Quasi-birth-and-death processes with restricted transitions and its applications

In this paper, we identify a class of quasi-birth-and-death (QBD) processes where the transitions to higher (respectively lower) levels are restricted to occur only from (respectively to) a subset of the phase space. These restrictions induce a specific structure in the or matrix of the QBD process,...

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Autores:
Tipo de recurso:
Fecha de publicación:
2010
Institución:
Universidad del Rosario
Repositorio:
Repositorio EdocUR - U. Rosario
Idioma:
eng
OAI Identifier:
oai:repository.urosario.edu.co:10336/28471
Acceso en línea:
https://doi.org/10.1016/j.peva.2010.04.003
https://repository.urosario.edu.co/handle/10336/28471
Palabra clave:
Markov chains
Quasi-birth-and-death processes
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Summary:In this paper, we identify a class of quasi-birth-and-death (QBD) processes where the transitions to higher (respectively lower) levels are restricted to occur only from (respectively to) a subset of the phase space. These restrictions induce a specific structure in the or matrix of the QBD process, which can be exploited to reduce the time required to compute these matrices. We show how this reduction can be achieved by first defining and solving a censored process, and then solving a Sylvester matrix equation. To illustrate the applicability and computational gains obtained with this approach, we consider several examples where the referred structures either arise naturally or can be induced by adequately modeling the system at hand. The examples include the general MAP/PH/1 queue, a priority queue with two customer classes, an overflow queueing system and a wireless relay node.