Queueing Systems

, 63:437 | Cite as

On the Gittins index in the M/G/1 queue

  • Samuli Aalto
  • Urtzi Ayesta
  • Rhonda Righter


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.


M/G/1 Gittins index policy Optimal scheduling Bathtub hazard rate 

Mathematics Subject Classification (2000)

60K25 90B36 68M20 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.TKK Helsinki University of TechnologyEspooFinland
  2. 2.LAAS-CNRSToulouseFrance
  3. 3.IkerbasqueBCAM—Basque Center for Applied MathematicsDerioSpain
  4. 4.University of California at BerkeleyBerkeleyUSA

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