Product forms for availability

    Research output: Contribution to journalArticleAcademicpeer-review

    4 Citations (Scopus)
    19 Downloads (Pure)

    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 -