In a previous paper we demonstrated that the well known matrix-geometric solution of Quasi-Birth-and-Death processes is valid also if we introduce Rational Arrival
Process (RAP) components. Here we extend those results and we offer an alternative
proof by using results obtained by Tweedie.
We prove the matrix-geometric form for a certain kind of operators on the stationary measure for discrete time Markov chains of GI/M/1 type. We apply this
result to an embedded chain with RAP components. We then discuss the straight-
forward modification of the standard algorithms for calculating the matrix R in the
traditional QBD framework.
Finally we present examples demonstrating great reductions in dimensionality
from the traditional QBD framework to the QBD - RAP framework.
- Rational Arrival Processes
- Quasi-Birth-and-Death Processes
- Matrix- Analytic Methods
- Algorithmic Probability