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2011
Springer

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

10 years 6 months ago
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 (resp. lower) levels are restricted to occur only from (resp. to) a subset of the phase space. These restrictions induce a specific structure in the R or G matrix of the QBD, 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.
Juan F. Pérez, Benny Van Houdt
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where PE
Authors Juan F. Pérez, Benny Van Houdt
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