SRPT for Multiserver Systems
Performance Evaluation, vol. 127-128, Nov. 2018, pp. 154-175. Also in 36th International Symposium on Computer Performance, Modeling, Measurements, and Evaluation (Performance 2018), Toulouse, France, December 2018.
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Isaac Grosof, Ziv Scully, Mor Harchol-Balter
Carnegie Mellon University
The Shortest Remaining Processing Time (SRPT) scheduling policy and its variants have been extensively studied in both theoretical and practical settings. While beautiful results are known for single-server SRPT, much less is known for multiserver SRPT. In particular, stochastic analysis of the M/G/k under SRPT is entirely open. Intuition suggests that multiserver SRPT should be optimal or near-optimal for minimizing mean response time. However, the only known analysis of multiserver SRPT is in the worst-case adversarial setting, where SRPT can be far from optimal. In this paper, we give the first stochastic analysis bounding mean response time of the M/G/k under SRPT. Using our response time bound, we show that multiserver SRPT has asymptotically optimal mean response time in the heavy-traffic limit. The key to our bounds is a strategic combination of stochastic and worst-case techniques. Beyond SRPT, we prove similar response time bounds and optimality results for several other multiserver scheduling policies.
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