Asymptotic Behavior of Total Times For Jobs That Must Start Over If a Failure Occurs

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dc.creatorAsmussen, Soeren
dc.creatorFiorini, Pierre
dc.creatorLipsky, Lester
dc.creatorRolski, Tomasz
dc.creatorSheahan, Robert
dc.date2007-06-04
dc.date.accessioned2026-07-07T08:04:02Z
dc.date.available2026-07-07T08:04:02Z
dc.descriptionMany processes must complete in the presence of failures. Different systems respond to task failure in different ways. The system may resume a failed task from the failure point (or a saved checkpoint shortly before the failure point), it may give up on the task and select a replacement task from the ready queue, or it may restart the task. The behavior of systems under the first two scenarios is well documented, but the third ({\em RESTART}) has resisted detailed analysis. In this paper we derive tight asymptotic relations between the distribution of {\em task times} without failures to the {\em total time} when including failures, for any failure distribution. In particular, we show that if the task time distribution has an unbounded support then the total time distribution $H$ is always heavy-tailed. Asymptotic expressions are given for the tail of $H$ in various scenarios. The key ingredients of the analysis are the Cramér--Lundberg asymptotics for geometric sums and integral asymptotics, that in some cases are obtained via Tauberian theorems and in some cases by bare-hand calculations.
dc.identifierhttps://arxiv.org/abs/0706.0403
dc.identifierhttp://arxiv.org/abs/0706.0403
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/129800
dc.subjectProbability
dc.subject68M20
dc.titleAsymptotic Behavior of Total Times For Jobs That Must Start Over If a Failure Occurs
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