Abstract
For an M/G/1 queue with the objective of minimizing the mean number of jobs in the system, the Gittins index rule is known to be optimal among the set of non-anticipating policies. We develop properties of the Gittins index. For a single-class queue it is known that when the service time distribution is of type Decreasing Hazard Rate (New Better than Used in Expectation), the Foreground---Background (First-Come-First-Served) discipline is optimal. By utilizing the Gittins index approach, we show that in fact, Foreground---Background and First-Come-First-Served are optimal if and only if the service time distribution is of type Decreasing Hazard Rate and New Better than Used in Expectation, respectively. For the multi-class case, where jobs of different classes have different service distributions, we obtain new results that characterize the optimal policy under various assumptions on the service time distributions. We also investigate distributions whose hazard rate and mean residual lifetime are not monotonic.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
