A fluid approach to total-progeny-dependent birth-and-death processes

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...

Path integral approach to birth-death processes on a lattice

2014 The Fock space formalism for classical objects first introduced by Doi is cast in a path integral form and applied to general birth-death processes on a lattice. The introduction of suitable auxiliary variables allows one to formulate random walks with memory and irreversible aggregation processes in a Markovian way, which is treatable in this formalism. Existing field theories of such pro...

A fluid queue modulated by two independent birth-death processes

Keywords: Fluid queue Markov process Buffer occupancy distribution IEEE 802.11 wireless networks Performance measures a b s t r a c t We present a fluid queue model driven by two independent finite state birth–death processes with the objective to study the buffer occupancy distribution in any intermediate node in a communication network. In a communication network, at any node, the arrival and...

Quasistationary Distributions for 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.