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      • Department of Electrical and Electronics Engineering
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      Infinite-and finite-buffer Markov fluid queues: a unified analysis

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      Author(s)
      Akar, N.
      Sohraby, K.
      Date
      2004
      Source Title
      Journal of Applied Probability
      Print ISSN
      0021-9002
      Electronic ISSN
      1475-6072
      Publisher
      Applied Probability Trust
      Volume
      41
      Issue
      2
      Pages
      557 - 569
      Language
      English
      Type
      Article
      Item Usage Stats
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      247
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      Abstract
      In this paper, we study Markov fluid queues where the net fluid rate to a single-buffer system varies with respect to the state of an underlying continuous-time Markov chain. We present a novel algorithmic approach to solve numerically for the steady-state solution of such queues. Using this approach, both infinite- and finite-buffer cases are studied. We show that the solution of the infinite-buffer case is reduced to the solution of a generalized spectral divide-and-conquer (SDC) problem applied on a certain matrix pencil. Moreover, this SDC problem does not require the individual computation of any eigenvalues and eigenvectors. Via the solution for the SDC problem, a matrix-exponential representation for the steady-state queue-length distribution is obtained. The finite-buffer case, on the other hand, requires a similar but different decomposition, the so-called additive decomposition (AD). Using the AD, we obtain a modified matrix-exponential representation for the steady-state queue-length distribution. The proposed approach for the finite-buffer case is shown not to have the numerical stability problems reported in the literature.
      Keywords
      Computer network
      Generalized Newton iteration
      Markov fluid queue
      Performance analysis
      Spectral divide-and-conquer problem
      Stochastic fluid model
      Permalink
      http://hdl.handle.net/11693/24279
      Published Version (Please cite this version)
      http://dx.doi.org/10.1239/jap/1082999086
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