Product forms for availability

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Abstract

This paper shows and illustrates that product form expressions for the steady state distribution, as known for queueing networks, can also be extended to a class of availability models. This class allows breakdown and repair rates from one component to depend on the status of other components. Common resource capacities and repair priorities, for example, are included. Conditions for the models to have a product form are stated explicitly. This product form is shown to be insensitive to the distributions of the underlying random variables, i.e. to depend only on their means. Further it is briefly indicated how queueing for repair can be incorporated. Novel product form examples are presented of a simple series/parallel configuration, a fault tolerant database system and a multi-stage interconnection network.
Original languageEnglish
Pages (from-to)283-302
Number of pages20
JournalApplied stochastic models and data analysis
Volume4
Issue number8
DOIs
Publication statusPublished - 1992

Fingerprint

Product Form
Repair
Availability
Queueing networks
Multistage Interconnection Networks
Random variables
Fault-tolerant Systems
Steady-state Distribution
Queueing Networks
Queueing
Database Systems
Breakdown
Random variable
Configuration
Resources
Series
Model
Class

Keywords

  • Availability modelling
  • Insensitivity
  • Product form

Cite this

@article{1c0aa1bfe3d749c7a85f4bc8dc2a7fa1,
title = "Product forms for availability",
abstract = "This paper shows and illustrates that product form expressions for the steady state distribution, as known for queueing networks, can also be extended to a class of availability models. This class allows breakdown and repair rates from one component to depend on the status of other components. Common resource capacities and repair priorities, for example, are included. Conditions for the models to have a product form are stated explicitly. This product form is shown to be insensitive to the distributions of the underlying random variables, i.e. to depend only on their means. Further it is briefly indicated how queueing for repair can be incorporated. Novel product form examples are presented of a simple series/parallel configuration, a fault tolerant database system and a multi-stage interconnection network.",
keywords = "Availability modelling, Insensitivity, Product form",
author = "Eric Smeitink and {van Dijk}, {Nico M.} and Haverkort, {Boudewijn R.H.M.}",
year = "1992",
doi = "10.1002/asm.3150080404",
language = "English",
volume = "4",
pages = "283--302",
journal = "Applied Stochastic Models in Business and Industry",
issn = "1524-1904",
publisher = "Wiley",
number = "8",

}

Product forms for availability. / Smeitink, Eric; van Dijk, Nico M.; Haverkort, Boudewijn R.H.M.

In: Applied stochastic models and data analysis, Vol. 4, No. 8, 1992, p. 283-302.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Product forms for availability

AU - Smeitink, Eric

AU - van Dijk, Nico M.

AU - Haverkort, Boudewijn R.H.M.

PY - 1992

Y1 - 1992

N2 - This paper shows and illustrates that product form expressions for the steady state distribution, as known for queueing networks, can also be extended to a class of availability models. This class allows breakdown and repair rates from one component to depend on the status of other components. Common resource capacities and repair priorities, for example, are included. Conditions for the models to have a product form are stated explicitly. This product form is shown to be insensitive to the distributions of the underlying random variables, i.e. to depend only on their means. Further it is briefly indicated how queueing for repair can be incorporated. Novel product form examples are presented of a simple series/parallel configuration, a fault tolerant database system and a multi-stage interconnection network.

AB - This paper shows and illustrates that product form expressions for the steady state distribution, as known for queueing networks, can also be extended to a class of availability models. This class allows breakdown and repair rates from one component to depend on the status of other components. Common resource capacities and repair priorities, for example, are included. Conditions for the models to have a product form are stated explicitly. This product form is shown to be insensitive to the distributions of the underlying random variables, i.e. to depend only on their means. Further it is briefly indicated how queueing for repair can be incorporated. Novel product form examples are presented of a simple series/parallel configuration, a fault tolerant database system and a multi-stage interconnection network.

KW - Availability modelling

KW - Insensitivity

KW - Product form

U2 - 10.1002/asm.3150080404

DO - 10.1002/asm.3150080404

M3 - Article

VL - 4

SP - 283

EP - 302

JO - Applied Stochastic Models in Business and Industry

JF - Applied Stochastic Models in Business and Industry

SN - 1524-1904

IS - 8

ER -