Fluid models with jumps

Elena Tzenova, Ivo J B F Adan, Vidyadhar G. Kulkarni

    Research output: Contribution to journalArticle

    Abstract

    □ In this paper we study a general stochastic fluid model with a single infinite capacity buffer, where the buffer content can change continuously as well as by instantaneous upward jumps. The continuous as well as the instantaneous change is modulated by an external environment process modelled as a finite state continuous time Markov chain. The Laplace-Stieltjes transform of the steady-state joint distribution of the buffer content and the state of the environment is determined explicitly in terms of the solutions of a generalized eigenvalue problem. The methodology is illustrated by several well-known queueing problems.

    Original languageEnglish (US)
    Pages (from-to)37-55
    Number of pages19
    JournalStochastic Models
    Volume21
    Issue number1
    DOIs
    StatePublished - Nov 28 2005

    Fingerprint

    Laplace transforms
    Fluid Model
    Markov processes
    Buffer
    Jump
    Instantaneous
    Fluids
    Laplace-Stieltjes Transform
    Generalized Eigenvalue Problem
    Steady-state Distribution
    Continuous-time Markov Chain
    Queueing
    Joint Distribution
    Stochastic Model
    Methodology

    ASJC Scopus subject areas

    • Modeling and Simulation

    Cite this

    Tzenova, E., Adan, I. J. B. F., & Kulkarni, V. G. (2005). Fluid models with jumps. Stochastic Models, 21(1), 37-55. https://doi.org/10.1081/STM-200046459

    Fluid models with jumps. / Tzenova, Elena; Adan, Ivo J B F; Kulkarni, Vidyadhar G.

    In: Stochastic Models, Vol. 21, No. 1, 28.11.2005, p. 37-55.

    Research output: Contribution to journalArticle

    Tzenova, E, Adan, IJBF & Kulkarni, VG 2005, 'Fluid models with jumps', Stochastic Models, vol. 21, no. 1, pp. 37-55. https://doi.org/10.1081/STM-200046459
    Tzenova E, Adan IJBF, Kulkarni VG. Fluid models with jumps. Stochastic Models. 2005 Nov 28;21(1):37-55. https://doi.org/10.1081/STM-200046459
    Tzenova, Elena ; Adan, Ivo J B F ; Kulkarni, Vidyadhar G. / Fluid models with jumps. In: Stochastic Models. 2005 ; Vol. 21, No. 1. pp. 37-55.
    @article{66ee5099cfe04d2f8f789bfa33827095,
    title = "Fluid models with jumps",
    abstract = "□ In this paper we study a general stochastic fluid model with a single infinite capacity buffer, where the buffer content can change continuously as well as by instantaneous upward jumps. The continuous as well as the instantaneous change is modulated by an external environment process modelled as a finite state continuous time Markov chain. The Laplace-Stieltjes transform of the steady-state joint distribution of the buffer content and the state of the environment is determined explicitly in terms of the solutions of a generalized eigenvalue problem. The methodology is illustrated by several well-known queueing problems.",
    author = "Elena Tzenova and Adan, {Ivo J B F} and Kulkarni, {Vidyadhar G.}",
    year = "2005",
    month = "11",
    day = "28",
    doi = "10.1081/STM-200046459",
    language = "English (US)",
    volume = "21",
    pages = "37--55",
    journal = "Stochastic Models",
    issn = "1532-6349",
    publisher = "Taylor and Francis Ltd.",
    number = "1",

    }

    TY - JOUR

    T1 - Fluid models with jumps

    AU - Tzenova, Elena

    AU - Adan, Ivo J B F

    AU - Kulkarni, Vidyadhar G.

    PY - 2005/11/28

    Y1 - 2005/11/28

    N2 - □ In this paper we study a general stochastic fluid model with a single infinite capacity buffer, where the buffer content can change continuously as well as by instantaneous upward jumps. The continuous as well as the instantaneous change is modulated by an external environment process modelled as a finite state continuous time Markov chain. The Laplace-Stieltjes transform of the steady-state joint distribution of the buffer content and the state of the environment is determined explicitly in terms of the solutions of a generalized eigenvalue problem. The methodology is illustrated by several well-known queueing problems.

    AB - □ In this paper we study a general stochastic fluid model with a single infinite capacity buffer, where the buffer content can change continuously as well as by instantaneous upward jumps. The continuous as well as the instantaneous change is modulated by an external environment process modelled as a finite state continuous time Markov chain. The Laplace-Stieltjes transform of the steady-state joint distribution of the buffer content and the state of the environment is determined explicitly in terms of the solutions of a generalized eigenvalue problem. The methodology is illustrated by several well-known queueing problems.

    UR - http://www.scopus.com/inward/record.url?scp=24144482562&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=24144482562&partnerID=8YFLogxK

    U2 - 10.1081/STM-200046459

    DO - 10.1081/STM-200046459

    M3 - Article

    VL - 21

    SP - 37

    EP - 55

    JO - Stochastic Models

    JF - Stochastic Models

    SN - 1532-6349

    IS - 1

    ER -