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1. S. Aalto and U. Ayesta, On the nonoptimality of the foreground-background discipline for IMRL service times, Journal of Applied Probability, vol. 43, pp. 523-534, 2006 (bib)

   Abstract: It is known that for decreasing hazard rate (DHR) service times, the foreground-background discipline (FB) minimizes the mean delay in the M/G/1 queue among all work-conserving and non-anticipating service disciplines. It is believed that a similar result is valid for increasing mean residual lifetime (IMRL) service times. However, on the one hand, we point out a flaw in an earlier proof of this latter result and construct a counter-example that demonstrates that FB is not necessarily optimal within class IMRL. On the other hand, we prove that the mean delay for FB is smaller than that of the processor-sharing discipline within class IMRL, giving a weaker version of an earlier hypothesis.