Achievable Performance of Blind Policies in Heavy Traffic

TL;DR

This paper demonstrates that in heavy traffic, the Randomized Multilevel Feedback algorithm performs nearly as well as the Shortest Remaining Processing Time algorithm, with a proven tight bound on average sojourn time.

Contribution

It establishes a tight bound on the performance of blind policies in heavy traffic, combining competitive analysis and applied probability techniques.

Findings

Randomized Multilevel Feedback is nearly optimal in heavy traffic

The performance bound is tight up to a constant factor

The analysis combines techniques from competitive analysis and applied probability

Abstract

For a GI/GI/1 queue, we show that the average sojourn time under the (blind) Randomized Multilevel Feedback algorithm is no worse than that under the Shortest Remaining Processing Time algorithm times a logarithmic function of the system load. Moreover, it is verified that this bound is tight in heavy traffic, up to a constant multiplicative factor. We obtain this result by combining techniques from two disparate areas: competitive analysis and applied probability.