On Two-dimensional Markov Chains in the Positive Quadrant with Partial Spatial Homogeneity

Abstract

We consider the problem of classifying Markov chains on the quarter plane Z 2 + which possess a property of partial spatial homogeneity. Such chains arise frequently in the study of queueing and loss networks and have been previously studied, notably by Malyshev and Menshikov and by Fayolle. However existing results are either given under restrictive… (More)

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