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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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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.

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Authors and Affiliations

  1. Electrical and Electronics Engineering Department, Bilkent University, Bilkent, Ankara, 06800, Turkey

    Nail Akar & Omer Gursoy

  2. Department of Networked Systems and Services, Budapest University of Technology and Economics, Magyar Tudosok krt. 2, Budapest, 1117, Hungary

    Gabor Horvath

  3. MTA-BME Information Systems Research Group, Magyar Tudosok krt. 2, Budapest, 1117, Hungary

    Miklos Telek

Authors
  1. Nail Akar
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  2. Omer Gursoy
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  3. Gabor Horvath
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  4. Miklos Telek
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Correspondence to Nail Akar.

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This work is partially supported by the OTKA K-123914 grant.

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Akar, N., Gursoy, O., Horvath, G. et al. Transient and First Passage Time Distributions of First- and Second-order Multi-regime Markov Fluid Queues via ME-fication. Methodol Comput Appl Probab 23, 1257–1283 (2021). https://doi.org/10.1007/s11009-020-09812-y

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  • DOI: https://doi.org/10.1007/s11009-020-09812-y

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