Preventing Large Sojourn Times Using SMART Scheduling

Recently, the class of SMART scheduling policies 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 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. Subject classifications: Queues: Priority, Limit Theorems. Probability: Stochastic model applications Area of review: Stochastic models ∗Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands, [email protected] †Computer Science Department, Carnegie Mellon University, 5000 Forbes Avenue Pittsburgh, PA, USA, [email protected] ‡CWI, P.O. Box 94079, 1090 GB Amsterdam §Department of Mathematics & Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands, [email protected]