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Generalised reward generator for stochastic fluid models

Citation

Samuelson, A and O'Reilly, MM and Bean, NB, Generalised reward generator for stochastic fluid models, Proceedings of the Ninth International Conference on Matrix-Analytic Methods in Stochastic Models, 28-30 June 2016, Budapest, Hungary, pp. 27-34. ISBN 9781450321389 (2016) [Refereed Conference Paper]


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Abstract

We construct a generalised reward matrix Z(s). which is an extension of the fluid generator Q(s) of a stochastic fluid model (SFM). We classify the generators that are projections of Z(s), including the generator Q(s), and discuss the application of the resulting generators in different contexts.

As one application example, for the case with nonzero mean drift, we derive a new Riccati equation for the key matrix Ψ, which records the probabilities of the first return to the original level.

The Riccati equation has the form Ψ + ΨM-+Ψ = M+-, where parameters M+- and M-+ are block matrices in the matrix M, which records the expected number of visits to the original level, before the unbounded fluid drifts to ∞.

Finally, we derive the explicit form Ψ = M+- (I + M--)-1.

Item Details

Item Type:Refereed Conference Paper
Keywords:Markov chains, stochastic fluid models, tandem
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:Samuelson, A (Ms Aviva Samuelson)
Author:O'Reilly, MM (Dr Malgorzata O'Reilly)
ID Code:112933
Year Published:2016
Funding Support:Australian Research Council (LP140100152)
Deposited By:Mathematics and Physics
Deposited On:2016-12-05
Last Modified:2017-09-26
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