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Type: Journal article
Title: Doubling algorithms for stationary distributions of fluid queues: A probabilistic interpretation
Author: Bean, N.
Nguyen, G.
Poloni, F.
Citation: Performance Evaluation, 2018; 125:1-20
Publisher: Elsevier BV
Issue Date: 2018
ISSN: 0166-5316
Statement of
Nigel Bean, Giang T. Nguyen, Federico Poloni
Abstract: Fluid queues are mathematical models frequently used in stochastic modeling. Their stationary distributions involve a key matrix recording the conditional probabilities of returning to an initial level from above, often known in the literature as the matrix Ψ. Here, we present a probabilistic interpretation of the family of algorithms known as doubling, which are currently the most effective algorithms for computing the return probability matrix Ψ. To this end, we first revisit the links described in Ramaswami (1999) and da Silva Soares and Latouche (2002) between fluid queues and Quasi-Birth–Death processes; in particular, we give new probabilistic interpretations for these connections. We generalize this framework to give a probabilistic meaning for the initial step of doubling algorithms, and include also an interpretation for the iterative step of these algorithms. Our work is the first probabilistic interpretation available for doubling algorithms.
Keywords: Doubling algorithms; Stochastic fluid flows; Quasi-birth–death processes; Stationary distribution
Description: Available online 19 June 2018
Rights: © 2018 Elsevier B.V. All rights reserved.
RMID: 0030095016
DOI: 10.1016/j.peva.2018.06.001
Grant ID:
Appears in Collections:Mathematical Sciences publications

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