513

Uniform Bounds for Scheduling with Job Size Estimates

@inproceedings{Scully2021UniformBF,
  title={Uniform Bounds for Scheduling with Job Size Estimates},
  author={Ziv Scully and Isaac Grosof and Michael Mitzenmacher},
  booktitle={Information Technology Convergence and Services},
  year={2021}
}

• Ziv Scully, Isaac Grosof, M. Mitzenmacher
• Published in
  Information Technology…
  1 October 2021
• Mathematics

We consider the problem of scheduling to minimize mean response time in M/G/1 queues where only estimated job sizes (processing times) are known to the scheduler, where a job of true size s has estimated size in the interval [ βs, αs ] for some α ≥ β > 0. We evaluate each scheduling policy by its approximation ratio , which we define to be the ratio between its mean response time and that of Shortest Remaining Processing Time (SRPT), the optimal policy when true sizes are known. Our question: is there a scheduling policy that (a) has approximation ratio near 1 when α and β are near 1, (b) has approximation ratio bounded by some function of α and β even when they are far from 1, and (c) can be implemented without knowledge of α and β ? We first show that naively running SRPT using estimated sizes in place of true sizes is not such a policy: its approximation ratio can be arbitrarily large for any fixed β < 1. We then provide a simple variant of SRPT for estimated sizes that satisfies criteria (a), (b), and (c). In particular, we prove its approximation ratio approaches 1 uniformly as α and β approach 1. This is the first result showing this type of convergence for M/G/1 scheduling. We also study the Preemptive Shortest Job First (PSJF) policy, a cousin of SRPT. We show that, unlike SRPT, naively running PSJF using estimated sizes in place of true sizes satisfies criteria (b) and (c), as well as a weaker version of (a).