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The analysis of cyclic stochastic fluid flows with time-varying transition rates

Citation

Margolius, B and O'Reilly, MM, The analysis of cyclic stochastic fluid flows with time-varying transition rates, Queueing Systems, 82, (1-2) pp. 43-73. ISSN 0257-0130 (2016) [Refereed Article]

Copyright Statement

Copyright 2015 Springer Science+Business Media New York

DOI: doi:10.1007/s11134-015-9456-8

Abstract

We consider a stochastic fluid model (SFM) {(X(t), J(t)), t ≥ 0} driven by a continuous-time Markov chain {J(t), t ≥ 0} with a time-varying generator T(t) and cycle of length 1 such that T(t) = T(t + 1) for all t ≥ 0. We derive theoretical expressions for the key periodic measures for the analysis of the model, and develop efficient methods for their numerical computation. We illustrate the theory with numerical examples. This work is an extension of the results in Bean et al. (Stoch. Models 21(1):149184, 2005) for a standard SFM with time-homogeneous generator, and suggests a possible alternative approach to that developed by Yunan and Whitt (Queueing Syst. 71(4):405444, 2012).

Item Details

Item Type:Refereed Article
Keywords:cyclic stochastic fluid models, nonstationary queues, queues with time-varying arrivals, stochastic fluid model
Research Division:Mathematical Sciences
Research Group:Statistics
Research Field:Stochastic Analysis and Modelling
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:O'Reilly, MM (Dr Malgorzata O'Reilly)
ID Code:102284
Year Published:2016
Funding Support:Australian Research Council (DP1111663)
Deposited By:Mathematics and Physics
Deposited On:2015-08-10
Last Modified:2017-11-01
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