Quasi-Birth-and-Death Processes, Lattice Path Counting, and Hypergeometric Functions

This paper considers a class of quasi-birth-and-death processes for which explicit solutions can be obtained for the rate matrix R and the associated matrix G. The probabilistic interpretations of these matrices allow us to describe their elements in terms of paths on the two-dimensional lattice. Then determining explicit expressions for the matrices becomes equivalent to solving a lattice path counting problem, the solution of which is derived using path decomposition, Bernoulli excursions, and hypergeometric functions. A few applications are provided, including classical models for which we obtain some new results.

By: Johan S. H. van Leeuwaarden; Mark S. Squillante; Erik M. M. Winands

Published in: Journal of Applied Probability, volume 46, (no 2), pages 502-520 in 2009

Please obtain a copy of this paper from your local library. IBM cannot distribute this paper externally.

Questions about this service can be mailed to reports@us.ibm.com .