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On the Gittins index in the M/G/1 queue Samuli Aalto1
 

Summary: On the Gittins index in the M/G/1 queue
Samuli Aalto1
, Urtzi Ayesta2,3,
, Rhonda Righter4
1
TKK Helsinki University of Technology, Finland
2
BCAM - Basque Center for Applied Mathematics, Spain
3
LAAS-CNRS, France
4
University of California at Berkeley, USA
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 prop-
erties 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.

  

Source: Ayesta, Urtzi - Laboratoire d'Analyse et d'Architecture des Systèmes du CNRS

 

Collections: Engineering