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https://hdl.handle.net/2440/135811
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Type: | Journal article |
Title: | RAP-modulated fluid processes: First passages and the stationary distribution |
Author: | Bean, N.G. Nguyen, G.T. Nielsen, B.F. Peralta, O. |
Citation: | Stochastic Processes and their Applications, 2022; 149:308-340 |
Publisher: | Elsevier BV |
Issue Date: | 2022 |
ISSN: | 0304-4149 1879-209X |
Statement of Responsibility: | Nigel G. Beana, Giang T. Nguyen, Bo F. Nielsen, Oscar Peralta |
Abstract: | We construct a stochastic fluid process with an underlying piecewise deterministic Markov process (PDMP) akin to the one used in the construction of the rational arrival process (RAP) in Asmussen and Bladt (1999) which we call the RAP-modulated fluid process. As opposed to the classic Markov-modulated fluid process driven by a Markov jump process, the underlying PDMP of a RAP-modulated fluid process has a continuous state space and is driven by matrix parameters which may not be related to an intensity matrix. Through novel techniques we show how well-known formulae associated to the Markov-modulated fluid process, such as first passage probabilities and the stationary distribution of its queue, translate to its RAP-modulated counterpart. |
Keywords: | Stochastic fluid process; Rational arrival process; Matrix-exponential distribution; First passage probability; Stationary distribution |
Rights: | © 2022 Elsevier B.V. All rights reserved. |
DOI: | 10.1016/j.spa.2022.03.013 |
Grant ID: | http://purl.org/au-research/grants/arc/DP180103106 |
Published version: | http://dx.doi.org/10.1016/j.spa.2022.03.013 |
Appears in Collections: | Mathematical Sciences publications |
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