Mean first passage times in fluid queues

Vidyadhar G. Kulkarni, Elena Tzenova

    Research output: Contribution to journalArticle

    Abstract

    A stochastic fluid queueing system describes the input-output flow of a fluid in a storage device, called a buffer. The rates at which the fluid enters and leaves the buffer depend on a random environment process. The external governing process is an irreducible CTMC and the fluid from the buffer is emptied at a constant rate μ. Let X(t) denote the buffer content at time t and I(t) denote the state of the random environment at time t. In this paper we present a method for computing the mean first passage times in the (X(t), t ≥ 0) process, as well as in the bivariate ((X(t), I(t)), t ≥ 0) process. We derive a system of first-order non-homogeneous linear differential equations for the mean first passage times which can easily be solved using well-known techniques. The method developed here can be readily implemented for computational purposes. We present two examples illustrating how to find explicitly the analytical solution to a small two-state problem and how to obtain numerical solutions to a multistate problem.

    Original languageEnglish (US)
    Pages (from-to)308-318
    Number of pages11
    JournalOperations Research Letters
    Volume30
    Issue number5
    DOIs
    StatePublished - Jan 1 2002

    Fingerprint

    Fluid Queue
    Mean First Passage Time
    Buffer
    Fluid
    Fluids
    Random Environment
    Denote
    Multi-state
    Queueing System
    Rate Constant
    Linear differential equation
    Analytical Solution
    Differential equations
    Numerical Solution
    First-order
    First passage time
    Queue
    Computing
    Output

    Keywords

    • Buffer
    • First passage times
    • Fluid models

    ASJC Scopus subject areas

    • Software
    • Management Science and Operations Research
    • Industrial and Manufacturing Engineering
    • Applied Mathematics

    Cite this

    Mean first passage times in fluid queues. / Kulkarni, Vidyadhar G.; Tzenova, Elena.

    In: Operations Research Letters, Vol. 30, No. 5, 01.01.2002, p. 308-318.

    Research output: Contribution to journalArticle

    Kulkarni, Vidyadhar G. ; Tzenova, Elena. / Mean first passage times in fluid queues. In: Operations Research Letters. 2002 ; Vol. 30, No. 5. pp. 308-318.
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