Søren Asmussen, Aarhus

Tail Probabilities for a Computer Reliability Problem

Abstract

A job like the execution of a computer program or the transfer of a
file has an execution time with distribution F. The job may fail at a
time distributed according to G, and is then restarted.  If H is the
distribution of the total execution time allowing for multiple
restarts, what can be said about the tail of H?

The answer is that H is always heavy-tailed (except if F has a finite
support). The precise form of the tail comes out from a delicate
balance between the tails of F and G, and is presented in the
logarithmic asymptotics form familiar from large deviations theory. A
main tool in the analysis  is the Cram\'er-Lundberg asymptotics of
light-tailed geometric sums.

Joint work with Lester Lipsky, Robert Sheahan (Storrs, Connecticut)
and Pierre Fiorini (Portland, Maine).