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.

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Mathematics of Operations Research
Rare events: Asymptotics, Algorithms, Applications , Bridging Probabilistic and Competitive Analysis of Scheduling Policies
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Bansal, N., Kamphorst, B., & Zwart, B. (2018). Achievable performance of blind policies in heavy traffic. Mathematics of Operations Research, 43(3), 949–964. doi:10.1287/moor.2017.0890