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Journals ACM SIGMETRICS Performance Evaluation Review Volume 35 Issue 1

Mean Delay Optimization for the M/G/1 Queue with Pareto Type Service Times Samuli Aalto TKK Helsinki University of Technology, Finland Urtzi Ayesta LAAS-CNRS, France samuli.aalto@tkk.  urtzi@laas.fr Categories and Subject Descriptors C.4 [Performance of Systems]: Performance Attributes; F.2.2 [Nonnumerical Algorithms and Problems]: Sequencing and Scheduling; G.3 [Probability and Statistics]: Queueing Theory General Terms Performance Keywords Mean delay, M/G/1, scheduling, Pareto distribution, Gittins index 1. INTRODUCTION We consider the optimal scheduling problem in the M/G/1 queue with the objective to minimize the mean delay (i.e., sojourn time). We assume that jobs are served according to a work conserving and nonanticipating (scheduling) discipline . A discipline is work conserving if it does not idle when there are jobs waiting, and nonanticipating if the remaining service times of jobs are unknown for the scheduler. Let denote the family of such disciplines. In particular we note that the Shortest-Remaining-Processing-Time (SRPT) discipline does not belong to . It is known that for Decreasing Hazard Rate (DHR) service times, the Foreground-Background (FB) discipline is optimal in , whereas the First-Come-First-Served (FCFS) discipline minimizes the mean delay for the service time distributions that belong to the New Better than Used in Expectation (NBUE) class [6,

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Mean delay optimization for the M/G/1 queue with pareto type service times

Aalto, Samuli; Ayesta, Urtzi
ACM SIGMETRICS Performance Evaluation Review , Volume 35 (1)
Association for Computing Machinery – Jun 12, 2007

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