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Stochastic Models Volume 36, 2020 - Issue 2: 10th International Conference on Matrix-Analytic Methods for Stochastic Models
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Articles

Construction of algorithms for discrete-time quasi-birth-and-death processes through physical interpretation

Aviva SamuelsonSchool of Natural Sciences, University of Tasmania, Hobart, TAS, Australia; ;ARC Centre of Excellence for Mathematical and Statistical Frontiers, Melbourne, Australia; Correspondence[email protected]
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,
Małgorzata M. O’ReillySchool of Natural Sciences, University of Tasmania, Hobart, TAS, Australia; ;ARC Centre of Excellence for Mathematical and Statistical Frontiers, Melbourne, Australia; View further author information
&
Nigel G. BeanARC Centre of Excellence for Mathematical and Statistical Frontiers, Melbourne, Australia; ;School of Mathematical Sciences, University of Adelaide, Adelaide, SA, AustraliaView further author information
Pages 193-222 | Received 30 May 2019, Accepted 16 Mar 2020, Published online: 30 Mar 2020

References

  •  Bean, N.; Ngyuen, G.; Poloni, F. A new algorithm for time-dependent first-return probabilities of a fluid queue. In Matrix-Analytic Methods in Stochastic Models University of Tasmania: Hobart, Australia, 2019; 18–22.
  •  Bean, N.; Latouche, G.; Taylor, P. Physical interpretations for quasi-birth-and-death process algorithms. Queueing Models Serv. Manage. 2018, 1, 58–78.
  •  Bean, N. G.; O’Reilly, M. M. Spatially-coherent uniformization of a stochastic fluid model to a quasi-birth-and-death process. Perform. Eval. 2013, 70, 578–592.
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  •  Bean, N. G.; O’Reilly, M. M.; Taylor, P. G. Algorithms for the Laplace–Stieltjes transforms of first return times for stochastic fluid flows. Methodol. Comput. Appl. Probab. 2008, 10, 381–408.
  •  Bini, D.; Meini, B. On cyclic reduction applied to a class of toeplitz-like matrices arising in queueing problems. In Computations with Markov Chains; Stewart, W.J., Eds. Springer: Boston, MA, 1995.
  •  da Silva Soares, A. Fluid queues: Building upon the analogy with QBD processes. PhD thesis, Université Libre de Bruxelles, 2005.
  •  Lancaster, P. Explicit solutions of linear matrix equations. SIAM Rev. 1970, 12, 544–566.
  •  Latouche, G.; Ramaswami, V. Introduction to matrix analytic methods in stochastic modeling. Soc. Ind. Math. 1999, 5, 90–304.
  •  M. F, N. Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Dover Publications: United States, 1981.
  •  Nguyen, G. T.; F. Poloni, Componentwise accurate fluid queue computations using doubling algorithms. Numer. Math. 2015, 130, 763–792.
  •  Ramaswami, V. Matrix analytic methods for stochastic fluid flows. ITC16: International Teletraffic Congress 1999, 1019–1030.
  •  Samuelson, A.; Haigh, A.; O'Reilly, M. M.; Bean, N. G. Stochastic model for maintenance in continuously deteriorating systems. Eur. J. Oper. Res. 2017, 259, 1169–1179.
  •  Samuelson, A.; O’Reilly, M. M.; Bean, N. G. On the generalised reward generator for stochastic fluid models: new Riccati equation for Ψ. Stochastic Models 2017, 33, 495–523.
  •  Sonenberg, N. Networks of interacting stochastic fluid models. PhD thesis, University of Melbourne, 2017.

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