Samuelson, A and O'Reilly, MM and Bean, NB, Generalised reward generator for stochastic fluid models, Proceedings of the 9th International Conference on Matrix-Analytic Methods in Stochastic Models, 28-30 June 2016, Budapest, Hungary, pp. 27-34. ISBN 9781450321389 (2016) [Refereed Conference Paper]
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 Type:||Refereed Conference Paper|
|Keywords:||Markov chains, stochastic fluid models, tandem|
|Research Division:||Mathematical Sciences|
|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)|
|Funding Support:||Australian Research Council (LP140100152)|
|Deposited By:||Mathematics and Physics|
|Downloads:||15 View Download Statistics|
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