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On the generalized reward generator for stochastic fluid models: a new equation for Ψ

Samuelson, A, O'Reilly, MM ORCID: 0000-0003-3898-3957 and Bean, NG 2017 , 'On the generalized reward generator for stochastic fluid models: a new equation for Ψ' , Stochastic Models, vol. 33, no. 4 , pp. 495-523 , doi: 10.1080/15326349.2017.1347883.

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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.

Item Type: Article
Authors/Creators:Samuelson, A and O'Reilly, MM and Bean, NG
Keywords: stochastic fluid models, generalized reward generator, Laplace-Stieltjes transforms, matrix-analytic methods
Journal or Publication Title: Stochastic Models
Publisher: Marcel Dekker Inc
ISSN: 1532-6349
DOI / ID Number: 10.1080/15326349.2017.1347883
Copyright Information:

Copyright 2017 Taylor & Francis

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