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On a unifying product form framework for redundancy models
- Source :
- Rapport LAAS n° 18047. 2018, Performance Evaluation, Performance Evaluation, 2018, 127-128, pp.93-119. ⟨10.1016/j.peva.2018.09.008⟩, Performance Evaluation, Elsevier, 2018, 127-128, pp.93-119. ⟨10.1016/j.peva.2018.09.008⟩
- Publication Year :
- 2018
- Publisher :
- Elsevier BV, 2018.
-
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 Visschers et al., (2012), and show that c . o . c . (under the assumption of i.i.d. copies) can be analyzed by a generalization of Visschers et al., (2012) 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 has 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 power of d (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.
- Subjects :
- Exponential distribution
Redundancy-d
Computer science
Computer Networks and Communications
Generalization
Système d'exploitation
0211 other engineering and technologies
Réseaux et télécommunications
02 engineering and technology
01 natural sciences
Combinatorics
010104 statistics & probability
Redundancy (information theory)
Architectures Matérielles
Server
Cancel-on-start
0202 electrical engineering, electronic engineering, information engineering
Redundancy (engineering)
0101 mathematics
Queue
[ INFO.INFO-RO ] Computer Science [cs]/Operations Research [cs.RO]
Mathematics
020203 distributed computing
021103 operations research
Stationary distribution
business.industry
Product-form distribution
[INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO]
Queueing system
Systèmes embarqués
[ INFO.INFO-PF ] Computer Science [cs]/Performance [cs.PF]
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
[INFO.INFO-PF]Computer Science [cs]/Performance [cs.PF]
Hardware and Architecture
Independence assumption
Modeling and Simulation
Product (mathematics)
Closed-form expression
business
[ MATH.MATH-PR ] Mathematics [math]/Probability [math.PR]
Software
Computer network
Subjects
Details
- ISSN :
- 01665316
- Database :
- OpenAIRE
- Journal :
- Performance Evaluation
- Accession number :
- edsair.doi.dedup.....7780c5f9b55cf64139e13e3bf5458f70