The bivariate maximum process and quasi-stationary structure of birth-death processes

Stationary Distribution of a Perturbed Quasi-birth-and-death Process

Quasi-stationary Distributions for Birth-death Processes with Killing

The Karlin-McGregor representation for the transition probabilities of a birth-death process with an absorbing bottom state involves a sequence of orthogonal polynomials and the corresponding measure. This representation can be generalized to a setting in which a transition to the absorbing state (killing) is possible from any state rather than just one state. The purpose of this paper is to in...

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...

Quasi-Birth-and-Death Processes with Rational Arrival Process Components

In this paper we introduce the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process components. We use the physical interpretation of a Rational Arrival Process (RAP), developed by Asmussen and Bladt, to consider such a Markov process. We exploit this interpretation to develop an analytic method for such a process, that parallels the analysis of a traditional QBD. We d...

Domain of attraction of the quasi-stationary distribution for the linear birth and death process

Article history: Received 14 October 2010 Available online 14 July 2011 Submitted by M. Peligrad