Preventing Large Sojourn Times Using SMART Scheduling

Authors:
Misja Nuyens;Adam Wierman;Bert Zwart
Affiliations:
Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands;Computer Science Department, California Institute of Technology, Pasadena, California 91125;H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Venue:
Operations Research
Year:
2008

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Abstract

Recently, the so-called class of SMART scheduling policies has been introduced to formalize the common heuristic of “biasing toward small jobs.” We study the tail of the sojourn-time (response-time) distribution under both SMART policies and the foreground-background policy (FB) in the GI/GI/1 queue. We prove that these policies behave very well under heavy-tailed service times. Specifically, we show that the sojourn-time tail under all SMART policies and FB is similar to that of the service-time tail, up to a constant, which makes the SMART class superior to first-come-first-served (FCFS). In contrast, for light-tailed service times, we prove that the sojourn-time tail under FB and SMART is larger than that under FCFS. However, we show that the sojourn-time tail for a job of size y under FB and all SMART policies still outperforms FCFS as long as y is not too large.