## Failure Recovery via RESTART: Wallclock Models

Publikation: Working paperForskning

### Standard

Failure Recovery via RESTART: Wallclock Models. / Asmussen, Søren; Rønn-Nielsen, Anders.

Århus : Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet, 2010.

Publikation: Working paperForskning

### Harvard

Asmussen, S & Rønn-Nielsen, A 2010 'Failure Recovery via RESTART: Wallclock Models' Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet, Århus.

### APA

Asmussen, S., & Rønn-Nielsen, A. (2010). Failure Recovery via RESTART: Wallclock Models. Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet.

### CBE

Asmussen S, Rønn-Nielsen A. 2010. Failure Recovery via RESTART: Wallclock Models. Århus: Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet.

### MLA

Asmussen, Søren og Anders Rønn-Nielsen Failure Recovery via RESTART: Wallclock Models. Århus: Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet. 2010., 20 s.

### Vancouver

Asmussen S, Rønn-Nielsen A. Failure Recovery via RESTART: Wallclock Models. Århus: Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet. 2010 mar 4.

### Author

Asmussen, Søren ; Rønn-Nielsen, Anders. / Failure Recovery via RESTART: Wallclock Models. Århus : Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet, 2010.

### Bibtex

@techreport{1eb0dde8240f4244aa0706656453f685,
title = "Failure Recovery via RESTART: Wallclock Models",
abstract = "A task such as the execution of a computer program or the transfer of a file on a communications link may fail and then needs to be restarted. Let the ideal task time be a constant $\ell$ and the actual task time $X$, a random variable. Tail asymptotics for $\mathbb{P}(X>x)$ is given under three different models: 1: a time-dependent failure rate $\mu(t)$ and a constant work rate $r(t)\equiv 1$; 2: Poisson failures and a time-dependent deterministic work rate $r(t)$; 3: as 2, but $r(t)$ is random and a function of a finite Markov process. Also results close to being necessary and sufficient are presented for $X$ to be finite a.s. The results complement those of Asmussen, Fiorini, Lipsky, Rolski & Sheahan [Math. Oper. Res. 33, 932--944, 2008] who took $r(t)\equiv 1$ and assumed the failure rate to be a function of the time elapsed since the last restart rather than wallclock time.",
keywords = "change of measure, computer reliability, fluid model, gaps, inhomogeneous Poisson process, Markov-modulation, Markov renewal theorem, tail asymptotics, time transformation",
author = "S{\o}ren Asmussen and Anders R{\o}nn-Nielsen",
year = "2010",
month = mar,
day = "4",
language = "English",
publisher = "Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet",
type = "WorkingPaper",
institution = "Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet",

}

### RIS

TY - UNPB

T1 - Failure Recovery via RESTART: Wallclock Models

AU - Asmussen, Søren

AU - Rønn-Nielsen, Anders

PY - 2010/3/4

Y1 - 2010/3/4

N2 - A task such as the execution of a computer program or the transfer of a file on a communications link may fail and then needs to be restarted. Let the ideal task time be a constant $\ell$ and the actual task time $X$, a random variable. Tail asymptotics for $\mathbb{P}(X>x)$ is given under three different models: 1: a time-dependent failure rate $\mu(t)$ and a constant work rate $r(t)\equiv 1$; 2: Poisson failures and a time-dependent deterministic work rate $r(t)$; 3: as 2, but $r(t)$ is random and a function of a finite Markov process. Also results close to being necessary and sufficient are presented for $X$ to be finite a.s. The results complement those of Asmussen, Fiorini, Lipsky, Rolski & Sheahan [Math. Oper. Res. 33, 932--944, 2008] who took $r(t)\equiv 1$ and assumed the failure rate to be a function of the time elapsed since the last restart rather than wallclock time.

AB - A task such as the execution of a computer program or the transfer of a file on a communications link may fail and then needs to be restarted. Let the ideal task time be a constant $\ell$ and the actual task time $X$, a random variable. Tail asymptotics for $\mathbb{P}(X>x)$ is given under three different models: 1: a time-dependent failure rate $\mu(t)$ and a constant work rate $r(t)\equiv 1$; 2: Poisson failures and a time-dependent deterministic work rate $r(t)$; 3: as 2, but $r(t)$ is random and a function of a finite Markov process. Also results close to being necessary and sufficient are presented for $X$ to be finite a.s. The results complement those of Asmussen, Fiorini, Lipsky, Rolski & Sheahan [Math. Oper. Res. 33, 932--944, 2008] who took $r(t)\equiv 1$ and assumed the failure rate to be a function of the time elapsed since the last restart rather than wallclock time.

KW - change of measure

KW - computer reliability

KW - fluid model

KW - gaps

KW - inhomogeneous Poisson process

KW - Markov-modulation

KW - Markov renewal theorem

KW - tail asymptotics

KW - time transformation

M3 - Working paper

BT - Failure Recovery via RESTART: Wallclock Models

PB - Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet

CY - Århus

ER -