Mathematics – Probability
Scientific paper
2007-06-04
Mathematics
Probability
Scientific paper
Many 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 Cram\'er--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.
Asmussen Soeren
Fiorini Pierre
Lipsky Lester
Rolski Tomasz
Sheahan Robert
No associations
LandOfFree
Asymptotic Behavior of Total Times For Jobs That Must Start Over If a Failure Occurs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Asymptotic Behavior of Total Times For Jobs That Must Start Over If a Failure Occurs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Asymptotic Behavior of Total Times For Jobs That Must Start Over If a Failure Occurs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-726692