This paper shows that row-continuous Markov chains with one or two boundaries have transient probabilities with matrix-geometric structure. Also explored is the relationship between the Green's function method and the matrix-geometric structure. Also explored is the relationship between the...

Applied Probability and Stochastic Processes is an edited work written in honor of Julien Keilson. This volume has attracted a host of scholars in applied probability, who have made major contributions to the field, and have written survey and state-of-the-art papers on a variety of applied...