Evaluating Availability under Heavy-tailed Repair Time

Copyright © (2007) by IEEE. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distrubuted for profit. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee.

The time to recover from failures has a great impact on the availability of Information Technology (IT) systems. We find that the repair times have heavy-tailed power law distributions with scaling exponents close
to one for two IT systems, an in-house system hosted by IBM and a high performance computing system at the Los Alamos National Laboratory.
This means that the repair times of these systems have infinite variance and may also have infinite mean.
As a result, a claasical metrics based on thie mean time to repair are not suitable for evaluating the availability of these systems.
We propose a new metric, the T-year return value, for evaluating the reliability of IT systems.
The $T$-year return value refers to the value that the mean repair time exceeds on average once every $T$ years estimated based on the extreme value theory. We evaluate the $T$-year return values of
the two IT systems and find that the $T$-year return value can well represent the system availability.

By: Sei Kato and Takayuki Osogami

Published in: , volume , (no ), pages in 2007


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