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

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Samuelson, A and O'Reilly, MM and Bean, NG, Construction of algorithms for discrete-time quasi-birth-and-death processes through physical interpretation, Proceedings of the 10th International Conference on Matrix-Analytic Methods in Stochastic Models, 13-15 February 2019, Hobart, Australia, pp. 53-57. (2019) [Refereed Conference Paper]


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Abstract

We apply physical interpretations to construct algorithms for the key matrix 𝐆 in discrete-time quasi-birth-and-death (dtQBD) and its 𝓏-transform 𝐆(𝓏), motivated by the work on stochastic fluid models (SFMs) in [13]. In this methodology, we first write a summation expression for 𝐆(𝓏) by considering a physical interpretation similar to that of an algorithm in [13]. Next, we construct the corresponding iterative scheme, and prove its convergence to 𝐆(𝓏).

In particular, here we consider the physical interpretation of Algorithm 1 for 𝚿(𝑠) in [13], and use a similar physical interpretation for 𝐆(𝓏) partitioned into three sections, each expressed in terms of matrices analogous to block matrices in the fluid generator 𝐐(𝑠) in stochastic fluid models.

Item Details

Item Type:Refereed Conference Paper
Keywords:patient admission scheduling problem
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 Philosophy and Religious Studies
UTAS Author:Samuelson, A (Ms Aviva Samuelson)
UTAS Author:O'Reilly, MM (Associate Professor Malgorzata O'Reilly)
ID Code:131252
Year Published:2019
Funding Support:Australian Research Council (LP140100152)
Deposited By:Mathematics and Physics
Deposited On:2019-03-08
Last Modified:2019-10-16
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