# On the non-optimality of the FB discipline for the IMRL service times

##
Urtzi Ayesta

### LAAS CNRS

### Résumé:

It is known that for DHR (Decreasing Hazard Rate) service times the FB
(Foreground-Background) discipline minimizes the mean delay in the M/G/1
queue among all work-conserving and non-anticipating service
disciplines. It is also believed that a similar result is valid for IMRL
(Increasing Mean Residual Lifetime) service times. However, we point out
a ï¬,aw in an earlier proof of this latter result and construct a
counter-example that demonstrates that FB is not necessarily optimal
within class IMRL. We will conclude the talk discussing the application
of the Gittins index policy to the problem.

This is a joint work with Samuli Aalto (TKK)