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Type: Journal article
Title: On the generalized reward generator for stochastic fluid models: a new equation for Ψ
Other Titles: On the generalized reward generator for stochastic fluid models: a new equation for Psi
Author: Samuelson, A.
O Reilly, M.
Bean, N.
Citation: Stochastic Models, 2017; 33(4):495-523
Publisher: Taylor & Francis
Issue Date: 2017
ISSN: 1532-6349
Statement of
Aviva Samuelson, Małgorzata M. O’Reilly and Nigel G. Bean
Abstract: We construct a generalized reward matrix Z(s), which is an extension of the fluid generator Q(s) of a stochastic fluid model (SFM). We consider the generators that are projections of Z(s), including the generator Q(s), and discuss the application of the resulting generators in different contexts. One such projection, Z⁺(s), is used to define a matrix M, which records the expected number of crossings of level 0. We use the elements of M and its physical interpretation to derive an explicit equation for the matrix ψ, which is a key building block to many other performance measures. Work on algorithmic techniques to efficiently compute M are in progress.
Keywords: Generalized reward generator; Laplace-Stieltjes transforms; matrix-analytic methods; stochastic fluid models
Rights: © 2017 Taylor & Francis
DOI: 10.1080/15326349.2017.1347883
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Mathematical Sciences publications

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