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

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

We consider the numerical computation of stationary distributions for level dependent quasi-birth-and-death processes. An algorithm based on matrix continued fractions is presented and compared to standard solution techniques. Its computational efficiency and numerical stability is demonstrated by numerical examples.

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...

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

Quasi - Birth - Death Processes

1 Description of the Model This case study is analog to the one described in [2]. We considered a system consisting of a fixed number of m processors and an infinite queue for storing job requests. The processing speed of a processor is described by the rate γ, while λ describes the incoming rate of new jobs. If a new job arrives while at least one processor is idle, the job will be processed d...

On the Α-classification of Birth-death and Quasi-birth-death Processes

In several recent papers criteria for the α-classification of birthdeath and quasi-birth-death processes have been proposed. In this paper the relations between the various criteria are brought to light.