Numerical solution of level dependent quasi-birth-and-death processes

Exhaustive vacation queue with dependent arrival and service processes

This paper presents a more general class of MAP/MAP/1 exhaustive vacation queue, in which the Markov modulated arrival and service processes are dependent. This model class requires the evaluation of the busy period of quasi birth death process with arbitrary initial level, which is a new analysis element. The model is analyzed by applying matrix analytic methods for the underlying quasi birth ...

Level-Dependent Quasi-Birth-and-Death Processes

This article defines and describes the level-dependent quasi-birth-and-death (LDQBD) process, a generalization of the homogeneous (or level-independent) quasi-birth-and-death (QBD) process. Like its level-independent counterpart, the LDQBD process is a bivariate Markov process whose transition probability matrix (or infinitesimal generator matrix) exhibits a block tri-diagonal structure. Howeve...

On the numerical solution of Kronecker-based infinite level-dependent QBD processes

Infinite level-dependent quasi-birth-and-death (LDQBD) processes can be used to model Markovian systems with countably infinite multidimensional state spaces. Recently it has been shown that sums of Kronecker products can be used to represent the nonzero blocks of the transition rate matrix underlying an LDQBD process for models from stochastic chemical kinetics. This paper extends the form of ...

General QBD Processes with Applications to Overload Control

In this paper we introduce a general class of level dependent Quasi-Birth-and-Death (QBD) processes and their stationary solution. We obtain the complete characterization of their fundamental matrices in terms of minimal non-negative solution of number of matrix quadratic equations. Our results will provide mixed-geometric solution for the stationary solution of level dependent chains. Applicat...

Quasistationary Distributions for Level-dependent Quasi-birth-and-death Processes