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      Transient and first passage time distributions of first- and second-order Multi-Regime Markov Fluid Queues via ME-fication

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      Author(s)
      Akar, Nail
      Gürsoy, Ömer
      Horvath, G.
      Telek, M.
      Date
      2020
      Source Title
      Methodology and Computing in Applied Probability
      Print ISSN
      1387-5841
      Publisher
      Springer
      Language
      English
      Type
      Article
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      Abstract
      We propose a numerical method to obtain the transient and first passage time distributions of first- and second-order Multi-Regime Markov Fluid Queues (MRMFQ). The method relies on the observation that these transient measures can be computed via the stationary analysis of an auxiliary MRMFQ. This auxiliary MRMFQ is constructed from the original one, using sample path arguments, and has a larger cardinality stemming from the need to keep track of time. The conventional method to approximately model the deterministic time horizon is Erlangization. As an alternative, we propose the so-called ME-fication technique, in which a Concentrated Matrix Exponential (CME) distribution replaces the Erlang distribution for approximating deterministic time horizons. ME-fication results in much lower state-space dimensionalities for the auxiliary MRMFQ than would be with Erlangization. Numerical results are presented to validate the effectiveness of ME-fication along with the proposed numerical method.
      Keywords
      Multi-regime Markov fluid queues
      Matrix exponential distributions
      Transient distribution
      First passage time distribution
      Permalink
      http://hdl.handle.net/11693/75912
      Published Version (Please cite this version)
      https://dx.doi.org/10.1007/s11009-020-09812-y
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      • Department of Electrical and Electronics Engineering 4012
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