Construction of algorithms for discrete-time quasi-birth-and-death processes through physical interpretation
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 . In this methodology, we first write a summation expression for 𝐆(𝓏) by considering a physical interpretation similar to that of an algorithm in . 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 , 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.
Australian Research Council
Publication titleProceedings of the 10th International Conference on Matrix-Analytic Methods in Stochastic Models
EditorsS Hautphenne, M O'Reilly, and F Poloni
Department/SchoolCollege Office - College of Sciences and Engineering
PublisherAustralian Mathematical Sciences Institute
Place of publicationAustralia
Event title10th International Conference on Matrix-Analytic Methods in Stochastic Models
Event VenueHobart, Australia
Date of Event (Start Date)2019-02-13
Date of Event (End Date)2019-02-15
Rights statementCopyright the authors