Transient and First Passage Time Distributions of First- and Second-order Multi-regime Markov Fluid Queues via ME-fication

Nail Akar (), Omer Gursoy (), Gabor Horvath () and Miklos Telek ()
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Nail Akar: Bilkent University
Omer Gursoy: Bilkent University
Gabor Horvath: Budapest University of Technology and Economics
Miklos Telek: MTA-BME Information Systems Research Group

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 4, 1257-1283

Abstract: 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; 60J25; 65C40; 60K25; 60J65 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-020-09812-y

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