Queueing Systems

, Volume 82, Issue 1–2, pp 43–73 | Cite as

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

Article

Abstract

We consider a stochastic fluid model (SFM) \(\{(\widehat{X}(t),J(t)),t\ge 0\}\) driven by a continuous-time Markov chain \(\{J(t),t\ge 0 \}\) with a time-varying generator \(T(t)\) and cycle of length 1 such that \(T(t)=T(t+1)\) for all \(t\ge 0\). 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):149–184, 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):405–444, 2012).

Keywords

Nonstationary queues Queues with time-varying arrivals Stochastic fluid model Cyclic stochastic fluid model 

Mathematics Subject Classification

76M35 60H99 60J99 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Cleveland State UniversityClevelandUSA
  2. 2.University of TasmaniaHobartAustralia

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