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Abstract: Recently, the class of SMART scheduling policies (disciplines) has been introduced in order 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 FB and all SMART policies is similar to that of the service time tail, up to a constant, which makes the SMART class superior to 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.
Operations Research 56(1): 88-101 (2008)