HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information

# On a unifying product form framework for redundancy models

2 IRIT-RMESS - Réseaux, Mobiles, Embarqués, Sans fil, Satellites
IRIT - Institut de recherche en informatique de Toulouse
4 LAAS-SARA - Équipe Services et Architectures pour Réseaux Avancés
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : In this paper, we present a unifying analysis for redundancy systems with cancel-on-start ($c.o.s.$) and cancel-on-complete ($c.o.c.$) with exponentially distributed service requirements. With $c.o.s.$ ($c.o.c.$) all redundant copies are removed as soon as one of the copies starts (completes) service. As a consequence, $c.o.s.$ does not waste any computing resources, as opposed to $c.o.c.$. We show that the $c.o.s.$ model is equivalent to a queueing system with multi-type jobs and servers, which was analyzed in \cite{Visschers12},and show that $c.o.c.$ (under the assumption of i.i.d. copies) can be analyzed by a generalization of \cite{Visschers12} where state-dependent departure rates are permitted. This allows us to show that the stationary distribution for both the $c.o.c.$ and $c.o.s.$ models have a product form. We give a detailed first-time analysis for $c.o.s$ and derive a closed form expression for important metrics like mean number of jobs in the system, and probability of waiting. We also note that the $c.o.s.$ model is equivalent to Join-Shortest-Work queue with redundancy (JSW($d$)). In the latter, an incoming job is dispatched to the server with smallest workload among $d$ randomly chosen ones. Thus, all our results apply mutatis-mutandis to JSW($d$).{Comparing the performance of $c.o.s.$ with that of $c.o.c.$ with i.i.d copies gives the unexpected conclusion (since $c.o.s.$ does not waste any resources) that $c.o.s.$ is worse in terms of mean number of jobs. As part of ancillary results, we illustrate that this is primarily due to the assumption of i.i.d copies in case of $c.o.c.$ (together with exponentially distributed requirements) and that such assumptions might lead to conclusions that are qualitatively different from that observed in practice.
Document type :
Journal articles
Domain :

Cited literature [21 references]

https://hal.archives-ouvertes.fr/hal-01713937
Contributor : Tejas Bodas Connect in order to contact the contributor
Submitted on : Tuesday, May 22, 2018 - 5:42:08 PM
Last modification on : Thursday, May 19, 2022 - 12:52:14 PM
Long-term archiving on: : Wednesday, September 26, 2018 - 1:30:12 AM

### File

red_cos.pdf
Files produced by the author(s)

### Citation

Urtzi Ayesta, Tejas Bodas, Ina Maria Verloop. On a unifying product form framework for redundancy models. Performance Evaluation, Elsevier, 2018, 127-128, pp.93-119. ⟨10.1016/j.peva.2018.09.008⟩. ⟨hal-01713937v2⟩

Record views